Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies

go-math-grade-3-chapter-4-multiplication-facts-and-strategies-answer-key

Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies helps both Students and Teachers out there to get all the concepts underlying. HMH Go Math Grade 3 Answer Key will familiarize you with different models of Multiplication Facts and Strategies Questions in Exercises.  Understand the logic behind each of the concepts taking the help of HMH Go Math Solution Key Grade 3. Go Math Answer Key Grade 3 Chapter 4 Multiplication Facts and Strategies will give you problem-solving skills rather than giving you simple answers.

Go Math Grade 3 Chapter 4 Multiplication Facts and Strategies Answer Key

Learning the basics of earlier grade chapters is quite necessary to lay a stronger foundation for higher grades. Practice using the Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies as much as possible and clear the assessments or homework with utmost confidence. Prepare which ever concept you wish to learn through the direct links available and make your learning effective.

Lesson 1: Multiply with 2 and 4

Lesson 2: Multiply with 5 and 10

Lesson 3: Multiply with 3 and 6

Lesson 4: Algebra • Distributive Property

Lesson 5: Multiply with 7

Mid-Chapter Checkpoint

Lesson 6: Algebra • Associative Property of Multiplication

Lesson 7: Algebra • Patterns on the Multiplication Table

Lesson 8: Multiply with 8

Lesson 9: Multiply with 9

Lesson 10: Problem Solving • Multiplication

Chapter 4 Review/Test

Multiply with 2 and 4 Page No 195

Write a multiplication sentence for the model.

Question 1.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 2 and 4 img 1
Think: There are 2 groups of
5 counters.

Answer:
2 × 5 = 10

Explanation:
Draw 2 counters. Place 5 Objectives in 2 counters. Count the total number of objectives and them. Add 5 + 5 to get the answer. Finally, you get 10.

Question 2.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 2 and 4 img 2
______ × ______ = ______

Find the product.

Answer:
4×3 = 12

Explanation:
Look at the above figure. You can see 4 Counters and 3 objectives on each counter. So, you have to multiply 4×3. When you multiply with 4, you can first multiply with 2 and then double the product. Multiply 3 with 2. You will get 2×3 is 6. Now, double the number 6. The final answer is 12.

Question 3.
2
× 6
——–
________

Answer:
2×6 = 12

Explanation:
When there is a multiplication requires with 2, you can double the given number 6 to get the final answer. The answer is 6+6 = 12.

Question 4.
4
× 8
———
________

Answer:
4×8 = 32

Explanation:
You can double 2×8 to get 4×8. Multiply 8 with 2. You will get 16. Then, double the product to get the answer to 4×8. You will get 16+16 = 32. So, you get the final answer as 32.

Question 5.
2
× 3
——–
________

Answer:
2×3 = 6

Explanation:
Draw two counters. Place three objectives in two counters. Now, add the objectives in two counters. The final answer is 3+3 = 6. So, 2×3=6 is the answer.

Question 6.
4
× 6
———
_________

Answer:
4×6 = 24

Explanation:
You can double 2×6 to get 4×6. Multiply 6 with 2. You will get 12. Then, double the product to get the answer to 4×6. You will get 12+12 = 24. So, you get the final answer as 24.

Question 7.
4
× 4
———
_________

Answer:
4×4 = 16

Explanation:
Multiply 4 with 2. 2×4 = 8. Now, double the number 8. 8+8 = 16. The answer for 4×4 is 16

Question 8.
2
× 7
——–
_________

Answer:
2×7 = 14

Explanation:
The given multiplication is 2×7. The answer to any number multiplies with 2 is double of that number. So, the 2×7 can find by doing 7+7. The answer is 7+7 = 14. So, the final answer is 2×7 = 14.

Question 9.
4
× 5
———
_________

Answer:
4×5 = 20

Explanation:
Firstly, multiply 2×5 to get the answer for 4×5. Then, double the answer of 2×5 to get the final answer. So, do 2×5 = 10. Double the number 10 to get the 4×5 Answer. The double of 10 is 10+10 = 20. The answer to 4×5 is 20.

Question 10.
2
× 4
——–
_________

Answer:
2×4 = 8

Explanation:
The multiplication begins with 2. So, you can double 4 to get the answer of 2×4. The double of 4 is 4+4 = 8. The answer for 2×4 is 8.

Problem Solving

Question 11.
On Monday, Steven read 9 pages of his new book. To finish the first chapter on Tuesday, he needs to read double the number of pages he read on Monday. How many pages does he need to read on Tuesday?
__________ pages

Answer:
18

Explanation:
Steven read 9 pages of his new book on Monday. He wants to finish his first chapter on Tuesday. To finish the chapter, he needs to double the number of pages he read on Monday.

Double of pages read on Monday = 9 x 2 =18.

Steven needs to read 18 pages on Tuesday.

Question 12.
Courtney’s school is having a family game night. Each table has 4 players. There are 7 tables in all. How many players are at the game night?
__________ players

Answer:
28

Explanation:
From the given information Courtney’s school is having a family game night. Each table has 4 players. There are 7 tables in all. So, every table has 4 players. To know the total number of players at the game night, we need to multiply 7 with 4.

Total Number of players at the game night = 7 x 4 = 28.

Multiply with 2 and 4 Lesson Check Page No 196

Lesson Check

Question 1.
Which multiplication sentence matches the model?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 2 and 4 img 3
Options:
a. 3 × 2 = 6
b. 4 × 2 = 8
c. 4 × 4 = 16
d. 4 × 8 = 32

Answer:
b

Explanation:
The above figure consists of 4 counters. Also, each counter has two objectives in it. So, we need to multiply the number of counters with a number of objectives. The answer is 4×2 = 8.

Question 2.
Find the product.
2
× 8
——-
________
Options:
a. 10
b. 14
c. 16
d. 18

Answer:
c

Explanation:
To solve the 2×8, double the number 8. The answer for 2×8 is 8+8. So, the final answer is 2×8 = 16.

Question 3.
Sean made a picture graph to show his friends’ favorite colors. This is the key for the graph.
Each Ο = 2 friends.
How many friends does Ο Ο Ο Ο stand for?
Options:
a. 4
b. 8
c. 20
d. 40

Answer:
b

Explanation:
Sean made 4 picture graphs to show his friends’ favorite colors. Each Ο represents 2 friends. So, to find the final answer, we need to add all the colors. As there are 4 picture graphs you need to do 2+2+2+2 = 8. There are 8 friends available.

Question 4.
The table shows the lengths of some walking trails.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 2 and 4 img 4
How many feet longer is Mountain Trail than Harmony Trail?
Options:
a. 216 feet
b. 264 feet
c. 316 feet
d. 528 feet

Answer:
c

Explanation:
In the above table, we can see three different walking trails lengths of three persons. The walking trail length of the Mountain is 844feets. The walking trail length of Lake is 792 feet. Also, the Harmony walking trail length is 528 feet. To get How many feet longer is Mountain Trail than Harmony Trail, we need to subtract Harmony walking trail length from Mountain Trail length. So, now we have to do 844-528 which is equal to 316 feet. So, Mountain Trail walked 316 feet than Harmony trail.

Question 5.
Find the sum.
5 2 7
+ 1 5 4
———-
Options:
a. 373
b. 581
c. 671
d. 681

Answer:
c

Explanation:
Break apart the addends from the given values. Start with the hundreds. Then, add each place value.
Let’s write 527 as 500+20+7 and 154 as 100+50+4.
Sum up the above two values. Then you get 600+70+11. Add the ones and then add the 10’s and 100’s. The final answer is 681.

Question 6.
A bar graph shows that sports books received 9 votes. If the scale is 0 to 20 by twos, where should the bar end for the sports books?
Options:
a. between 8 and 10
b. on 10
c. on 8
d. between 6 and 8

Answer:
c

Explanation:
As per the given data, the sports books received 9 votes. If we take a bar graph with a scale of 0 to 20 by twos, the graph is 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. So, the number 9 will lies between numbers 8 to 10. Therefore, the answer is between 8 and 10.

Multiply with 5 and 10 Page No 201

Find the product.

Question 1.
5 × 7 = 35

Answer:
35

Explanation:
Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35.

Question 2.
5 × 1 = _______

Answer:
5

Explanation:
Any number multiplied by 1 is the same number. So, the answer is 5.

Question 3.
2 × 10 = _______

Answer:
20

Explanation:
A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 20.

Question 4.
________ = 8 × 5

Answer:
40

Explanation:
From Commutative Law of Multiplication, you can write 8 x 5 = 5 x 8. So, to find the multiplication of 5 x 8, Skip count by 5’s until you say 8 numbers. 5, 10, 15, 20, 25, 30, 35, 40. Now, the count of the number is 8. So, the answer for 5 x 8 is 40. Therefore, the answer for 8 x 5 is 40.

Question 5.
1 × 10 = ________

Answer:
10

Explanation:
Multiplication of any number with 1 is the same number. So, 1 x 10 = 10.

Question 6.
_______ = 4 × 5

Answer:
20

Explanation:
Using the Commutative Law of Multiplication, you can write 4 x 5 = 5 x 4. Now, Skip count by 5’s until you say 4 numbers. 5, 10, 15, 20. Therefore, the answer for 5 x 4 is 20.

Question 7.
5 × 10 = _______

Answer:
50

Explanation:
Skip-count by 5’s 10 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. The answer for 5 x 10 is 50.

Question 8.
7 × 5 = ________

Answer:
35

Explanation:
Write 7 x 5 as 5 x 7 according to the Commutative Law of Multiplication. Now do multiply for 5 x 7. skip-count by 5’s seven times. Now, you can write as 5, 10, 15, 20, 25, 30, 35. The answer for 5 x 7 is 35. So, the answer for 7 x 5 also 35.

Question 9.
_______ = 5 × 5

Answer:
25

Explanation:
Skip-count by 5’s 5 times. You can get 5, 10, 15, 20, 25. The answer for 5 x 5 is 25.

Question 10.
5 × 8 = _________

Answer:
40

Explanation:
You can Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40.

Question 11.
______ = 5 × 9

Answer:
45

Explanation:
The multiplication of 5 × 9 is calculated as Skip-count by 5’s 9 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45. The final answer for 5 × 9 is 45.

Question 12.
10 × 0 = _________

Answer:
0

Explanation:
Multiplication of any number with 0 is 0. So, the answer for 10 x 0 is 0.

Question 13.
5
× 6
——–
________

Answer:
30

Explanation:
Skip count by 5’s until you say 6 numbers. 5, 10, 15, 20, 25, 30. So, the answer for 5 x 6 is 35.

Question 14.
10
× 7
———
________

Answer:
70

Explanation:
Add 10’s until you say 7 numbers. Now, you can write as 10 + 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. There are seven 10’s available. So, the answer is 70.

Question 15.
5
× 3
——–
________

Answer:
15

Explanation:
Skip count by 5’s until you say 3 numbers. Write like 5, 10, 15. The answer for 5 x 3 is 15.

Question 16.
10
× 4
——–
_________

Answer:
40

Explanation:
Add 10’s until you say 4 numbers. Then, write like 10 + 10 + 10 + 10 to get the answer. The answer for 10 x 4 is 40.

Question 17.
5
× 0
——-
_________

Answer:
0

Explanation:
Multiplication of any number with 0 is 0. So, the answer for 5 x 0 is 0.

Question 18.
10
× 8
——-
__________

Answer:
80

Explanation:
You have to add 10’s until you say 8 numbers. Write as 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. There are eight 10’s available. So, the answer for 10 x 8 is 80.

Question 19.
5
× 2
——-
__________

Answer:
10

Explanation:
Skip count by 5’s until you say 2 numbers. Write like 5, 10. The answer for 5 x 2 is 10.

Question 20.
10
× 6
——–
_________

Answer:
60

Explanation:
Add 10’s until you say 6 numbers. Write as 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. So, the answer for 10 x 6 is 60.

Problem Solving

Question 21.
Ginger takes 10 nickels to buy some pencils at the school store. How many cents does Ginger have to spend?
________ cents

Answer:
50

Explanation:
From the given data, Ginger takes 10 nickels to buy some pencils at the school store. One nickel can be treated as 5 cents. So, 10 nickels value is 10 nickels x 5 cents = 50 cents.

Ginger has to spend 50 cents to buy some pencils at the school store.

Question 22.
The gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. How many players are there in all?
__________ players

Answer:
15

Explanation:
As per the given data, the gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. The number of players in there in all = 3 basketball courts x 5 players = 15 players.

15 players are available in total.

Multiply with 5 and 10 Lesson Check Page No 202

Question 1.
Mrs. Hinely grows roses. There are 6 roses on each of her 10 rose bushes. How many roses in all are on Mrs. Hinely’s rose bushes?
Options:
a. 16
b. 54
c. 60
d. 66

Answer:
60

Explanation:
There are 10 rose bushes available. In each rose bush, Mrs. Hinely growing 6 roses. So, to find the number of roses, you need to multiply 10 x 6. The multiplication of 10 x 6 is 60. The number of roses in all are on Mrs. Hinely’s rose bushes are 60.

Question 2.
Find the product.
5
× 8
——-
Options:
a. 8
b. 16
c. 35
d. 40

Answer:
40

Explanation:
Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40.

Spiral Review

Question 3.
Mr. Miller’s class voted on where to go for a field trip. Use the picture graph to find which choice had the most votes.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 5 and 10 img 5
Options:
a. Science Center
b. Aquarium
c. Zoo
d. Museum

Answer:
c. Zoo

Explanation:
From the given figure, Mr. Miller’s class voted for a field trip. From the table, every start represents 2 votes. It is mentioned that for the Science Center, Mr. Miller’s given two starts. As one star represents 2 votes, he gave 4 votes for Science Center. Similarly, Aquarium = 3 and a half stars. The half star represents one vote. So, the number of votes given for the Aquarium is 7. For Zoo, he has given 4 stars. So, every start means 2 votes. The total number of votes is 8. Finally, the number of starts for the Museum is 2. So, the total number of votes is 4.

Mr. Miller’s class is given a high number of votes for Zoo. So, Mr. Miller’s class wishes to go for Zoo.

Question 4.
Zack made this table for his survey.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 5 and 10 img 6
How many students were surveyed in all?
Options:
a. 38
b. 43
c. 47
d. 49

Answer:
c. 47

Explanation:
Zack prepared a table of flavors and votes. So, every vote represents one person. By adding the total number of votes, we can get the total number of students participated in ina survey.
Add 16 + 10 + 9 + 12 = 47. 47 students were surveyed in all to vote for their favorite juice.

Question 5.
Which of the following numbers is even?
25, 28, 31, 37
Options:
a. 25
b. 28
c. 31
d. 37

Answer:
b. 28

Explanation:
Even numbers are divided by 2. Also, even numbers end with a digit of 0, 2, 4, 6, or 8. So, the given number out of the given numbers is 28. It is ended with 8 and also it can divide by 2.

Question 6.
Estimate the sum.
4 7 9
+ 8 9
———
Options:
a. 568
b. 400
c. 500
d. 600

Answer:
a. 568

Explanation:
Add the ones. Regroup the ones as tens and ones. So, 9 + 9 = 18. Remain the 8 same and add the 1 to the tens. Add the tens. Regroup the tens as hundreds and tens. Now, add 7 + 8 + 1 = 16. place the 6 in the tens place and move the 1 to hundreds. Add the hundreds now. 4 + 1 = 5. So, now place the numbers in order. The final answer is 568.

Note:The option is modified for the above question. There is no correct answer available in the given options. So, option a is changed to the correct answer. The answer is explained with the place value to add two addends method.

Multiply with 3 and 6 Page No 207

Find the product.

Question 1.
6 × 4 = 24
Think: You can use doubles.
3 × 4 = 12
12 + 12 = 24

Answer:
24

Explanation:
By using doubles, we can find a 6 x 4 value. First, multiply the factor with half of 6. So, now we can do 3 x 4 = 12. Now, we can double the value of 3 x 4. That is 12 + 12 = 24. So, the answer for 6 x 4 = 24.

Question 2.
3 × 7 = _______

Answer:
21

Explanation:
Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21.

Question 3.
________ = 2 × 6

Answer:
12

Explanation:
With the Commutative Law of Multiplication, you can write 2 x 6 as 6 x 2. Multiply the factor 2 with 5 and then add the factor to it to get the final answer. First, multiply the factor with 5. That is 5 x 2 = 10. Now, add the factor with the answer of 5 x 2. 10 +2 = 12. The answer for 6 x 2 is 12. So, the answer for 2 x 6 is 12.

Question 4.
________ = 3 × 5

Answer:
15

Explanation:
You can skip count by 3’s until you say 5 numbers. 3, 6, 9, 12, 15. So, the final answer for 3 x 5 is 15.

Question 5.
1 × 3 = ________

Answer:
3

Explanation:
Multiplication of any number with 1 is the same number. So, 1 x 3 = 3.

Question 6.
________ = 6 × 8

Answer:
48

Explanation:
Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48.

Question 7.
3 × 9 = ________

Answer:
27

Explanation:
Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27.

Question 8.
_______ = 6 × 6

Answer:
36

Explanation:
Use doubles to find the answer of 6 x 6. Firstly, multiply 3 x 6 = 18. Then, double the value of 3 x 6. 18 + 18 = 36. The answer for 6 x 6 is 36.

Question 9.
4
× 3
——
________

Answer:
12

Explanation:
Write 4 x 3 as 3 x 4 according to the Commutative Law of Multiplication. Now do multiplication for 3 x 4. skip-count by 3’s four times. Now, you can write as 3, 6, 9, 12. The answer for 3 x 4 is 12. So, the answer for 4 x 3 also 12.

Question 10.
6
× 5
——
_________

Answer:
30

Explanation:
Multiply the given factor 5 with 5. Then, add 5 to the answer to get the answer for 6 x 5. Firstly, multiply 5 x 5 = 25. Add 5 to 25. 5 + 25 = 30. So, the answer for 6 x 5 is 30.

Question 11.
2
× 3
——
_________

Answer:
6

Explanation:
Using the Commutative Law of Multiplication, you can write 2 x 3 = 3 x 2. Now, Skip count by 3’s until you say 2 numbers. 3, 6. Therefore, the answer to 3x 2 is 6. The answer for 2 x 3 is 6.

Question 12.
6
× 3
——–
_________

Answer:
18

Explanation:
Double the value of 3 x 3 to get the answer for 6 x 3. The answer for 3 x 3 = 9. Now, double the value of 9. The answer for 6 x 3 is 9 + 9 = 18.

Question 13.
10
× 6
——-
_________

Answer:
60

Explanation:
Using the Commutative Law of Multiplication, you can write as 10 x 6 = 6 x 10. Now, multiply the 10 with 5. The answer is 5 x 10 = 50. Now, add the 10 to 50 to get the answer. The answer for 6 x 10 is 10 + 50 = 60. So, the answer for 10 x 6 is 60.

Question 14.
3
× 6
——-
__________

Answer:
18

Explanation:
Skip-count by 3’s 6 times. You can write as 3, 6, 9, 12, 15, 18. The answer for 3 x 6 is 18.

Question 15.
7
× 6
——-
__________

Answer:
42

Explanation:
With the help of the Commutative Law of Multiplication, you can change 7 x 6 to 6 x 7. Double the value of 3 x 7 to get 6 x 7. Now, do 3 x 7 = 21. Double the 21. 21 + 21 = 42. The answer for 6 x 7 = 42. So, the answer for 7 x 6 is 42.

Question 16.
3
× 0
——-
_________

Answer:
0

Explanation:
Multiplication of any number with 0 is 0. So, the answer for 3 x 0 is 0.

Question 17.
9
× 6
——-
__________

Answer:
54

Explanation:
Write 9 x 6 as 6 x 9 using the Commutative Law of Multiplication. Multiply the 9 with 5. 5 x 9 = 45. Now add the 45 to the 9. So, the answer for 6 x 9 is 45 + 9 = 54. Therefore, the answer for 9 x 6 is 54.

Question 18.
3
× 3
——-
__________

Answer:
9

Explanation:
Skip count by 3’s until you say 3 numbers. 3, 6, 9. So, the answer for 3 x 3 is 9.

Question 19.
10
× 3
——–
___________

Answer:
30

Explanation:
Use Commutative Law of Multiplication to write 10 x 3 to 3 x 10. Now, skip count by 3’s until you say 10 numbers. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. So, the answer for 3 x 10 is 30. Therefore, the answer for 10 x 3 is 30.

Question 20.
1
× 6
——–
________

Answer:
6

Explanation:
Multiplication of any number with 1 is the same number. So, 1 x 6 = 6.

Problem Solving

Question 21.
James got 3 hits in each of his baseball games. He has played 4 baseball games. How many hits has he had in all?
_________ hits

Answer:
12 hits

Explanation:
As per the given data, James got 3 hits in each of his baseball games. He has played 4 baseball games. To find the number of hits has he had in all, we need to multiply, 3 hits x 4 baseball games. So, the answer is 3 x 4 = 12 hits.

Question 22.
Mrs. Burns is buying muffins. There are 6 muffins in each box. If she buys 5 boxes, how many muffins will she buy?
__________ muffins

Answer:
30 muffins

Explanation:
From the provided information, Mrs. Burns is buying muffins. She is going to buy 5 boxes each has 6 muffins in it. So, to find the total number of muffins, we need to multiply, number of boxes and number of muffins in it. The total number of muffins = 6 x 5 = 30. She is going to buy 30 muffins.

Multiply with 3 and 6 Lesson Check Page No 208

Question 1.
Paco buys a carton of eggs. The carton has 2 rows of eggs. There are 6 eggs in each row. How many eggs are in the carton?
Options:
a. 8
b. 12
c. 14
d. 24

Answer:
b. 12

Explanation:
From the given data, Paco buys a carton of eggs. The carton has 2 rows in it. Every row has 6 eggs. To find the number of eggs, we need to multiply the number of rows and the number of eggs for each row. Therefore, the number of eggs in the carton are 2 x 6 = 12. 12 eggs are available in the carton.

Question 2.
Find the product.
9
× 3
——
Options:
a. 18
b. 24
c. 27
d. 36

Answer:
c. 27

Explanation:
Use Commutative Law of Multiplication to write 9 x 3 to 3 x 9. Now, skip count by 3’s until you say 9 numbers. 3, 6, 9, 12, 15, 18, 21, 24, 27. So, the answer for 3 x 9 is 27. Therefore, the answer for 9 x 3 is 27.

Spiral Review

Question 3.
Find the difference.
5 6 8
– 2 8 3
———
Options:
a. 285
b. 325
c. 385
d. 851

Answer:
a. 285

Explanation:
Subtract the ones. 8 – 3 = 5. Then, Subtract the tens. 6 < 8. So, regroup 5 hundreds 6 tens equal to 4 hundreds 8 tens. 16 – 8 = 8. Subtract the hundreds and add them to check the answer. 4 – 2 = 2. The final answer is 285.

Question 4.
Dwight made double the number of baskets in the second half of the basketball game than in the first half. He made 5 baskets in the first half. How many baskets did he make in the second half?
Options:
a. 7
b. 9
c. 10
d. 20

Answer:
c. 10

Explanation:
Given that Dwight made double the number of baskets in the second half of the basketball game than in the first half. He made 5 baskets in the first half. So, to find the second half baskets, we need to double the baskets in the first half. Baskets in the second half = 5 x 2 = 10.

Question 5.
In Jane’s picture graph, the ???? smile symbol represents two students. One row in the picture graph has 8 symbols. How many students does that represent?
Options:
a. 40
b. 32
c. 24
d. 16

Answer:
d. 16

Explanation:
From Jane’s picture graph, the ???? smile symbol represents 2 students. The one row in the picture graph has 8 symbols. To find the total number of students, we need to multiply the number of smiles and the number of students for each smile. The number of students for a row is 8 x 2 = 16.

Question 6.
What multiplication sentence does this array show?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 3 and 6 img 7
Options:
a. 5 × 6 = 30
b. 6 × 6 = 36
c. 5 × 5 = 25
d. 1 × 6 = 6

Answer:
a. 5 × 6 = 30

Explanation:
The given array shows that it has 6 boxes for a row and 5 boxes for a column. So, by multiplying the number of rows x number of columns the correct answer is 6 x 5 = 30. By using the Commutative Law of Multiplication, we can write 6 x 5 = 5 x 6. So, the answer from the given options is 5 × 6 = 30.

Distributive Property Page No 213

Write one way to break apart the array.
Then find the product.

Question 1.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Distributive Property img 8
(3 × 7) + (3 × 7)
42

Answer:
42

Explanation:
The given array is 6 x 7. Use the Distributive Property to get the final answer. Break the array rows to make two smaller arrays with the facts 3 and 3. Now, you can write the given array as (3 + 3) x 7. Then, multiply each addend with 7. The equation becomes (3 x 7) +(3 x 7). Now simplify and add them to get the final answer. 21 + 21 = 42.

Question 2.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Distributive Property img 9
_________

Answer:
32

Explanation:
The given array has 8 columns and 4 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 2 and 2. To get the answer, we have to write 4 x 8. By doing smaller arrays, you can write it as (2 + 2) x 8. Multiply each addend with 8. The equation becomes (2 x 8) +(2 x 8). Now simplify and add them to get the final answer. 16 + 16 = 32.

Question 3.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Distributive Property img 10
___________

Answer:
54

Explanation:
The given figure has 9 columns and 6 rows. Use Distributive Property to get the answer of a given array. Let’s break the array rows with two smaller arrays with the facts 3 and 3. Now, write the equation as 6 x 9 = (3 + 3) x 9. Multiply each 3 with 9. 27 + 27. The final answer is 54.

Question 4.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Distributive Property img 11
_________

Answer:
56

Explanation:
The given array has 8 columns and 7 rows. With the help of Distributive Property, you can solve the given array. Break the array columns with two smaller arrays with the facts 4 and 4. Write the equation as (7 x 4) + (7 x 4) = 28 + 28 = 56.

Problem Solving

Question 5.
There are 2 rows of 8 chairs set up in the library for a puppet show. How many chairs are there in all? Use the Distributive Property to solve.
____________ chairs

Answer:
16

Explanation:
From the given information, there are 2 rows of 8 chairs set up in the library for a puppet show. So, in the array, there are 2 rows and 8 columns. To find the answer, we have to multiply 2 x 8. Using Distributive Property, we can solve 2 x 8. Sum the number 2 with facts 1 and 1. So, we can write as (1 + 1) x 8. Simplify the answer by multiplying each addend to 8. (1 x 8) + (1 x 8) = 8 + 8 = 16. There are 16 chairs available in 2 rows.

Question 6.
A marching band has 4 rows of trumpeters with 10 trumpeters in each row. How many trumpeters are in the marching band? Use the Distributive Property to solve.
___________ trumpeters

Answer:
40

Explanation:
From the given information, a marching band has 4 rows of trumpeters with 10 trumpeters in each row. To know the number of trumpeters, we have to calculate 4 x 10. With the help of Distributive Property, you can separate the one number with its sums. Now write the 4 with its sums 2 and 2. (2 + 2) x 10. Now, you can multiply each addend with 10. (2 x 10) + (2 x 10) = 20 + 20 = 40. 40 trumpeters are in the marching band.

Distributive Property Lesson Check Page No 214

Question 1.
Which number sentence is an example of the Distributive Property?
Options:
a. 7 × 6 = 6 × 7
b. 7 × (2 × 3) = (7 × 2) × 3
c. 7 × 6 = (7 × 3) + (7 × 3)
d. 7 + 6 = 7 + 3 + 3

Answer:
c. 7 × 6 = (7 × 3) + (7 × 3)

Explanation:
Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 6 = (7 × 3) + (7 × 3) is the correct answer.

Question 2.
What is one way to break apart the array?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Distributive Property img 12
Options:
a. (2 × 6) + (2 × 6)
b. (4 × 2) + (4 × 2)
c. (4 × 4) + (4 × 4)
d. (6 × 3) + (6 × 3)

Answer:
a. (2 × 6) + (2 × 6)

Explanation:
The given figure has 6 columns and 4 rows. By using Distributive Property, you can find the answer easily. Let’s break the array rows with two smaller arrays with the facts 2 and 2. Now, write the equation as 4 x 6 = (2 + 2) x 6. Multiply each 2 with 6. the equation can be written as (2 x 6) + (2 x 6).

Spiral Review

Question 3.
The school auditorium has 448 chairs set out for the third grade performance. What is 448 rounded to the nearest ten?
Options:
a. 500
b. 440
c. 450
d. 400

Answer:
c. 450

Explanation:
Given that the school auditorium has 448 chairs set out for the third-grade performance. The 448 number lies between 440 and 450. 448 is closer to 450 than it is to 440. So, 448 rounds to 450.

Question 4.
Find the difference.
4 0 0
– 2 9 6
———-
Options:
a. 104
b. 114
c. 204
d. 296

Answer:
a. 104

Explanation:
Subtract the ones. 0<6. so regroup 0 tens 0 ones = 1 tens 4 ones. Now, do 10 – 6 = 4. Then, Subtract the tens. 9 = 9. So, so regroup. 4 hundred 9 tens = 3 hundred 4 tens. 9 – 9 = 0. Subtract the hundreds and add them to check the answer. 3 – 2 = 1. The final answer is 104.

Question 5.
There are 622 fruit snacks in one crate and 186 in another crate. How many fruit snacks are there in all?
6 2 2
+ 1 8 6
———-
Options:
a. 436
b. 708
c. 768
d. 808

Answer:
d. 808

Explanation:
Break apart the addends from the given values. Start with the hundreds. Then, add each place value. Let’s write 622 as 600 + 20 + 2 and 186 as 100 + 80 + 6.
Sum up the above two values. Then you get 700 + 100 + 8. Add the ones and then add the 10’s and 100’s. The final answer is 808.

Question 6.
Which sport do 6 students play?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Distributive Property img 13
a. Football
b. Baseball
c. Basketball
d. Soccer

Answer:
a. Football

Explanation:
From the given picture, it is mentioned that the sports students play and the number of students for that game. As mentioned, Football needs 6 students. Baseball needs 12 students. Basketball needs 10 students. Also, Soccer needs 16 students. So, the answer is Football sport required 6 students to play.

Multiply with 7 Page No 219

Find the product.

Question 1.
6 × 7 = 42

Answer:
42

Explanation:
By using doubles, we can find a 6 x 7 value. First, multiply the factor with half of 6. So, now we can do 3 x 7 = 21. Now, we can double the value of 3 x 7. That is 21 + 21 = 42. So, the answer for 6 x 7 = 42.

Question 2.
________ = 7 × 9

Answer:
63

Explanation:
Use the Distributive Property to find the value of 7 x 9. If we take 7 rows and 9 columns of an array, then we can break the array into two smaller arrays with the facts of 9. Now, write the 7 x 9 as 7 x (6 + 3). Multiply the facts with the 7. Then, you get (7 x 6) + (7 x 3). Therefore, you get the answer as 42 + 21 = 63.

Question 3.
_______ = 1 × 7

Answer:
7

Explanation:
Multiplication of any number with 1 is the same number. So, 1 x 7 = 7.

Question 4.
3 × 7 = _______

Answer:
21

Explanation:
Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21.

Question 5.
7 × 7 = ________

Answer:
49

Explanation:
Let us take the array has 7 columns and 7 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 4 and 3. To get the answer, we have to write 7 x 7. By doing smaller arrays, you can write it as (4 + 3) x 7. Multiply each addend with 7. The equation becomes (4 x 7) +(3 x 7). Now simplify and add them to get the final answer. 28 + 21 = 49.

Question 6.
_______ = 2 × 7

Answer:
14

Explanation:
Draw two counters. Place seven objectives in two counters. Now, add the objectives in two counters. The final answer is 7 + 7 = 14. So, 2×7 = 14 is the answer.

Question 7.
7 × 8 = _________

Answer:
56

Explanation:
Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 8 = (7 × 4) + (7 × 4) = 28 + 28 = 56.

Question 8.
______ = 4 × 7

Answer:
28

Explanation:
Firstly, multiply 2×7 to get the answer for 4×7. Then, double the answer of 2×7 to get the final answer. So, do 2×7 = 14. Double the number 14 to get the 4×7 Answer. The double of 14 is 14 +14 = 28. The answer to 4×7 is 28.

Question 9.
7
× 5
——-
__________

Answer:
35

Explanation:
From Commutative Law of Multiplication, you can write 7 x 5 = 5 x 7. So, to find the multiplication of 5 x 7, skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. Therefore, the answer for 7 x 5 is 35.

Question 10.
7
× 1
——-
_________

Answer:
7

Explanation:
Using the Commutative Law of Multiplication, you can write 7 x 1 = 1 x 7. Multiplication of any number with 1 is the same number. So, 1 x 7 = 7.

Question 11.
6
× 7
——-
__________

Answer:
42

Explanation:
Use doubles to find the answer of 6 x 7. Firstly, multiply 3 x 7 = 21. Then, double the value of 3 x 7. 21 + 21 = 42. The answer for 6 x 7 is 42.

Question 12.
7
× 4
——-
__________

Answer:
28

Explanation:
Write 7 x 4 as 4 x 7 according to the Commutative Law of Multiplication. Now, do multiplication for 4 x 7. You can double 2×7 to get 4×7. Multiply 7 with 2. You will get 14. Then, double the product to get the answer to 4×7. You will get 14 +14 = 28. So, you get the final answer as 28.

Question 13.
2
× 7
——-
___________

Answer:
14

Explanation:
The given multiplication is 2×7. The answer to any number multiplies with 2 is double of that number. So, the 2×7 can find by doing 7+7. The answer is 7+7 = 14. So, the final answer is 2×7 = 14.

Question 14.
10
× 7
——
____________

Answer:
70

Explanation:
A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 70.

Question 15.
3
× 7
——-
____________

Answer:
21

Explanation:
Skip count by 3’s until you say 7 numbers. Write like 3, 6, 9, 12, 15, 18, 21. The answer for 3 x 7 is 21.

Question 16.
7
× 9
——
___________

Answer:
63

Explanation:
Use the Distributive Property to find the value of 7 x 9. If we take 7 rows and 9 columns of an array, then we can break the array into two smaller arrays with the facts of 9. Now, write the 7 x 9 as 7 x (6 + 3). Multiply the facts with the 7. Then, you get (7 x 6) + (7 x 3). Therefore, you get the answer as 42 + 21 = 63.

Question 17.
8
× 7
——-
__________

Answer:
56

Explanation:
Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer.

Question 18.
7
× 0
——
__________

Answer:
0

Explanation:
Multiplication of any number with 0 is 0. So, the answer for 7 x 0 is 0.

Problem Solving

Question 19.
Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings?
$ __________

Answer:
$21

Explanation:
From the given information, Julie buys a pair of earrings for $7. She also wants to buy 2 more pairs of earrings for her 2 friends. So, a total she needs to but 3 pairs of earrings. To know the total amount she is going to spend on earrings, we need to multiply the total number of earrings pair with a cost for each earring. So, we can do 3 x $7 = $21. Julie needs to spend $21 to buy 3 pairs of earrings.

Question 20.
Owen and his family will go camping in 8 weeks. There are 7 days in 1 week. How many days are in 8 weeks?
_________ days

Answer:
56 days

Explanation:
Given that Owen and his family will go camping in 8 weeks. There are 7 days in 1 week. So, to calculate the total number of days in 8 weeks, multiply 8 x 7 = 56. There are 56 days in 8 weeks.

Multiply with 7 Lesson Check Page No 220

Question 1.
Find the product.
7
× 8
——
Options:
a. 54
b. 56
c. 64
d. 66

Answer:
b. 56

Explanation:
Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 8 = (7 × 4) + (7 × 4) = 28 + 28 = 56.

Question 2.
What product does the array show?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 7 img 14
Options:
a. 14
b. 17
c. 21
d. 24

Answer:
c. 21

Explanation:
The given array has 7 columns and 3 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 1 and 2. To get the answer, we have to write 3 x 7. By doing smaller arrays, you can write it as (1 + 2) x 7. Multiply each addend with 8. The equation becomes (1 x 7) +(2 x 7). Now simplify and add them to get the final answer. 7 + 14 = 21.

Spiral Review

Question 3.
Which statement is true about the numbers below?
6, 12, 18, 24, 30
Options:
a. All of the numbers are odd.
b. Some of the numbers are odd.
c. All of the numbers are even.
d. Some of the numbers are even.

Answer:
c. 21

Explanation:
All the given numbers are divided by 2. So, the answer is All of the numbers are even

Question 4.
How many more people chose retriever than poodle?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 7 img 15
Options:
a. 31
b. 39
c. 41
d. 49

Answer:
b. 39

Explanation:
To know more people chose retriever than poodle, we have to do subtraction from retriever to poodle. So, 65 – 26 = 39. 39 more people chose retriever than poodle.

Question 5.
What is 94 rounded to the nearest ten?
Options:
a. 90
b. 94
c. 95
d. 100

Answer:
a. 90

Explanation:

94 is between 90 and 100. 94 is closer to 90 than is to 100. 94 rounded to the nearest ten is 90.

Question 6.
Jack has 5 craft sticks. He needs 4 times that number for a project. How many craft sticks does Jack need altogether?
Options:
a. 9
b. 16
c. 20
d. 24

Answer:
c. 20

Explanation:
Jack has 5 craft sticks. He needs 4 times that number for a project. To find the total number of craft sticks does Jack needs altogether are 5 x 4 = 20. 20 craft sticks need to Jack.

Mid-Chapter Checkpoint Page No 221

Vocabulary

Choose the best term from the box to complete the sentence.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Mid -Chapter Checkpoint img 16

Question 1.
A __________ of 4 is any product that has 4 as one of its factors.
_________

Answer:
Commutative Property of Multiplication

Question 2.
This is an example of the ______________ .
3 × 8 = (3 × 6) + (3 × 2)
This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
__________

Answer:
Distributive Property of Multiplication

Concepts and Skills

Write one way to break apart the array.
Then find the product.

Question 3.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Mid -Chapter Checkpoint img 17
__________

Answer:
7 x 5 = 35

Explanation:

The provided array has 7 columns and 5 rows. Let’s simplify the answer by using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 2 and 3. Now, do 7 x 5. By doing smaller arrays, you can write it as 7 x (2 + 3). Multiply 7 with 2 and 7 with 3. Write (7 x 2) + (7 x 3). Now add them to get the final answer. 14 + 21 = 35.

Question 4.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Mid -Chapter Checkpoint img 18
__________

Answer:
9 x 4 = 36

Explanation:
The given array has 9 columns and 4 rows. Now, do 9 x 4. Using Distributive Property break the array rows to make two smaller arrays with the 4 facts 2 and 2. Now, add 9 x (2 + 2). Multiply 9 with 2 and 9 with 2. Write (9 x 2) + (9 x 2). Now add them to get the final answer. 18 + 18 = 36.

Find the product.

Question 5.
3 × 1 = __________

Answer:
3

Explanation:
Using Commutative Law of Multiplication, Write 3 x 1 = 1 x 3. Multiplication of any number with 1 is the same number. So, 1 x 3 = 3.

Question 6.
5 × 6 = _________

Answer:
30

Explanation:
Skip-count by 5’s 6 times. You can write as 5, 10, 15, 20, 25, 30. The answer for 5 x 6 is 30.

Question 7.
________ = 7 × 7

Answer:
49

Explanation:
Use Distributive Property, to get the answer. Given 7 x 7. Write the facts for 7. 7 = 4 + 3. Now, write 7 x 7 = 7 x (4 + 3). Multiply 7 with 4 and 7 with 3. (7 x 4) + (7 x 3) = 28 + 21 = 49.

Question 8.
2 × 10 = _________

Answer:
20

Explanation:
Double the 10 to get the answer for 2 x 10. So, now write 10 + 10 = 20. The answer for 2 x 10 = 20.

Question 9.
2
× 1
——–
_________

Answer:
2

Explanation:
Add 1 + 1 to get 2 x 1. 1 + 1 = 2. The answer for 2 x 1 = 2.

Question 10.
6
× 6
——–
_________

Answer:
36

Explanation:
Use doubles to get of 6 x 6. First, multiply 3 x 6 = 18. Then, double the value of 3 x 6. 18 + 18 = 36. The answer for 6 x 6 is 36.

Question 11.
8
× 7
——-
__________

Answer:
56

Explanation:
Use Distributive Property to find 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer.

Question 12.
6
× 0
——
___________

Answer:
0

Explanation:

Multiplication of any number with 0 is 0. So, the answer for 10 x 0 is 0.

Question 13.
3
× 8
——-
__________

Answer:
24

Explanation:
Skip-count by 3’s 8 times. You can write as 3, 6, 9, 12, 15, 18, 21, 24. The answer for 3 x 8 is 24.

Mid-Chapter Checkpoint Page No 222

Question 14.
Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all?
__________ legs

Answer:
36

Explanation:
Given that Lori saw 6 lightning bugs. Each lightning bugs had 6 legs. To find the total number of legs, do 6 x 6 = 36. The lightning bugs have 36 in all.

Question 15.
Zach walked his dog twice a day, for 7 days. Moira walked her dog three times a day for 5 days. Whose dog was walked more times? How many more?
Type below:
_________

Answer:
Moira’s dog walked more than Zach’s dog. It walked one time more than Zach’s dog.

Explanation:
Zach walked his dog twice a day, for 7 days. So, Zach dog walked 7 x 2 = 14 times in total. Moira walked her dog three times a day for 5 days. Moira dog walked 3 x 5 = 15 days. So, Moira’s dog walked more times than Zach dog. It walked one time more than Zach’s dog.

Question 16.
Annette buys 4 boxes of pencils. There are 8 pencils in each box. Jordan buys 3 boxes of pencils with 10 pencils in each box. Who buys more pencils? How many more?
Type below:
__________

Answer:
Annette has more pencils than Jordan. He has 2 pencils more than Jordan.

Explanation:
Annette buys 4 boxes of pencils. Each box has 8 pencils in it. So, Annette has 4 x 8 = 32 pencils. Jordan buys 3 boxes of pencils with 10 pencils in each box. So, he has 3 x 10 = 30 pencils. Annette has 2 pencils more than Jordan.

Question 17.
Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days?
_________ pictures

Answer:
28

Explanation:
Shelly can paint 4 pictures in a day. In 7 days, she can paint 7 x 4 = 28 pictures.

Associative Property of Multiplication Page No 227

Write another way to group the factors.
Then find the product.

Question 1.
(3 × 2) × 5
3 × (2 × 5)
30

Answer:
30

Explanation:
Using Associative Property of Multiplication, we can write (3 × 2) × 5 = 3 × (2 × 5).
Find (3 × 2) × 5. Multiply 3 x 2 = 6. Then, multiply 6 x 5 = 30.
Find 3 x (2 x 5). Multiply 2 x 5 = 10. Then, multiply 3 x 10 = 30.
So, (3 × 2) × 5 = 3 × (2 × 5). The product value is 30.

Question 2.
(4 × 3) × 2 =
________

Answer:
(4 × 3) × 2 = 4 x (3 x 2)
24

Explanation:
Use Associative Property of Multiplication to write other group the factors. (4 × 3) × 2 = 4 x (3 x 2). Now, multiply 4 x 3 = 12. Then, multiply 12 x 2 = 24. So, (4 × 3) × 2 = 24.

Question 3.
2 × (2 × 8) =
________

Answer:
2 × (2 × 8) = (2 x 2) x 8
32

Explanation:
With Associative Property of Multiplication, 2 × (2 × 8) = (2 x 2) x 8. Now, multiply 2 x 8 = 16. Then, multiply 16 x 2 = 32. So, 2 × (2 × 8) = 32.

Question 4.
9 × (2 × 1) =
________

Answer:
9 × (2 × 1) = (9 × 2) × 1
18

Explanation:
Using Associative Property of Multiplication, we can write 9 × (2 × 1) = (9 × 2) × 1. Now, multiply 2 x 1 = 2. Then, multiply 2 x 9 = 18. So, 9 × (2 × 1) = 18.

Question 5.
2 × (3 × 6) =
________

Answer:
2 × (3 × 6) = (2 x 3) x 6
36

Explanation:
With the help of Associative Property of Multiplication, we can write 2 × (3 × 6) = (2 x 3) x 6. Now, multiply 2 x 3 = 6. Then, multiply 6 x 6 = 36. So, 2 × (3 × 6) = 36.

Question 6.
(4 × 2) × 5 =
________

Answer:
(4 × 2) × 5 = 4 x (2 x 5)
40

Explanation:
Use Associative Property of Multiplication, to write (4 × 2) × 5 = 4 x (2 x 5). Now, multiply 2 x 5 = 10. Then, multiply 4 x 10 = 40. So, (4 × 2) × 5 = 40.

Use parentheses and multiplication properties.
Then, find the product.

Question 7.
9 × 1 × 5
( 9 × 1 ) × 5 = ________

Answer:
( 9 × 1 ) × 5 = 9 x (1 x 5)
45

Explanation:
Use Associative Property of Multiplication. ( 9 × 1 ) × 5 = 9 x (1 x 5). Now, multiply 9 x 1 = 9. Then, multiply 9 x 5 = 45. So, ( 9 × 1 ) × 5 = 45.

Question 8.
3 × 3 × 2
( 3 × 3 ) × 2 = _________

Answer:
( 3 × 3 ) × 2 =
18

Explanation:
Use Associative Property of Multiplication. ( 3 × 3 ) × 2 = 3 x (3 x 2). Now, multiply 3 x 3 = 9. Then, multiply 9 x 2 = 18. So, ( 3 × 3 ) × 2 = 18.

Question 9.
2 × 4 × 3
( 2 × 4 ) × 3 = _________

Answer:
( 2 × 4 ) × 3 = 2 x (4 x 3)
24

Explanation:
Now use Associative Property of Multiplication. ( 2 × 4 ) × 3 = 2 x (4 x 3). Now, multiply 2 x 4 = 8. Then, multiply 8 x 3 = 24. So, ( 2 × 4 ) × 3 = 24.

Question 10.
5 × 2 × 3
( 5 × 2 ) × 3 = _________

Answer:
( 5 × 2 ) × 3 = 5 x (2 x 3)
30

Explanation:
Use Associative Property of Multiplication. ( 5 × 2 ) × 3 = 5 x (2 x 3). Now, multiply 5 x 2 = 10. Then, multiply 10 x 3 = 30. So, ( 5 × 2 ) × 3 = 30.

Question 11.
7 × 1 × 5
( 7 × 1 ) × 5 = ________

Answer:
( 7 × 1 ) × 5 = 7 x (1 x 5)
35

Explanation:
Use Associative Property of Multiplication. ( 7 × 1 ) × 5 = 7 x (1 x 5). Now, multiply 7 x 1 = 7. Then, multiply 7 x 5 = 35. So, ( 7 × 1 ) × 5 = 35.

Question 12.
8 × 2 × 3
( 8 × 2 ) × 3 = _________

Answer:
( 8 × 2 ) × 3 = 8 x (2 x 3)
48

Explanation:
Use Associative Property of Multiplication. ( 8 × 2 ) × 3 = 8 x (2 x 3). Now, multiply 8 x 2 = 16. Then, multiply 16 x 3 = 48. So, ( 8 × 2 ) × 3 = 48.

Question 13.
7 × 2 × 3
( 7 × 2 ) × 3 = ________

Answer:
( 7 × 2 ) × 3 = 7 x (2 x 3)
42

Explanation:
Use Associative Property of Multiplication. ( 7 × 2 ) × 3 = 7 x (2 x 3). Now, multiply 2 x 3 = 6. Then, multiply 7 x 6 = 42. So, ( 7 × 2 ) × 3 = 42.

Question 14.
4 × 1 × 3
( 4 × 1 ) × 3 = ________

Answer:
12

Explanation:
Use Associative Property of Multiplication. ( 4 × 1 ) × 3 = 4 x (1 x 3). Now, multiply 4 x 1 = 4. Then, multiply 4 x 3 = 12. So, ( 4 × 1 ) × 3 = 12.

Question 15.
10 × 2 × 4
( 10 × 2 ) × 4 = ________

Answer:
80

Explanation:
Use Associative Property of Multiplication. ( 10 × 2 ) × 4 = 10 x (2 x 4). Now, multiply 2 x 4 = 8. Then, multiply 10 x 8 = 80. So, ( 10 × 2 ) × 4 = 80.

Problem Solving

Question 16.
Beth and Maria are going to the county fair. Admission costs $4 per person for each day. They plan to go for 3 days. How much will the girls pay in all?
$ _________

Answer:
$24

Explanation:
From the given information, County fair admission costs $4 per person for each day. To go for 3 days, it costs, 3 x $4 = $12. Beth and Maria are going to the county fair. So, 2 members are going to the county fair. The total amount is 2 X $12 = $24.

Question 17.
Randy’s garden has 3 rows of carrots with 3 plants in each row. Next year he plans to plant 4 times the number of rows of 3 plants. How many plants will he have next year?
_________ plants

Answer:
36

Explanation:
From the given information, Randy’s garden has 3 rows of carrots with 3 plants in each row. So, 3 x 3 = 9. To plant 4 times the number of rows of 3 plants, 9 x 4 = 36. 36 plants will have to plant by Randy’s garden next year.

Associative Property of Multiplication Lesson Check Page No 228

Question 1.
There are 2 benches in each car of a train ride. Two people ride on each bench. If a train has 5 cars, how many people in all can be on a train?
Options:
a. 4
b. 9
c. 10
d. 20

Answer:
d. 20

Explanation:
Given that there are 2 benches in each car of a train ride. If a train has 5 cars in total, the number of benches = 5 x 2 = 10. From the given information, two people ride on each bench. So, 10 x 2 = 20 people will travel on a train if the train has 5 cars.

Question 2.
Crystal has 2 CDs in each box. She has 3 boxes on each of her 6 shelves. How many CDs does Crystal have in all?
Options:
a. 6
b. 12
c. 18
d. 36

Answer:
d. 36

Explanation:
The crystal has 3 boxes on each of her 6 shelves. So, she has 3 x 6 = 18 boxes with her. Each box has 2 CDs in it. So, 2 x 18 = 36 CDs available at crystal.

Spiral Review

Question 3.
Find the sum.
4 7 2
+ 1 8 6
——–
Options:
a. 658
b. 648
c. 558
d. 286

Answer:
30

Explanation:

Add the ones. Add 2 + 6 =8. Then, Add the tens. Regroup hundreds and tens. Add 7 + 8 = 15. Remember to carry over. Add the hundreds. Add 4 + 1 + 1 = 6. Place the one’s, ten’s and hundreds to get the sum. The sum is 658.

Question 4.
Trevor made a picture graph to show how many minutes each student biked last week. This is his key.
Each Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Associative Property of Multiplication img 19 = 10 minutes.
What Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Associative Property of Multiplication img 20 does stand for?
Options:
a. 2 minutes
b. 10 minutes
c. 20 minutes
d. 25 minutes

Answer:
d. 25 minutes

Explanation:
Given Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Associative Property of Multiplication img 19 = 10 minutes. So, half time symbol = 5 minutes.  Therefore, Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Associative Property of Multiplication img 20 = 10 + 10 + 5 = 25 minutes.

Question 5.
Madison has 142 stickers in her collection. What is 142 rounded to the nearest ten?
Options:
a. 40
b. 140
c. 150
d. 200

Answer:
b. 140

Explanation:
The 142 lies between 140 and 150. But the 142 is closer to 140 than it is to 150. So, 142 is rounded to the 140.

Question 6.
There are 5 pages of photos. Each page has 6 photos. How many photos are there in all?
Options:
a. 12
b. 20
c. 24
d. 30

Answer:
d. 30

Explanation:
Given that there are 5 pages of photos. And, each page has 6 photos. Total photos = 5 x 6 = 30.

Patterns on the Multiplication Table Page No 233

Is the product even or odd? Write even or odd.

Question 1.
2 × 7 = even
Think: Products with 2 as a factor are even.

Answer:
even

Explanation:
Products with 2 as a factor are even.

Question 2.
4 × 6 = ________

Answer:
even

Explanation:
The numbers end with 0, 2, 4, 6, 8 are even numbers. So, 24 is even number. The 4 × 6 an even number.

Question 3.
8 × 3 = ________

Answer:
even

Explanation:
8 is an even number. 3 is an odd number. The product of an odd number and an even number is even. The answer is even.

Question 4.
2 × 3 = _________

Answer:
even

Explanation:
Products with 2 as a factor are even.

Question 5.
9 × 9 = ________

Answer:
odd

Explanation:
9 is an odd number. The product of two odd numbers is an odd number. The answer is odd.

Question 6.
5 × 7 = _________

Answer:
odd

Explanation:
The numbers end with 1,3, 5, 7, 9 are odd numbers. So, 35 is an odd number. The 5 × 7 an odd number.

Question 7.
6 × 3 = ________

Answer:
even

Explanation:
6 is an even number. 3 is an odd number. The product of an odd number and an even number is even. The answer is even.

Use the multiplication table. Describe a pattern you see.

Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Patterns on the Multiplication Table img 21

Question 8.
in the column for 5
_________

Answer:
The one’s digits repeat 0 and 5. Each number is 5 more than the number above it.

Explanation:
Each number is added with 5. One’s digit is repeated with 0 and 5.

Question 9.
in the row for 10
________

Answer:
Add 10. All the products are even. The one’s digit is always 0.

Explanation:
All the products are even. Also, the one’s digit is always 0. Add 10 for every product to get the next number to it.

Question 10.
in the rows for 3 and 6
Type below:
_________

Answer:
The products of 6 are the products of 3 doubled.

Explanation:
Add 3 for row 3. The products of 6 are the products of 3 doubled.

Question 11.
Carl shades a row in the multiplication table. The products in the row are all even. The ones digits in the products repeat 0, 4, 8, 2, 6. What row does Carl shade?
Carl shaded row for _________

Answer:
The row for 4.

Explanation:
From the given data, the answer is row 4.

Question 12.
Jenna says that no row or column contains products with only odd numbers. Do you agree? Explain.
_________

Answer:
Yes, Either the products are all even, or there is an even and odd number pattern.

Explanation:
Jenna said correctly. Either the products are all even, or there is an even and odd number pattern.

Patterns on the Multiplication Table Lesson Check Page No 234

Question 1.
Which has an even product?
Options:
a. 1 × 9
b. 3 × 3
c. 5 × 7
d. 4 × 9

Answer:
d. 4 × 9

Explanation:
The product of an odd number and an even number is even. The answer is 4 × 9.

Question 2.
Which describes this pattern?
10, 15, 20, 25, 30
Options:
a. Even and then odd
b. Add 10.
c. Subtract 5.
d. Multiply by 5.

Answer:
a. Even and then odd

Explanation:
The given pattern is the combination of even and add.

Spiral Review

Question 3.
Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. She buys 2 more cans. How many tennis balls does she now have in all?
Options:
a. 12
b. 9
c. 7
d. 6

Answer:
a. 12

Explanation:
Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. So, she has 2 x 3 = 6 balls. She buys 2 more cans. So, again 2 cans with 3 tennis balls = 2 x 3 =6. Total = 6 + 6 = 12. 12 tennis balls she is going to have with her.

Question 4.
Use the picture graph.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Patterns on the Multiplication Table img 22
How many students have green eyes?
Options:
a. 4
b. 8
c. 12
d. 16

Answer:
d. 16

Explanation:
From the given picture, Green eyes have 4 circles. Each circle =4. 4 x 4 = 16. 16 students have green eyes.

Question 5.
Sasha bought 3 boxes of pencils. If each box has 6 pencils, how many pencils did Sasha buy in all?
Options:
a. 9
b. 12
c. 18
d. 24

Answer:
b. 12

Explanation:
Sasha bought 3 boxes of pencils. If each box has 6 pencils, 3 x 6 = 12 pencils Sasha can buy in all.

Question 6.
Find the sum.
2 1 9
+ 7 6 3
———–
Options:
a. 992
b. 982
c. 976
d. 972

Answer:
b. 982

Explanation:
Break apart the addends from the given values. Start with the hundreds. Then, add each place value.
Let’s write 219 as 200+10+9 and 763 as 700+60+3.
Sum up the above two values. Then you get 900+70+12. Add the ones and then add the 10’s and 100’s. The final answer is 982.

Multiply with 8 Page No 239

Find the product.

Question 1.
8 × 10 = 80

Answer:
80

Explanation:
8 × 10 = (2 x 4) x 10
Use the Associative Property.
8 × 10 = 2 x (4 x 10)
Multiply. 4 × 10
8 × 10 = 2 x 40
Double the product.
8 × 10 = 40 + 40
8 × 10 = 80

Question 2.
8 × 8 = ________

Answer:
64

Explanation:
Factor 8 is an even number. 4+ 4
8 x 4 = 32.
32 doubled is 64.
8 x 8 = 64.

Question 3.
8 × 5 = ________

Answer:
40

Explanation:
8 × 5 = (2 x 4) x 5
Use the Associative Property.
8 × 5 = 2 x (4 x 5)
Multiply. 4 × 5
8 × 5 = 2 x 20
Double the product.
8 × 5 = 20 + 20
8 × 5 = 40

Question 4.
3 × 8 = ________

Answer:
24

Explanation:
Factor 8 is an even number. 4+ 4
3 x 4 = 12.
12 doubled is 24.
3 x 8 = 24.

Question 5.
_______ = 4 × 8

Answer:
32

Explanation:
Factor 8 is an even number. 4+ 4
4 x 4 = 16.
16 doubled is 32.
4 x 8 = 32.

Question 6.
8 × 7 = ________

Answer:
56

Explanation:
8 × 7 = (2 x 4) x 7
Use the Associative Property.
8 × 7 = 2 x (4 x 7)
Multiply. 4 × 7
8 × 7 = 2 x 28
Double the product.
8 × 7 = 28 + 28
8 × 7 = 56.

Question 7.
6 × 8 = ________

Answer:
48

Explanation:
Factor 8 is an even number. 4+ 4
6 x 4 = 24.
24 doubled is 48.
6 x 8 = 48.

Question 8.
_______ = 9 × 8

Answer:
72

Explanation:
Factor 8 is an even number. 4+ 4
9 x 4 = 36.
36 doubled is 72.
9 x 8 = 72.

Question 9.
8
× 2
——
________

Answer:
16

Explanation:
Using the Commutative Law of Multiplication, 2 x 8 = 8 x 2.
Factor 8 is an even number. 4+ 4
2 x 4 = 8.
8 doubled is 16.
2 x 8 = 16.
So, 8 x 2 =16.

Question 10.
6
× 8
——-
________

Answer:
48

Explanation:
Factor 8 is an even number. 4+ 4
6 x 4 = 24.
24 doubled is 48.
6 x 8 = 48.

Question 11.
8
× 7
——
_________

Answer:
56

Explanation:
Using the Commutative Law of Multiplication, 8 x 7 = 7 x 8.
Factor 8 is an even number. 4+ 4
7 x 4 = 28.
28 doubled is 56.
7 x 8 = 56.

Question 12.
0
× 8
——-
____________

Answer:
0

Explanation:

Multiplication of any number with 0 is 0. So, the answer for 0 x 8 is 0.

Question 13.
8
× 5
——
___________

Answer:
40

Explanation:
8 × 5 = (2 x 4) x 5
Use the Associative Property.
8 × 5 = 2 x (4 x 5)
Multiply. 4 × 5
8 × 5 = 2 x 20
Double the product.
8 × 5 = 20 + 20
8 × 5 = 40.

Question 14.
8
× 8
——–
___________

Answer:
64

Explanation:
Factor 8 is an even number. 4+ 4
8 x 4 = 32.
32 doubled is 64.
8 x 8 = 64.

Question 15.
9
× 8
——-
___________

Answer:
72

Explanation:
Factor 8 is an even number. 4+ 4
9 x 4 = 36.
36 doubled is 72.
9 x 8 = 72.

Question 16.
8
× 3
——
___________

Answer:
24

Explanation:
8 × 3 = (2 x 4) x 3
Use the Associative Property.
8 × 3 = 2 x (4 x 3)
Multiply. 4 × 3
8 × 3 = 2 x 12
Double the product.
8 × 3 = 12 + 12
8 × 3 = 24.

Question 17.
8
× 1
——
___________

Answer:
8

Explanation:

Multiplication of any number with 1 is the same number. So, 1 x 8 = 8.

Question 18.
4
× 8
——
___________

Answer:
32

Explanation:
Factor 8 is an even number. 4+ 4
4 x 4 = 16.
16 doubled is 32.
4 x 8 = 32.

Problem Solving

Question 19.
There are 6 teams in the basketball league. Each team has 8 players. How many players are there in all?
____________ players

Answer:
48

Explanation:
Multiply 6 x 8 to get the total number of players. 6 x 8 = 48 players are in the basketball league.

Question 20.
Lynn has 4 stacks of quarters. There are 8 quarters in each stack. How many quarters does Lynn have in all?
___________ quarters

Answer:
32

Explanation:
Multiply 4 x 8 to find quarters in stacks. Lynn has 4 x 8 = 32 quarters in total.

Question 21.
Tomas is packing 7 baskets for a fair. He is placing 8 apples in each basket. How many apples are there in all?
___________ apples

Answer:
56

Explanation:
Multiply 7 x 8 to get the total number of apples. Tomas have 7 x 8 = 56 apples.

Question 22.
There are 10 pencils in each box. If Jenna buys 8 boxes, how many pencils will she buy?
_____________ pencils

Answer:
80

Explanation:
To get total pencils, if Jenna buys 8 boxes, multiply 10 x 8. So, Jenna buys 10 x 8 = 80 pencils.

Multiply with 8 Lesson Check Page No 240

Question 1.
Find the product.
5 × 8 = ■
Options:
a. 30
b. 32
c. 42
d. 40

Answer:
d. 40

Explanation:
Using Commutative Property of Multiplication, write 5 x 8 = 8 x 5
8 × 5 = (2 x 4) x 5
Use the Associative Property.
8 × 5 = 2 x (4 x 5)
Multiply. 4 × 5
8 × 5 = 2 x 20
Double the product.
8 × 5 = 20 + 20
8 × 5 = 40

Question 2.
There are 7 tarantulas in the spider exhibit at the zoo. Each tarantula has 8 legs. How many legs do the 7 tarantulas have in all?
Options:
a. 15
b. 49
c. 56
d. 63

Answer:
c. 56

Explanation:
Multiply 7 x 8 to find the 7 tarantulas legs. 7 tarantulas have 7 x 8 = 56 legs.

Spiral Review

Question 3.
Find the difference.
6 5 2
– 9 9
———
Options:
a. 99
b. 552
c. 553
d. 653

Answer:
c. 553

Explanation:
Subtract the ones. 2<9. so regroup 5 tens 2 ones = 4 tens 3 ones. Now, do 12 – 9 = 3. Then, Subtract the tens. 4 < 9. So, regroup 6 hundred 5 tens = 5 hundred 5 tens. 14 – 9 = 5. Subtract the hundreds and add them to check the answer. 5 – 0 = 5. The final answer is 553.

Question 4.
The school library received an order of 232 new books. What is 232 rounded to the nearest ten?
Options:
a. 200
b. 230
c. 240
d. 300

Answer:
b. 230

Explanation:
The 232 lies between 230 and 240. But the 232 is closer to 230 than it is to 240. So, 232 is rounded to the 230.

Question 5.
Sam’s picture graph shows that 8 students chose pizza as their favorite lunch. This is the key for the graph.
Each ☺ smile = 2 students.
How many ☺ smile should be next to pizza on Sam’s graph?
Options:
a. 2
b. 4
c. 6
d. 8

Answer:
b. 4

Explanation:
Given 1 smile = 2 students.
2 smiles = 4 students
3 smiles = 6 students
4 smiles = 8 students
4 smiles required for Sam for her next pizza on the graph.

Question 6.
Tashia buys 5 packages of oranges. Each package has 4 oranges. How many oranges in all does Tashia buy?
Options:
a. 1
b. 9
c. 20
d. 25

Answer:
d. 25

Explanation:
To know the total number of oranges, multiply 5 x 5. Tashia buys 5 x 5 = 25 oranges.

Multiply with 9 Page No 245

Find the product.

Question 1.
10 × 9 = 90

Answer:
90

Explanation:
The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 10 – 1 = 9. The sum of the digits in the product is always 9. So, to multiply 10 × 9, think the tens digit is 9 and the one’s digit is 0. The product is 90.

Question 2.
2 × 9 = ________

Answer:
18

Explanation:
9 = 3 + 6
2 × 9 = 2 x (3 + 6)
Multiply each addend by 2.
2 × 9 = (2 × 3) + (2 × 6)
Add the products.
2 × 9 = 6 + 12
2 × 9 = 18.

Question 3.
9 × 4 = ________

Answer:
36

Explanation:
9 = 3 + 6
9 × 4 = (3 + 6) x 4
Multiply each addend by 4.
9 × 4 = (3 x 4) + (6 x 4)
Add the products.
9 × 4 = 12 + 24
9 × 4 = 36.

Question 4.
0 × 9 = ________

Answer:
0

Explanation:

Multiplication of any number with 0 is 0. So, the answer for 0 x 9 is 0.

Question 5.
1 × 9 = ________

Answer:
9

Explanation:

Multiplication of any number with 1 is the same number. So, 1 x 9 = 9.

Question 6.
8 × 9 = ________

Answer:
72

Explanation:
9 = 3 + 6
8 × 9 = 8 x (3 + 6)
Multiply each addend by 8.
8 × 9 = (8 × 3) + (8 × 6)
Add the products.
8 × 9 = 24 + 48
8 × 9 = 72.

Question 7.
9 × 5 = ________

Answer:
45

Explanation:
9 = 3 + 6
9 × 5 = (3 + 6) x 5
Multiply each addend by 5.
9 × 5 = (3 x 5) + (6 x 5)
Add the products.
9 × 5 = 15 + 30
9 × 5 = 45.

Question 8.
6 × 9 = ________

Answer:
54

Explanation:
9 = 3 + 6
6 × 9 = 6 x (3 + 6)
Multiply each addend by 6.
6 × 9 = (6 × 3) + (6 × 6)
Add the products.
6 × 9 = 18 + 36
6 × 9 = 54.

Question 9.
9
× 4
——–
________

Answer:
36

Explanation:
9 = 3 + 6
9 × 4 = (3 + 6) x 4
Multiply each addend by 4.
9 × 4 = (3 x 4) + (6 x 4)
Add the products.
9 × 4 = 12 + 24
9 × 4 = 36.

Question 10.
5
× 9
——–
________

Answer:
45

Explanation:
9 = 3 + 6
5 × 9 = 5 x (3 + 6)
Multiply each addend by 5.
5 × 9 = (5 × 3) + (5 × 6)
Add the products.
5 × 9 = 15 + 30
5 × 9 = 45.

Question 11.
9
× 7
——–
________

Answer:
63

Explanation:
9 = 3 + 6
9 × 7 = (3 + 6) x 7
Multiply each addend by 7.
9 × 7 = (3 x 7) + (6 x 7)
Add the products.
9 × 7 = 21 + 42
9 × 7 = 63.

Question 12.
2
× 9
——–
________

Answer:
18

Explanation:
9 = 3 + 6
2 × 9 = 2 x (3 + 6)
Multiply each addend by 2.
2 × 9 = (2 × 3) + (2 × 6)
Add the products.
2 × 9 = 6 + 12
2 × 9 = 18.

Question 13.
9
× 9
——–
________

Answer:
81

Explanation:
The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 9 – 1 = 8. The sum of the digits in the product is always 9. So, add 1 to 8 to get one’s digit 1 + 8 = 9. The product is 81.

Question 14.
10
× 9
——–
________

Answer:
90

Explanation:
The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 10 – 1 = 9. The sum of the digits in the product is always 9. So, to multiply 10 × 9, think the tens digit is 9 and the one’s digit is 0. The product is 90.

Question 15.
3
× 9
——–
________

Answer:
27

Explanation:
9 = 3 + 6
3 × 9 = 3 x (3 + 6)
Multiply each addend by 3.
3 × 9 = (3 × 3) + (3 × 6)
Add the products.
3 × 9 = 9 + 18
3 × 9 = 27.

Question 16.
9
× 8
——–
________

Answer:
72

Explanation:
9 = 3 + 6
8 × 9 = 8 x (3 + 6)
Multiply each addend by 8.
8 × 9 = (8 × 3) + (8 × 6)
Add the products.
8 × 9 = 24 + 48
8 × 9 = 72.

Question 17.
6
× 9
——–
________

Answer:
54

Explanation:
9 = 3 + 6
6 × 9 = 6 x (3 + 6)
Multiply each addend by 6.
6 × 9 = (6 × 3) + (6 × 6)
Add the products.
6 × 9 = 18 + 36
6 × 9 = 54.

Question 18.
9
× 1
——–
________

Answer:
9

Explanation:
Multiplication of any number with 1 is the same number. So, 1 x 9 = 9.

Problem Solving

Question 19.
There are 9 positions on the softball team. Three people are trying out for each position. How many people in all are trying out?
___________ people

Answer:
27

Explanation:
To find the total number of people trying for a position on the softball team, multiply 9 x 3. 9 x 3 = 27 people are trying for a softball team position.

Question 20.
Carlos bought a book for $9. Now he would like to buy 4 other books for the same price. How much will he have to pay in all for the other 4 books?
$ _____________

Answer:
$36

Explanation:
Carlos bought a book for $9. Now he would like to buy 4 other books for the same price. So, to get them all 4 books, he needs to pay 4 x $9 = $36.

Multiply with 9 Lesson Check Page No 246

Question 1.
Find the product.
7 × 9 = ■
Options:
a. 63
b. 56
c. 45
d. 36

Answer:
a. 63

Explanation:
9 = 3 + 6
9 × 7 = (3 + 6) x 7
Multiply each addend by 7.
9 × 7 = (3 x 7) + (6 x 7)
Add the products.
9 × 7 = 21 + 42
9 × 7 = 63.

Question 2.
Clare buys 5 tickets for the high school musical. Each ticket costs $9. How much do the tickets cost in all?
Options:
a. $36
b. $40
c. $45
d. $52

Answer:
c. $45

Explanation:
Multiply 5 with $9 to get the total number of tickets. Clare buys 5 tickets for 5 x $9 = $45.

Spiral Review

Question 3.
The table shows the hair color of girls in Kim’s class. How many girls have brown hair?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiply with 9 img 23
Options:
a. 1
b. 3
c. 4
d. 6

Answer:
d. 6

Explanation:
From the given figure, there are 6 bars available in the Number of Girls for Brown. So, the answer is 6.

Question 4.
Miles picked up 9 shirts from the dry cleaners. It costs $4 to clean each shirt. How much did Miles spend to have all the shirts cleaned?
Options:
a. $13
b. $22
c. $36
d. $45

Answer:
c. $36

Explanation:
Miles spend 9 x $4 = $36 to have all the shirts cleaned.

Question 5.
In a picture graph, each picture of a baseball is equal to 5 games won by a team. The row for the Falcons has 7 baseballs. How many games have the Falcons won?
Options:
a. 40
b. 35
c. 12
d. 7

Answer:
a. 63

Explanation:
From given data, 1 baseball = 5 games. The row for the Falcons has 7 baseballs. So, Falcons won 7 x 5 = 35 games.

Question 6.
An array has 8 rows with 4 circles in each row. How many circles are in the array?
Options:
a. 12
b. 24
c. 32
d. 36

Answer:
a. 63

Explanation:
8 x 4 = 32 circles are in the array.

Multiplication Page No 251

Solve.

Question 1.
Henry has a new album for his baseball cards. He uses pages that hold 6 cards and pages that hold 3 cards. If Henry has 36 cards, how many different ways can he put them in his album?
Henry can put the cards in his album 5 ways.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiplication img 24

Answer:
5 ways

Explanation:
Henry can put the cards in 5 ways. They are
1. (1 x 6 cards pages) x (10 x 3 cards pages) = 6 cards + 30 cards = 36 cards.
2. (2 x 6 cards pages) x (8 x 3 cards pages) = 12 cards + 24 cards = 36 cards.
3. (3 x 6 cards pages) x (6 x 3 cards pages) = 18 cards + 18 cards = 36 cards.
4. (4 x 6 cards pages) x (4 x 3 cards pages) = 24 cards + 12 cards = 36 cards.
5. (5 x 6 cards pages) x (2 x 3 cards pages) = 30 cards + 6 cards = 36 cards.

Question 2.
Ms. Hernandez has 17 tomato plants that she wants to plant in rows. She will put 2 plants in some rows and 1 plant in the others. How many different ways can she plant the tomato plants? Make a table to solve.

Rows With 2 Plants___8_____7_______6_____5_____4________3_______2______1_
Rows With 1 Plants____1_____3______5______7______9_______11_____13_______15__
Total Plants____17_____17_____17______17_______17______17_______17______17__
Ms. Hernandez can plant the tomato plants___8___Ways.

Answer:
8 ways

Explanation:
Ms. Hernandez wants to grow 2 tomoto plants in one row and 1 in other row. The total number of plants should be 17. So,
1. (8 rows x 2 plants) x (1 row x 1plant) = 16 plants + 1 plant = 17 plants.
2. (7 rows x 2 plants) x (3 rows x 1plant) = 14 plants + 3 plant = 17 plantst.
3. (6 rows x 2 plants) x (5 rows x 1plant) = 12 plants + 5 plant = 17 plants.
4. (5 rows x 2 plants) x (7 rows x 1plant) = 10 plants + 7 plant = 17 plants.
5. (4 rows x 2 plants) x (9 rows x 1plant) = 8 plants + 9 plant = 17 plants.
6. (3 rows x 2 plants) x (11 rows x 1plant) = 6 plants + 11 plant = 17 plants.
7. (2 rows x 2 plants) x (13 rows x 1plant) = 4 plants + 13 plant = 17 plants.
8. (1 rows x 2 plants) x (15 rows x 1plant) = 2 plants + 15 plant = 17 plants.

Question 3.
Bianca has a total of 25¢. She has some nickels and pennies. How many different combinations of nickels and pennies could Bianca have? Make a table to solve.

Number of Nickels___1______2_______3______4__
Number of Pennies___20______15______10_______5__
Total Value___25¢______25¢______25¢______25¢___
Bianca could have___4___Combination of 25 ¢.

Answer:
4 ways

Explanation:
1 Nickel = 5 pennies.
Bianca can have combinations of nickels and pennies to get 25¢ are
1. 1 Nickel + 20 Pennies = 5 Pennies + 20 Pennies = 25 Pennies = 25¢
2. 2 Nickels + 15 Pennies = 10 Pennies + 15 Pennies = 25 Pennies = 25¢
3. 3 Nickels + 10 Pennies = 15 Pennies + 10 Pennies = 25 Pennies = 25¢
4. 4 Nickels + 5 Pennies = 20 Pennies + 5 Pennies = 25 Pennies = 25¢

Multiplication Lesson Check Page No 252

Question 1.
The table shows different ways that Cameron can display his 12 model cars on shelves. How many shelves will display 2 cars if 8 of the shelves each display 1 car?
Options:
a. 1
b. 2
c. 3
d. 4

Question 1.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiplication img 25

Answer:
b. 2

Explanation:
1. (Shelves with 1 car x 2) + (Shelves with 2 cars x 5) = 2 Cars + 10 Cars = 12 Cars
2. (Shelves with 1 car x 4) + (Shelves with 2 cars x 4) = 4 Cars + 8 Cars = 12 Cars
3. (Shelves with 1 car x 6) + (Shelves with 2 cars x 3) = 6 Cars + 6 Cars = 12 Cars
4. (Shelves with 1 car x 8) + (Shelves with 2 cars x 2) = 8 Cars + 4 Cars = 12 Cars
5. (Shelves with 1 car x 10) + (Shelves with 2 cars x 1) = 10 Cars + 2 Cars = 12 Cars
Therefore, 2 shelves will display 2 cars if 8 of the shelves each display 1 car.

Spiral Review

Question 2.
Find the sum.
3 1 7
+ 1 5 1
——–
Options:
a. 166
b. 268
c. 468
d. 568

Answer:
c. 468

Explanation:
Add the ones. Add 7 + 1 =8. Then, Add the tens. Add 1 + 5 = 6. Add the hundreds. Add 3 + 1 = 4. Place the one’s, ten’s and hundreds to get the sum. The sum is 468.

Question 3.
The school cafeteria has an order for 238 hot lunches. What is 238 rounded to the nearest ten?
Options:
a. 300
b. 240
c. 230
d. 200

Answer:
b. 240

Explanation:
The 238 lies between 230 and 240. But the 238 is closer to 240 than it is to 230. So, 238 is rounded to the 240.

Question 4.
Tyler made a picture graph to show students’ favorite colors. This is the key for his graph.
Each Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiplication img 26 = 3 votes.
If 12 students voted for green, how many Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Multiplication img 27 should there be in the green row of the graph?
Options:
a. 3
b. 4
c. 9
d. 12

Answer:
b. 4

Explanation:
Each circle = 3 votes. If 12 students voted for green, total votes = 12. Write 12 = 3 + 3 + 3 +3. So, 4 circles represent 12 votes.

Question 5.
There are 5 bikes in each bike rack at the school. There are 6 bike racks. How many bikes in all are in the bike racks?
Options:
a. 11
b. 24
c. 25
d. 30

Answer:
d. 30

Explanation:
To find the total bikes in the bike rack at the school, multiply 5 bikes x 6 bike racks. 5 x 6 = 30 bikes are available in bike racks.

Review/Test Page No 253

Question 1.
Mrs. Ruiz sorted spools of thread into 4 boxes. Each box holds 5 spools. How many spools of thread does Mrs. Ruiz have? Draw circles to model the problem. Then solve.
________ spools

Answer:
20 spools

Explanation:
4 boxes of spools x 5 spools = 20 spools. Mrs. Ruiz has 20 spools of thread.

Question 2.
For numbers 2a–2d, select True or False for each multiplication sentence.
a. 2 × 8 = 16
i. True
ii. False

Answer:
i. True

Explanation:
Double 8.
8 + 8 = 16.
So, 2 x 8 = 16.

Question 2.
b. 5 × 8 = 40
i. True
ii. False

Answer:
i. True

Explanation:
Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40.

Question 2.
c. 6 × 8 = 56
i. True
ii. False

Answer:
ii. False

Explanation:

Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48. So, 6 × 8 = 56 is false.

Question 2.
d. 8 × 8 = 64
i. True
ii. False

Answer:
i. True

Explanation:
Factor 8 is an even number. 4+ 4
8 x 4 = 32.
32 doubled is 64.
8 x 8 = 64.

Question 3.
Bella is planning to write in a journal. Some pages will have one journal entry on them, and other pages will have two journal entries on them. If Bella wants to make 10 entries, how many different ways can she write them in her journal?
________ different ways

Answer:
4 ways

Explanation:
1. (1 journal entry x 2) + (2 journal entries x 4) = 2 journals + 8 journals = 10 journals.
2. (1 journal entry x 4) + (2 journal entries x 3) = 4 journals + 6 journals = 10 journals.
3. (1 journal entry x 6) + (2 journal entries x 2) = 6 journals + 4 journals = 10 journals.
4. (1 journal entry x 8) + (2 journal entries x 1) = 8 journals + 2 journals = 10 journals.

Bella can use 4 ways to write journals.

Question 4.
There are 7 days in 1 week. How many days are there in 4 weeks?
_______ days

Answer:
28 days

Explanation:
1 week = 1 x 7 = 7 days.
4 weeks = 4 x 7 = 28 days.

Review/Test Page No 254

Question 5.
Circle groups to show 3 × (2 × 3).
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 28
Type below:
__________

Answer:
18

Explanation:

3 × (2 × 3) = 3 x 6 = 18.

Question 6.
Dale keeps all of his pairs of shoes in his closet. Select the number of shoes that Dale could have in his closet. Mark all that apply.
Options:
a. 3
b. 4
c. 6
d. 7
e. 8

Answer:
b. 4
c. 6
e. 8

Explanation:
Pair of shoes have 2 in number. So, the possible ways are always even. Dale could have 4, 6, 8 in his closet.

Question 7.
Lisa completed the table to describe the product of a mystery one-digit factor and each number.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 29
Part A
Give all of the possible numbers that could be Lisa’s mystery one-digit factor.
Type below:
__________

Answer:
0, 2, 4, 6, 8

Question 7.
Part B
Explain how you know that you have selected all of the correct possibilities.
Type below:
__________

Answer:
Given that the product numbers are even. The product of an even number with another number is even. So, we should take the mystery factor as an even number.

Review/Test Page No 255

Question 8.
Kate drew 7 octagons. An octagon has 8 sides. How many sides did Kate draw?
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 30
_________ sides

Answer:
56

Explanation:
Kate drew 7 octagons. An octagon has 8 sides. Kate draw 8 x 7 = 56 sides.

Question 9.
José buys 6 bags of flour. Each bag weighs 5 pounds. How many pounds of flour did José buy?
_________ pounds

Answer:
30 pounds

Explanation:
6 x 5 = 30. José spends 30 pounds to buy flours.

Question 10.
Break apart the array to show 8 × 6 = (4 × 6) + (4 × 6).
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 31

Answer:

 

Explanation:
Break the array of 4 columns and 6 rows to get the answer.

Question 11.
Circle the symbol that makes the multiplication sentence true.
9 × 6Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 32 3 × (3 × 9)
_________

Answer:
<

Explanation:
9 x 6 = 54
3 x 27 = 81
54 < 81.
So, 9 x 6 < 3 x (3 x 9)

Question 12.
Roberto wants to make $2.00 using dollars, half dollar, and quarters. How many different ways can he make $2.00?
__________ different ways

Answer:
18

Explanation:
0.25  – 8 |6 |4 |4 |2 |2 |0 |0 |0
0.50 – 0 |1 |2 |0 |3 |1 |2 |4 |0
1        -0 |0 |0 |1 |0 |1 |1 |0 |2

Review/Test Page No 256

Question 13.
A carpenter builds stools that have 3 legs each. How many legs does the carpenter use to build 5 stools? Use the array to explain how you know your answer is correct.
_________ legs

Answer:
15 legs

Explanation:
Each stool has 3 legs. To build 5 stools, 5 x 3 = 15 legs. 15 legs need to build 5 stools.

Question 14.
Etta buys some ribbon and cuts it into 7 pieces that are the same length. Each piece is 9 inches long. How long was the ribbon that Etta bought?
_________ inches

Answer:
63 inches

Explanation:
The length of the ribbon is 7 x 9 inches = 63 inches.

Question 15.
Antoine and 3 friends divide some pennies evenly among themselves. Each friend separates his pennies into 3 equal stacks with 5 pennies in each stack.
Write a multiplication sentence that shows the total number of pennies.
Type below:
_________

Answer:
4 x (5 x 3)

Explanation:
5 pennies into 3 equal stacks = 5 x 3 = 15.
15 stacks shared between 4 friends = 4 x 15 = 4 x (5 x 3).

Question 16.
Luke is making 4 first-aid kits. He wants to put 3 large and 4 small bandages in each kit. How many bandages does he need for the kits? Show your work.
_________ bandages

Answer:
28 bandages

Explanation:
Luke wants to put 3 large and 4 small bandages in each kit. So, total = 3 + 4 = 7 bandages.
He is making 4 first-aid kits. So, 4 x 7 bandages = 28 bandages.

Review/Test Page No 257

Question 17.
For numbers 17a–17d, select True or False for each equation.
a. 3 × 7 = 21
i. True
ii. False

Answer:
i. True

Explanation:

Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21. The answer is true.

Question 17.
b. 5 × 7 = 28
i. True
ii. False

Answer:
ii. False

Explanation:

Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. The answer is False.

Question 17.
c. 8 × 7 = 49
i. True
ii. False

Answer:
ii. False

Explanation:

Use Distributive Property to find 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer. The answer is False.

Question 17.
d. 9 × 7 = 63
i. True
ii. False

Answer:
i. True

Explanation:
9 = 3 + 6
9 × 7 = (3 + 6) x 7
Multiply each addend by 7.
9 × 7 = (3 x 7) + (6 x 7)
Add the products.
9 × 7 = 21 + 42
9 × 7 = 63.
The answer is true.

Question 18.
Circle the number that makes the multiplication sentence true.
10 × Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 33 = 40

Answer:
4

Explanation:
The value of 10 x4 = 40. So, the answer is 4.

Question 19.
For numbers 19a–19d, select Yes or No to indicate whether the number sentence has the same value as 8 × 6.
a. 8 + (4 × 2) = ■
i. yes
ii. no

Answer:
ii. no

Explanation:
8 x 6 = 48.
8 + (4 x 2) = 8 + 8 =16. The answer is no.

Question 19.
b. (8 × 4) + (8 × 2) = ■
i. yes
ii. no

Answer:
i. yes

Explanation:
8 x 6 = 48.
(8 x 4) + (8 x 2) = 32 + 16 = 48. The answer is yes.

Question 19.
c. (6 × 4) + (6 × 2) = ■
i. yes
ii. no

Answer:
ii. no

Explanation:
8 x 6 = 48.
(6 × 4) + (6 × 2) = 24 + 12 = 36. The answer is no.

Question 19.
d. 6 × (4 + 4) = ■
i. yes
ii. no

Answer:
i. yes

Explanation:
8 x 6 = 48.
6 × (4 + 4) = 6 x 8 = 48. The answer is yes.

Question 20.
Chloe bought 4 movie tickets. Each ticket cost $6. What was the total cost of the movie tickets?
$ _________

Answer:
$24

Explanation:
The total cost of the movie tickets = 4 x $6 = $24.

Question 21.
Write a multiplication sentence using the following numbers and symbols.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 34
Type below:
__________

Answer:
6 x (5 x 2) = 60

Explanation:
We can write as 6 x (5 x 2) = 60.

Review/Test Page No 258

Question 22.
Louis started a table showing a multiplication pattern.
Part A
Complete the table. Describe a pattern you see in the products.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 35
Type below:
__________

Answer:
12, 15, 18, 21, 24, 27, 30. Add 3 to the product to get the next product.

Explanation:
Add 3 to the product to get the next product.
9+3 = 12.
12 + 3 = 15.
15 + 3 = 18.
18 + 3 = 21.
21 + 3 = 24.
24 + 3 = 27.
27 + 3 = 30.

Question 22.
Part B
If you multiplied 3 × 37, would the product be an even number or an odd number? Use the table to explain your reasoning.
__________

Answer:
When an even number is multiplied by 3 (an odd number), the product is even. When an odd number is multiplied by 3, the product is odd, so the product of 3 × 37 would be odd.

Question 23.
Use the number line to show the product of 4 × 8.
Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Review/Test img 36
4 × 8 = _______

Answer:
32

Explanation:
Skip 2 numbers to get the product of 4 multiples. If you skip 2 numbers until you count 8, you can get 32. The answer is 32.

Conclusion

Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies include a clear-cut explanation for all the questions in it. We tried our best to help you understand the concept better by taking enough images, graphs. Firstly solve the problems on your own and tally your answers with the Go Math 3rd Grade Answer Key Ch 4 Multiplication Facts and Strategies.

In order to provide you a smooth learning experience, we have compiled all the Questions in Grade 3 Chapter 4 Multiplication Facts and Strategies in a comprehensive manner. Grab the opportunity and learn from Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice PDF too to make your learning fun.

Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables

go-math-grade-8-chapter-15-two-way-tables-answer-key

Hey guys! Are you searching for the Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables on various sites? If your answer is yes, then don’t worry you are on the right page. Here you can get the best answers for Go Math Grade 8 Chapter 15 Two-Way Tables. Students who are lagging in two-way tables can get them in this article. Make use of Go Math Grade 8 Answer Key Chapter 15 Two-way Tables and Download them for free.

Go Math Grade 8 Chapter 15 Two-Way Tables Answer Key

You can learn the concepts of frequency tables in Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables. It is the second essential teaching practice for the students of 8th standard. So, every student who love to learn math must go through the HMH Go Math Grade 8 Chapter 15 in an easy way. You can download and practice Go Math Grade 8 Solution Key Chapter 15 Two-Way Tables for free of cost. Click on the HMH Go Math Grade 8 Answer Key links and kickstart your preparation.

Lesson 1: Two-Way Frequency Tables

 Lesson 2: Two-Way Relative Frequency Tables

Model Quiz

Mixed Review

Guided Practice – Two-Way Frequency Tables – Page No. 454

Question 1.
In a survey of 50 students, 60% said that they have a cat. Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog. Complete the two-way table.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 1: Two-Way Frequency Tables img 1
a. Enter the total number of students surveyed in the bottom right cell of the table.
Type below:
_______________

Answer:
grade 8 chapter 15 image 1

Explanation:
In a survey of 50 students, 60% said that they have a cat.
In mathematical terms:
Cat = 0.6×50 = 30
If 60% have a cat, then 40% don’t have a cat
No Cat = (1 – 0.6) × 50 = 20
Because there are 2 options, Adding them will give the total amount of students
Total = Cat + No Cat = 50
Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog. So, in mathematical terms:
Dog = Cat × 0.7 + No Cat ×0.75 = 30 × 0.7 + 20 × 0.75 = 36
Following the same logic as before, if 70% of students who have a cat also have a dog, then 30% of them don’t have a dog. The same analysis for the students who do not have a cat.
No Dog = Cat × (1-0.7) + No Cat × (1-0.75) = 30 × (1-0.7) + 20 × (1-0.75) = 14
Again, the addition of the 2 options has to give the total amount of students
Total = 50

Question 1.
b. Fill in right column.
Type below:
_______________

Answer:
Of the students who have a cat, 70% also have a dog. Of the students who do not have a cat, 75% have a dog. In mathematical terms:
Dog = Cat × 0.7 + No Cat ×0.75 = 30 × 0.7 + 20 × 0.75 = 36

Question 1.
c. Fill in top row.
Type below:
_______________

Answer:
In a survey of 50 students, 60% said that they have a cat. In mathematical terms:
Cat = 0.6×50 = 30

Question 1.
d. Fill in second row.
Type below:
_______________

Answer:
If 60% have a cat, then 40% don’t have a cat
No Cat = (1 – 0.6) × 50 = 20

Question 1.
e. Fill in last row.
Type below:
_______________

Answer:
Because there are 2 options, the addition of them has to give the total amount of students
Total = Cat + No Cat = 50

Question 2.
The results of a survey at a school are shown. Is there an association between being a boy and being left-handed? Explain.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 1: Two-Way Frequency Tables img 2
_______________

Answer:
No, there isn’t any association between being a boy and being left-handed.
Boys are no more likely to be left-handed than right-handed.

ESSENTIAL QUESTION CHECK-IN

Question 3.
Voters were polled to see whether they supported Smith or Jones. Can you construct a two-way table of the results? Why or why not?
_______________

Answer:
You cannot construct a two-way table of the results. Because there is only one variable; voters. If there were two variables, such as men and women, a two-way table could be constructed.

15.1 Independent Practice – Two-Way Frequency Tables – Page No. 455

Question 4.
Represent Real-World Problems One hundred forty students were asked about their language classes. Out of 111 who take French, only 31 do not take Spanish. Twelve take neither French nor Spanish. Use this information to make a two-way table.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 1: Two-Way Frequency Tables img 3
Type below:
_______________

Answer:
grade 8 chapter 15 image 2

Question 5.
Represent Real-World Problems Seventh- and eighth-grade students were asked whether they preferred science or math.
a. Complete the two-way table.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 1: Two-Way Frequency Tables img 4
Type below:
_______________

Answer:
grade 8 chapter 15 image 3

Question 5.
b. Is there an association between being in eighth grade and preferring math? Explain.
_______________

Answer:
There is no association as such between being in eighth grade and preferring maths. But due to the total no. of eighth-grade students choosing maths is greater than the total no. of students in seventh grade preferring science. So, the eighth-grade students preferred.

Question 6.
Persevere in Problem Solving The table gives partial information on the number of men and women who play in the four sections of the Metro Orchestra.
a. Complete the table.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 1: Two-Way Frequency Tables img 5
Type below:
_______________

Answer:
grade 8 chapter 15 image 4

Question 6.
b. Is there an association between being a woman and playing strings? Explain.
_______________

Answer:
There is no association between being a woman and playing strings since the number of men playing string is less than women.

Two-Way Frequency Tables – Page No. 456

FOCUS ON HIGHER ORDER THINKING

Question 7.
Multi-Step The two-way table below shows the results of a survey of Florida teenagers who were asked whether they preferred surfing or snorkeling.
a. To the right of the number in each cell, write the relative frequency of the number compared to the total for the row the number is in. Round to the nearest percent.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 1: Two-Way Frequency Tables img 6
Type below:
_______________

Answer:
grade 8 chapter 15 image 9

Question 7.
b. Explain the meaning of the relative frequency you wrote beside 28.
Type below:
_______________

Answer:
The relative frequency shows the percentage of people aged 16-18 that prefer snorkeling.

Question 7.
c. To the right of each number you wrote in part a, write the relative frequency of each number compared to the total for the column the number is in. Are the relative frequencies the same? Why or why not?
Type below:
_______________

Answer:
grade 8 chapter 15 image 10

Question 7.
d. Explain the meaning of the relative frequency you wrote beside 28.
Type below:
_______________

Answer:
The relative frequency represents the percentage of people that prefer snorkeling that is aged 16-18.

Guided Practice – Two-Way Relative Frequency Tables – Page No. 462

Question 1.
In a class survey, students were asked to choose their favorite vacation destination. The results are displayed by gender in the two-way frequency table.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 2: Two-Way Relative Frequency Tables img 7
a. Find the total for each gender by adding the frequencies in each row. Write the row totals in the Total column.
Type below:
_______________

Answer:
grade 8 chapter 15 image 5
Girl = 7 + 3 + 2 = 12
Boy = 5 + 2 + 6 = 13

Question 1.
b. Find the total for each preferred vacation spot by adding the frequencies in each column. Write the column totals in the Total row.
Type below:
_______________

Answer:
Seashore = 7 + 5 = 12
Mountains = 3 + 2 = 5
Other = 2 + 6 = 8

Question 1.
c. Write the grand total (the sum of the row totals and the column totals) in the lower-right corner of the table.
Type below:
_______________

Answer:
grand total = 25

Question 1.
d. Create a two-way relative frequency table by dividing each number in the above table by the grand total. Write the quotients as decimals.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 2: Two-Way Relative Frequency Tables img 8
Type below:
_______________

Answer:
grade 8 chapter 15 image 6

Explanation:
7/25 = 0.28, 3/25 = 0.12; 2/25 = 0.08; 12/25 = 0.48
5/25 = 0.2; 2/25 = 0.08; 6/25 = 0.24; 13/25 = 0.52
12/25 = 0.48; 5/25 = 0.2; 8/25= 0.32; 25/25 = 1

Question 1.
e. Use the table to find the joint relative frequency of students surveyed who are boys and who prefer vacationing in the mountains.
_________

Answer:
Joint relative frequency of boys = 2/25 = 0.08
These boys who prefer vacationing in the mountains.

Question 1.
f. Use the table to find the marginal relative frequency of students surveyed who prefer vacationing at the seashore.
_________

Answer:
The marginal relative frequency of studnets = 12/25 = 0.48
These are the number of students who prefer vacationing in the seashore.

Question 1.
g. Find the conditional relative frequency that a student surveyed prefers vacationing in the mountains, given that the student is a girl. Interpret this result.
_________

Answer:
The condition relative frequency of girls of row = 3/12 = 0.25
And that of the column is 3/5 = 0.6
These are the number of girls who preferred vacationing in the mountains.

ESSENTIAL QUESTION CHECK-IN

Question 2.
How can you use a two-way frequency table to learn more about its data?
Type below:
_______________

Answer:
The two-way frequency table gives perfection and accuracy in calculating the data. It helps to calculate the total value two times while calculating the data of the row and to calculate the data of the column.

15.2 Independent Practice – Two-Way Relative Frequency Tables – Page No. 463

Stefan surveyed 75 of his classmates about their participation in school activities as well as whether they have a part-time job. The results are shown in the two-way frequency table. Use the table for Exercises 3–6.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 2: Two-Way Relative Frequency Tables img 9

Question 3.
a. Complete the table.
Type below:
_______________

Answer:
grade 8 chapter 15 image 7

Question 3.
b. Explain how you found the correct data to enter in the table.
Type below:
_______________

Answer:
1) In the first row of yes the values of sports only, Neither and total were provide. Also, in the 1st column of cubes only the values of No and total were providers. So, these values were subtracted and the value of yes was known.
2) The values in the 1st row of yes were added and subtracted from the total column. Hence the value in both columns was known. So, similarly, by adding and subtracting the values in the rows and columns the vacant values were known.

Question 4.
Create a two-way relative frequency table using decimals. Round to the nearest hundredth.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 2: Two-Way Relative Frequency Tables img 10
Type below:
_______________

Answer:
grade 8 chapter 15 image 8

Explanation:
Using the frequency table in problem 3, divide each number in each cell by 75, the grand total, and round to the nearest hundredth.
Job and clubs only: 10/75 = 0.13
Job and sports only: 12/75 = 0.16
Job and both clubs not sports: 20/75 = 0.27
Job and neither clubs nor sports: 9/75 = 0.12
Job total: 51/75 = 0.68
No jobs and clubs only: 5/75 = 0.07
No Job and sports only: 6/75 = 0.08
No job and both clubs and sports: 10/75 = 0.13
No Job and neither clubs nor sports: 3/75 = 0.04
No Job total: 24/75 = 0.32
Clubs only total: 15/75 = 0.2
Sports only total: 18/75 = 0.24
Both clubs and sports total: 30/75 = 0.4
Neither clubs nor sports total: 12/75 = 0.16
Total: 75/75 = 1.00
Use the totals above to create a two-way frequency table.

Question 5.
Give each relative frequency as a percent.
a. the joint relative frequency of students surveyed who participate in school clubs only and have part-time jobs
_________ %

Answer:
13%

Explanation:
The joint relative frequency of students surveyed who participate in school clubs only and have part-time jobs 0.13 or 13%
(Job and clubs only: 10/75 = 0.13)

Question 5.
b. the marginal frequency of students surveyed who do not have a part-time job
_________ %

Answer:
32%

Explanation:
The marginal frequency of students surveyed who do not have a part time job is 0.32 or 32%
(No job total: 24/75 = 0.32)

Question 5.
c. the conditional relative frequency that a student surveyed participates in both school clubs and sports, given that the student has a part-time job
_________ %

Answer:
39%

Explanation:
The conditional relative frequency that a student surveyed participates in both school clubs and sports, given that the student has a part-time job is 0.39 or 39%
(20/51 = 0.39)

Two-Way Relative Frequency Tables – Page No. 464

Question 6.
Discuss possible influences of having a part-time job on participation in school activities. Support your response with an analysis of the data.
Type below:
_______________

Answer:
The joint relative frequency of students surveyed who participate in school activities and have part-time jobs is 0.27 or 27%.
The joint relative frequency of students surveyed who participate in school activities and do not have part-time jobs is 0.13 or 13%.
This means that the students who have jobs are more likely to participate in school activities than the students who do not have jobs.

FOCUS ON HIGHER ORDER THINKING

Question 7.
The head of quality control for a chair manufacturer collected data on the quality of two types of wood that the company grows on its tree farm. The table shows the acceptance and rejection data.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Lesson 2: Two-Way Relative Frequency Tables img 11
a. Critique Reasoning To create a two-way relative frequency table for this data, the head of quality control divided each number in each row by the row total. Is this correct? Explain.
_______________

Answer:
No, it is not correct for the head of quality control to divide each number in each row by the row total to create a two-way relative frequency table. Each data value should have been divided by 600, the grand total, not by the row total.

Question 7.
b. Draw Conclusions Are any of the data the head of quality control entered into the two-way relative frequency table correctly? If so, which is and which isn’t? Explain.
Type below:
_______________

Answer:
Since the head of quality control divided incorrectly, the top two rows are incorrect. However, the bottom row has correct data because each number in the bottom row was divide by the grand total.

Question 8.
Analyze Relationships What is the difference between relative frequency and conditional relative frequency?
Type below:
_______________

Answer:
Relative frequency is found by dividing a frequency by the grand total while conditional relative frequency is found by dividing a frequency that is not in the Total row or the Total column by the frequency’s row total or column total.

Ready to Go On? – Model Quiz – Page No. 465

15.1 Two-Way Frequency Tables

Martin collected data from students about whether they played a musical instrument. The table shows his results. Use the table for Exercises 1–4.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Model Quiz img 12

Question 1.
Of the students surveyed, how many played an instrument?
__________ students

Answer:
90 students

Explanation:
Of the students surveyed, 90 students played an instrument

Question 2.
How many girls surveyed did NOT play an instrument?
__________ girls

Answer:
40 girls

Explanation:
(No. of boys did not play a musical instrument) + (No.of girls did not play a musical instrument) = (Total no. of students did not play an instrument)
70 + x = 110
x = 40
So, the no. of girls did not play a musical instrument = 40.

Question 3.
What is the relative frequency of a student playing an instrument? Write the answer as a percent.
________ %

Answer:
45%

Explanation:
The relative frequency of a student playing an instrument in this case, 90 out of 200 students play a musical instrument
(90/200) . 100 = 45%

Question 4.
What is the relative frequency of playing an instrument among boys? Write the answer as a decimal.
________ %

Answer:
38%

Explanation:
the relative frequency of playing an instrument among boys
(42/112) . 100 = 37.5% or 38%

15.2 Two-Way Relative Frequency Tables

Students were asked how they traveled to school. The two-way relative frequency table shows the results. Use the table for Exercises 5–7. Write answers as decimals rounded to the nearest hundredth.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Model Quiz img 13

Question 5.
What is the joint relative frequency of high school students who ride the bus?
________

Answer:
The joint relative frequency of high school students who ride the bus is 0.12

Question 6.
What is the marginal relative frequency of students surveyed who are in middle school?
________

Answer:
The marginal frequency of students surveyed in middle school is 0.42

Question 7.
What is the conditional relative frequency that a student rides the bus, given that the student is in middle school?
________

Answer:
0.62

Explanation:
The conditional relative frequency that a student rides the bus given that the student is in middle school.
Total no. of students going to bus = 0.26
Students who ride the bus (who are a middle school) = 0.42
Conditional relative frequency = 0.26/0.42 = 0.62

ESSENTIAL QUESTION

Question 8.
How can you use two-way tables to solve real-world problems?
Type below:
_______________

Answer:
Accuracy in the calculation of the data as it maintains decently in a suitable format. It helps to measure each and every frequency easily as the values are placed individually. Also, helps to measure the total of each row and column separately. So, since the data represented is suitable it makes the person understand and solve the problem.

Selected Response – Mixed Review – Page No. 466

The table gives data on the length of time that teachers at Tenth Avenue School have taught. Use the table for Exercises 1–5.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Mixed Review img 14

Question 1.
How many female teachers have taught for fewer than 10 years?
Options:
a. 4
b. 9
c. 21
d. 30

Answer:
c. 21

Explanation:
(No. of male teachers who have taught fewer than 10 years) + (No. of female teachers who have taught fewer than 10 years) = 30
9 + x = 30
x = 21
The number of female teachers who have taught fewer than 10 years is 21.

Question 2.
What is the relative frequency of teachers who have taught for 10 or more years?
Options:
a. 10%
b. 25%
c. 30%
d. 60%

Answer:
b. 25%

Explanation:
The relative frequency of teachers who have taught more than 10 or more years.
Total no. of teachers = 40
No. of teachers who taught more than 10 years = 10
Relative frequency = (10/40) . 100 = 25%

Question 3.
What is the relative frequency of having taught for fewer than 10 years among male teachers?
Options:
a. 0.09
b. 0.225
c. 0.6
d. 1.50

Answer:
c. 0.6

Explanation:
The relative frequency of male teachers who have taught fewer than 10 or more years.
Total no. of teachers = 15
No. of male teachers who taught for fewer than 10 years = 9
Relative frequency = (9/15) = 0.6

Question 4.
What is the joint relative frequency of female teachers who have taught for more than 10 years?
Options:
a. 4%
b. 10%
c. 16%
d. 25%

Answer:
b. 10%

Explanation:
The relative frequency of female teachers who taught for more than 10 years is 4/40 = 1/10 = 0.1 × 100 to calculate the data in percentage
10%

Question 5.
What is the marginal relative frequency of teachers who are female?
Options:
a. 0.16
b. 0.25
c. 0.4
d. 0.625

Answer:
d. 0.625

Explanation:
The total no. of teachers who are female = 25
Total no. of teachers = 40
Marginal frequency = 25/40 = 0.625

Question 6.
A triangle has an exterior angle of x°. Which of the following represents the measure of the interior angle next to it?
Options:
a. (180 − x)°
b. (x − 180)°
c. (90 − x)°
d. (x − 90)°

Answer:
a. (180 − x)°

Explanation:
The triangle has an exterior angle of x°. Let that angle be Angle ACD. So, the angle next to it is
Angle ACD + Angle ACB = 180º
Angle ACB = (180 − x)°

Question 7.
What is the volume of a cone that has a diameter of 12 cm and a height of 4 cm? Use 3.14 for π and round to the nearest tenth.
Options:
a. 25.12 cm3
b. 602.88 cm3
c. 150.72 cm3
d. 1,808.64 cm3

Answer:
c. 150.72 cm3

Explanation:
Diameter = 12cm
Radius r = 6cm
height h = 4cm
So, the volume of the cone = 1/3 . π . r². h
= 1/3 . 6 . 6 . 4 . 3.14 = 150.72 cm³

Mini-Task

Question 8.
The table gives data on books read by members of the Summer Reading Club.
Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables Mixed Review img 15
a. Find the relative frequency of a club member reading fewer than 25 books.
________ %

Answer:
25%

Explanation:
The relative frequency of a club member reading fewer than 25 books is
Total of 16 members read fewer than 25 books
16/64 = 0.25 or 25%

Question 8.
b. Find the relative frequency of reading fewer than 25 books among girl club members.
________ %

Answer:
14%

Explanation:
The relative frequency of a girl club member reading fewer than 25 books is
9/64 = 0.14 or 14%

Question 8.
c. Is there an association between being a girl and reading fewer than 25 books? Explain.
____________

Answer:
No, there isn’t any association between being a girl and reading fewer than 25 books. Because it is a choice depending on an individual to read as many books as he/she can and comparing with the boys reading fewer than 25 books because the number of girls reading these books is comparatively greater.

Conclusion:

Keep in touch with us to get the step by step explanation for Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables. Hope the information given by our team is beneficial for all the students of 8th standard. Build your self-confidence and prove yourself with the help of our Go Math Grade 8 Answer Key Chapter 15 Two-Way Tables. After your preparation, we suggest you to solve the problems given in the review test. All the Best!!!

Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison

go-math-grade-4-chapter-6-fraction-equivalence-and-comparison-answer-key

Gain some basic knowledge about the Fraction Equivalence and Comparison topics by accessing the free Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison. This resource of Go Math Grade 4 Answer Key aid your preparation for the standard tests. All the lessons covered in chapter 6 Fraction Equivalence and Comparison HMH Go Math Grade 4 Solution Key can be more efficient while your practice sessions. So, get the  Homework Help needed by referring to the Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison.

Go Math Grade 4 Chapter 6 Fraction Equivalence and Comparison Answer Key

Download Go Math Grade 4 Solution Key Chapter 6 Fraction Equivalence and Comparison and prepare the concepts whenever you wish. Take the help from the given resource and solve the Grade 4 chapter 6 Fraction Equivalence and Comparison regularly to score high. Refer to the detailed Solutions presented here in Go Math Grade 4 Chapter 6 Fraction Equivalence and Comparison Answer Key and review your answers.

Lesson 1: Investigate • Equivalent Fractions

Lesson 2: Generate Equivalent Fractions

Lesson 3: Simplest Form

Lesson 4: Common Denominators

Lesson 5: Problem Solving • Find Equivalent Fractions

Mid-Chapter Checkpoint

Lesson 6: Compare Fractions Using Benchmarks

Lesson 7: Compare Fractions

Lesson 8: Compare and Order Fractions

Review/Test

Common Core – Equivalent Fractions – Page No. 331

Equivalent Fractions
Use the model to write an equivalent fraction.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Equivalent Fractions img 1
\(\frac{4}{6}=\frac{2}{3}\)

Answer:
\(\frac{4}{6}=\frac{2}{3}\)

Explanation:
The first image has 4 parts shaded our of 6 parts. Divide \(\frac{8}{10}\) with 2. You will get \(\frac{2}{3}\). That means 2 parts are shaded out of 3 parts.

Question 2.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Equivalent Fractions img 2
\(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
The first image has 3 parts shaded our of 4 parts. Multiply \(\frac{8}{10}\) with 2. You will get \(\frac{6}{8}\). That means 6 parts are shaded out of 8 parts.

Tell whether the fractions are equivalent. Write = or ≠.

Question 3.
\(\frac{8}{10}\) _______ \(\frac{4}{5}\)

Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)

Explanation:
Multiply the numerator and denominator of 4 / 5 with 2
8 / 10 = (2 / 2 ) x (4 / 5 )
= 8 / 10
So, 8 / 10 = 4 / 5.

Question 4.
\(\frac{1}{2}\) _______ \(\frac{7}{12}\)

Answer:
\(\frac{1}{2}\) ≠ \(\frac{7}{12}\)

Explanation:
Multiply the numerator and denominator of 1 / 2 with 6
1 / 2 = (6 / 6) x (1 / 2)
= (6 / 12)
So, 1/2 ≠ 7 / 12

Question 5.
\(\frac{3}{4}\) _______ \(\frac{8}{12}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{8}{12}\)

Explanation:
Multiply the numerator and denominator of 3 / 4 with 3
3 / 4 = (3 / 3) x (3 / 4)
= (9 / 12)
So, 3 / 4 ≠ 8 / 12

Question 6.
\(\frac{2}{3}\) _______ \(\frac{4}{6}\)

Answer:
\(\frac{2}{3}\) = \(\frac{4}{6}\)

Explanation:
Multiply the numerator and denominator of 2 / 3 with 2
2 / 3 = (2 / 2) x ( 2 / 3 )
= 4 / 6
So, 2 / 3 = 4 / 6.

Question 7.
\(\frac{5}{8}\) _______ \(\frac{4}{10}\)

Answer:
\(\frac{5}{8}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 =(2 / 2) x (5 / 8)
= (10 / 16)
So, 5 / 8 ≠ 4 / 10

Question 8.
\(\frac{2}{6}\) _______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{6}\) = \(\frac{4}{12}\)

Explanation:
Multiply the numerator and denominator of 2 / 6 with 2
2 / 6 = (2 / 2) x (2 / 6)
= (4 / 12)
So, 2 / 6 = 4 / 12.

Question 9.
\(\frac{20}{100}\) _______ \(\frac{1}{5}\)

Answer:
\(\frac{20}{100}\) = \(\frac{1}{5}\)

Explanation:
Cross Multiply the 20 / 100 with 20 / 20
20 / 100 = (20 / 20) x (20 / 100)
= (1 / 5)
So, 20 / 100 = 1 / 5.

Question 10.
\(\frac{5}{8}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{5}{8}\) ≠ \(\frac{9}{10}\)

Explanation:
Multiply the numerator and denominator of 5 / 8 with 2
5 / 8 = (2 / 2) x (5 / 8)
= 10 / 16
So, 5 / 8 ≠ 9 / 10

Question 11.
Jamal finished \(\frac{5}{6}\) of his homework. Margaret finished \(\frac{3}{4}\) of her homework, and Steve finished \(\frac{10}{12}\) of his homework. Which two students finished the same amount of homework?
_______

Answer:
Jamal and Steve

Explanation:
As per the given data,
Jamal finished work = 5 /6 of his homework
Margaret finished work = 3 / 4th of her homework
Steve finished work = 10 / 12 of his homework
Multiply the numerator and denominator of 5/ 6 with 2
Then, (2 / 2) x (5 / 6) = 10 / 12
Then, Jamal and Steve finished the same amount of homework.

Question 12.
Sophia’s vegetable garden is divided into 12 equal sections. She plants carrots in 8 of the sections. Write two fractions that are equivalent to the part of Sophia’s garden that is planted with carrots.
Type below:
___________

Answer:
\(\frac{2}{3}\) and \(\frac{4}{6}\)

Explanation:
As per the given data,
Sophia’s vegetable garden is divided into 12 equal sections
She plants carrots in 8 of the sections out of 12 sections = 8 / 12
By simplifying the 8 / 12, we will get 4 / 6
Again simplify the 4 /6 by dividing method, you will get 2 /3
2 / 3 = (2 / 2) x (2 / 3)
= 4 / 6
Then, the equivalent fractions are 2 / 3, 4 /6

Common Core – Equivalent Fractions – Page No. 332

Question 1.
A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangle?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{6}\)
d. \(\frac{3}{4}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
As per the given data,
A rectangle is divided into 8 equal parts
Two parts are shaded
Then, the shaded area of rectangle = 2 / 8
By simplifying the 2/ 8, you will get 1/ 4
So, the shaded area of rectangle = 1 / 4

Question 2.
Jeff uses 3 fifth-size strips to model \(\frac{3}{5}\). He wants to use tenth-size strips to model an equivalent fraction. How many tenth-size strips will he need?
Options:
a. 10
b. 6
c. 5
d. 3

Answer:
b. 6

Explanation:
From the given data,
Jeff uses 3 fifth –size strips to model = 3 / 5 size strips
If he want to use tenth – size strips to an equivalent fraction = 1 / 10 size strips
The number of strips = x
(1 / 10) x = 3 / 5
x = 30/5
then, required number of tenth size trips = 6

Question 3.
Cassidy places 40 stamps on each of 8 album pages. How many stamps does she place in all?
Options:
a. 300
b. 320
c. 360
d. 380

Answer:
b. 320

Explanation:
As per the given data,
Cassidy places 40 stamps on each of 8 album pages = 8 x 40
= 320
So, total placed stamps on album pages by Cassidy = 320 stamps

Question 4.
Maria and 3 friends have 1,200 soccer cards. If they share the soccer cards equally, how many will each person receive?
Options:
a. 30
b. 40
c. 300
d. 400

Answer:
c. 300

Explanation:
As per the given data,
Maria and 3 friends have 1200 soccer cards
If soccer cards shared equally by four members = 1200/4
= 300
Then, each person received soccer cards = 300

Question 5.
Six groups of students sell 162 balloons at the school carnival. There are 3 students in each group. If each student sells the same number of balloons, how many balloons does each student sell?
Options:
a. 9
b. 18
c. 27
d. 54

Answer:
a. 9

Explanation:
As per the given, data,
Six groups of students sell 162 balloons at the school carnival
There are 3 students in each group
Then, total number of students in 6 groups = 6 x 3 = 18
If each student sells the same number of balloons = 162 / 18
= 9
Number of balloons sells by each student = 9

Question 6.
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
Who made an error and included a composite number?
Options:
a. Eric
b. Maya
c. Bella
d. Jordan

Answer:
d. Jordan

Explanation:
As per the given data,
Four students each made a list of prime numbers.
Eric: 5, 7, 17, 23
Maya: 3, 5, 13, 17
Bella: 2, 3, 17, 19
Jordan: 7, 11, 13, 21
21 is not a prime number
So, An error made by Jordan

Page No. 335

Question 1.
Complete the table below.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 3
Type below:
___________

Answer:
chapter 6 - Common Core - Image 3. jpg

Write two equivalent fractions.

Question 2.
\(\frac{4}{5}\)
\(\frac{4}{5}\) = \(\frac { 4×□ }{ 5×□ } \) = \(\frac{□}{□}\)
\(\frac{4}{5}\) = \(\frac { 4×□ }{ 5×□ } \) = \(\frac{□}{□}\)
\(\frac{4}{5}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\) = \(\frac{80}{100}\)

Explanation:
Two equivalent fractions of 4/5,
(4/5) x (2/2) = 8/10
And
(4/5) x (20/20) = 80/100
8/10 = (8/10) (10/10)
= (80/100)
So, the equivalent fractions of 4/5 = 8/10, 80/100

Question 3.
\(\frac{2}{4}\)
\(\frac{2}{4}\) = \(\frac { 2×□ }{ 4×□ } \) = \(\frac{□}{□}\)
\(\frac{2}{4}\) = \(\frac { 2×□ }{ 4×□ } \) = \(\frac{□}{□}\)
\(\frac{2}{4}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{2}{4}\) = \(\frac{4}{8}\) = \(\frac{8}{16}\)

Explanation:
Two equivalent fractions of 2/4,
(2/4) x (2/2) = 4/8
And
(2/4) x (4/4) = 8/16
4/8 = (4/8) (2/2)
= (8/16)
So, the equivalent fractions of 2/4 = 4/8, 8/16

Write two equivalent fractions.

Question 4.
\(\frac{3}{6}\)
\(\frac{3}{6}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{3}{6}\) = \(\frac{6}{12}\) = \(\frac{12}{24}\)

Explanation:
Two equivalent fractions of 3/6,
(3/ 6) x (2/2) = 6/12
And
(3/6) x (4/ 4) = 12/24
6/12 = (6/12) (2/2)
= (12/24)
So, the equivalent fractions of 3/6 = 6/12, 12/24

Question 5.
\(\frac{3}{10}\)
\(\frac{3}{10}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{3}{10}\) = \(\frac{6}{20}\) = \(\frac{12}{40}\)

Explanation:
Two equivalent fractions of 3/10,
(3/ 10) x (2/2) = 6/20
And
(3/10) x (4/ 4) = 12/40
6/20 = (6/20) (2/2)
= (12/40)
So, the equivalent fractions of 3/10 = 6/20, 12/40

Question 6.
\(\frac{2}{5}\)
\(\frac{2}{5}\) = \(\frac{□}{□}\) = \(\frac{□}{□}\)
Type below:
___________

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\) = \(\frac{8}{20}\)

Explanation:
Two equivalent fractions of 2/5,
(2/ 5) x (2/2) = 4/10
And
(2/5) x (4/ 4) = 8/20
4/10 = (4/10) (2/2)
= (8/20)
So, the equivalent fractions of 2/5 = 4/10, 8/20

Tell whether the fractions are equivalent. Write = or ≠.

Question 7.
\(\frac{5}{6}\) ______ \(\frac{10}{18}\)

Answer:
\(\frac{5}{6}\) ≠ \(\frac{10}{18}\)

Explanation:
Multiply the numerator and denominator of 5/6 with 2
5/6 =(2/2) x (5/6)
= (10/12)
So, 5/6 ≠ 10/ 18

Question 8.
\(\frac{4}{5}\) ______ \(\frac{8}{10}\)

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation:
Multiply the numerator and denominator of 4/5 with 2
4/5 =(2/2) x (4/5)
= (8/10)
So, 4/5 = 8/10

Question 9.
\(\frac{1}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{1}{5}\) ≠ \(\frac{4}{10}\)

Explanation:
Multiply the numerator and denominator of 1/5 with 4
1/5 =(4/4) x (1/5)
= (4/20)
So, 1/5 ≠ 4/10

Question 10.
\(\frac{1}{4}\) ______ \(\frac{2}{8}\)

Answer:
\(\frac{1}{4}\) = \(\frac{2}{8}\)

Explanation:
Multiply the numerator and denominator of 1/4 with 2
1/4 =(2/2) x (1/4)
= (2/8)
So, 1/4 = 2/8

Page No. 336

Use the recipe for 11–12.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 4

Question 11.
Kim says the amount of flour in the recipe can be expressed as a fraction. Is she correct? Explain.
______

Answer:
As per the given data, Kim says the amount of flour in the recipe can be expressed as a fraction. But in the recipe, 1 tablespoon flour is added. So, Kim says wrong.

Question 12.
How could you use a \(\frac{1}{8}\) – cup measuring cup to measure the light corn syrup?
Type below:
_________

Answer:
As per the given data,
By using the 1/8 cup measure the 9/12 cup light corn syrup
(9/12)/(1/8) = (9 x 8)/12
= (3 x 8)/4
= (3 x 2)
= 6
So, required 6 cups of 1/8 to measure the light corn syrup of 9/12.

Question 13.
Communicate Explain using words how you know a fraction is equivalent to another fraction.
Type below:
_________

Answer:
If you multiply the numerator and denominator of the first fraction by the same number and the products are the numerator and denominator of the second fraction, then the fractions are equivalent

Question 14.
Kyle drank \(\frac{2}{3}\) cup of apple juice. Fill in each box with a number from the list to generate equivalent fractions for \(\frac{2}{3}\). Not all numbers will be used.
Type below:
_________

Answer:
\(\frac{4}{6}\) and \(\frac{12}{18}\)

Explanation:
As per the given data,
Kyle drank 2/3 cup of apple juice
(2/3) x (2/2) = 4/6
(4/6) x (3/3) = 12/18
Equivalent fractions of 2/3 are 4/6 and 12/18

Common Core – Equivalent Fractions – Page No. 337

Write two equivalent fractions for each.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Equivalent Fractions img 5

Answer:
\(\frac{2}{6}\) and \(\frac{4}{12}\)

Explanation:
1/3
(1/3) x (2/2) = 2/6
(1/3) x (4/4) = 4/12
So, the equivalent fractions of 1/3 are 2/6 and 4/12

Question 2.
\(\frac{2}{3}\)
Type below:
_________

Answer:
\(\frac{4}{6}\) and \(\frac{8}{12}\)

Explanation:
2/3
(2/3) x (2/2) = 4/6
(2/3) x (4/4) = 8/12
Then, the equivalent fractions of 2/3 = 4/6 and 8/12

Question 3.
\(\frac{1}{2}\)
Type below:
_________

Answer:
\(\frac{2}{4}\) and \(\frac{4}{8}\)

Explanation:
1/2
(1/2) x (2/2) = 2/4
(1/2) x (4/4) = 4/8
Then, the equivalent fractions of 1/2 = 2/4, 4/8

Question 4.
\(\frac{4}{5}\)
Type below:
_________

Answer:
\(\frac{8}{10}\) and \(\frac{80}{100}\)

Explanation:
4/5
(4/5) x (2/2) = 8/10
(4/5) x (20/20) = 80/100
Then, the equivalent fractions of 4/5 = 8/10 and 80/100

Tell whether the fractions are equivalent. Write # or ≠.

Question 5.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
So, 1/4 = 3/12

Question 6.
\(\frac{4}{5}\) ______ \(\frac{5}{10}\)

Answer:
\(\frac{4}{5}\) ≠ \(\frac{5}{10}\)

Explanation:
4/5
Multiply numerator and denominator of 4/5 with 2
(4/5) x (2/2) = 8/10
Then 4/5 ≠ 5/10

Question 7.
\(\frac{3}{8}\) ______ \(\frac{2}{6}\)

Answer:
\(\frac{3}{8}\) ≠ \(\frac{2}{6}\)

Explanation:
3/8 ≠ 2/6

Question 8.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
Then, (3/4) x (2/2) = 6/8
So, 3/4 = 6/8

Question 9.
\(\frac{5}{6}\) ______ \(\frac{10}{12}\)

Answer:
\(\frac{5}{6}\) = \(\frac{10}{12}\)

Explanation:
5/6
Multiply the numerator and denominator with 2
(5/6) x (2/2) = 10/12
So, 5/6 = 10/12

Question 10.
\(\frac{6}{12}\) ______ \(\frac{5}{8}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{5}{8}\)

Explanation:
6/12 ≠ 5/8

Question 11.
\(\frac{2}{5}\) ______ \(\frac{4}{10}\)

Answer:
\(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 2
(2/5) x (2/2) = 4/10
So, 2/5 = 4/10

Question 12.
\(\frac{2}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{2}{4}\) ≠ \(\frac{3}{12}\)

Explanation:
2/4
Multiply the numerator and denominator of 2/4 with 3
(2/4) x (3/3) = 6/12
So, 2/4 ≠ 3/ 12

Question 13.
Jan has a 12-ounce milkshake. Four ounces in the milkshake are vanilla, and the rest is chocolate. What are two equivalent fractions that represent the fraction of the milkshake that is vanilla?
Type below:
_________

Answer:
\(\frac{1}{3}\) and \(\frac{2}{6}\)

Explanation:
As per the given data,
Jan has a 12-ounce milkshake
Four ounces in the milkshake are vanilla = 4/12 = 1/3
Then, 8-ounces in milkshake are chocolate = 8/12 = 2/3
4/12 = 1/3
By multiplying 1/3 with 2
(1/3) x (2/2) = 2/6
So, the equivalent fractions of vanilla milkshake are 1/3 and 2/6

Question 14.
Kareem lives \(\frac{4}{10}\) of a mile from the mall. Write two equivalent fractions that show what fraction of a mile Kareem lives from the mall.
Type below:
_________

Answer:
\(\frac{2}{5}\) and \(\frac{8}{20}\)

Explanation:
As per the given data,
Kareem lives 4/10 of a mile from the mall
To find the equivalent fractions of 4/10
Simplify the 4/10 = 2/5
Multiply the numerator and denominator of 2/5 with 4
(2/5) x (4/4) = 8/20
Then, the equivalent fraction of a mile Kareem lives from the mall = 2/5 and 8/20

Common Core – Equivalent Fractions – Page No. 338

Question 1.
Jessie colored a poster. She colored \(\frac{2}{5}\) of the poster red. Which fraction is equivalent to \(\frac{2}{5}\)?
Options:
a. \(\frac{4}{10}\)
b. \(\frac{7}{10}\)
c. \(\frac{4}{5}\)
d. \(\frac{2}{2}\)

Answer:
a. \(\frac{4}{10}\)

Explanation:
As per the given data,
Jessie colored a poster
She colored 2/5th of the poster red
Multiply the numerator and denominator of 2/5 with 2
Then, (2/5) x (2/2) = 4 /10
So, the equivalent fraction of 2/5 is 4/10

Question 2.
Marcus makes a punch that is \(\frac{1}{4}\) cranberry juice. Which two fractions are equivalent to \(\frac{1}{4}\)?
Options:
a. \(\frac{2}{5}, \frac{3}{12}\)
b. \(\frac{2}{8}, \frac{4}{12}\)
c. \(\frac{3}{4}, \frac{6}{8}\)
d. \(\frac{2}{8}, \frac{3}{12}\)

Answer:
d. \(\frac{2}{8}, \frac{3}{12}\)

Explanation:
As per the given data,
Marcus makes a punch that is 1/4th of cranberry juice
Multiply the numerator and denominator of 1/4 with 2
Then, (1/4) x (2/2) = 2/8
Multiply the numerator and denominator of 1/4 with 3
Then, (1/4) x (3/3) = 3/12
Equivalent fractions of 1/4 are 2/8 and 3/12

Question 3.
An electronics store sells a large flat screen television for $1,699. Last month, the store sold 8 of these television sets. About how much money did the store make on the television sets?
Options:
a. $160,000
b. $16,000
c. $8,000
d. $1,600

Answer:
b. $16,000

Explanation:
As per the given data,
An electronics store sells a large flat-screen television for $1,699
Last month, the store sold 8 of these television sets = 8 x $1,699 = $13,952. The money is about to $16,000.

Question 4.
Matthew has 18 sets of baseball cards. Each set has 12 cards. About how many baseball cards does Matthew have in all?
Options:
a. 300
b. 200
c. 150
d. 100

Answer:
b. 200

Explanation:
From the given data,
Matthew has 18 sets of basketball cards
Each set has 12 cards = 12 x 18
= 216
Total number of basketball cards with Matthew = 216. So, it is near to 200.

Question 5.
Diana had 41 stickers. She put them in 7 equal groups. She put as many as possible in each group. She gave the leftover stickers to her sister. How many stickers did Diana give to her sister?
Options:
a. 3
b. 4
c. 5
d. 6

Answer:
d. 6

Explanation:
As per the given data,
Diana has 41 stickers
She put them in 7 equal groups = 41/7
= 5 (remaining 6)
She gave the leftover stickers to her sister
The number of stickers Diana give to her sister = 6

Question 6.
Christopher wrote the number pattern below. The first term is 8.
8, 6, 9, 7, 10, …
Which is a rule for the pattern?
Options:
a. Add 2, add 3.
b. Add 6, subtract 3.
c. Subtract 6, add 3.
d. Subtract 2, add 3

Answer:
d. Subtract 2, add 3

Explanation:
From the given data,
Christopher wrote the number pattern = 8, 6, 9, 7, 10, …..
The first number in the pattern = 8
8 – 2 = 6 + 3 = 9 – 2 = 7 +3 = 10 ….
So, the rule for the above pattern is to subtract 2, add 3

Page No. 341

Question 1.
Write \(\frac{8}{10}\) in simplest form.
\(\frac{8}{10}\) = \(\frac { 8÷□ }{ 10÷□ } \) = \(\frac{□}{□}\)
\(\frac{□}{□}\)

Answer:
\(\frac{4}{5}\)

Explanation:
8/10 in simplest form
Divide the 8/10 with 2
(8/2)/(10/2) = 4/5
So, the simplest form of 8/10 is 4/5

Write the fraction in simplest form.

Question 2.
\(\frac{6}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

Explanation:
6/12 in simplest form
Divide the 6/12 with 6
(6/6)/(12/6) = 1/2
So, the simplest form of 6/12 is 1/2

Question 3.
\(\frac{2}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

Explanation:
2/10 in simplest form
Divide the 2/10 with 2
(2/2)/(10/2) = 1/5
So, the simplest form of 2/10 is 1/5

Question 4.
\(\frac{6}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
6/8 in simplest form
Divide the 6/8 with 2
(6/2)/(8/2) = 3/4
So, the simplest form of 6/8 is 3/4

Question 5.
\(\frac{4}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
4/6 in simplest form
Divide the 4/6 with 2
(4/2)/(6/2) = 2/3
So, the simplest form of 4/6 is 2/3

Write the fraction in simplest form.

Question 6.
\(\frac{9}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
9/12in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
So, the simplest form of 9/12 is 3/4

Question 7.
\(\frac{4}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

Explanation:
4/8in simplest form
Divide the 4/8 with 4
(4/4)/(8/4) = 1/2
So, the simplest form of 4/8 is 1/2

Question 8.
\(\frac{10}{12}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}\)

Explanation:
10/12 in simplest form
Divide the 10/12 with 2
(10/2)/(12/2) = 5/6
So, the simplest form of 10/12 is 5/6

Question 9.
\(\frac{20}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{5}\)

Explanation:
20 /100 in simplest form
Divide the 20/100 with 20
(20/20)/(100/20) = 1/5
So, the simplest form of 20/100 is 1/5

Tell whether the fraction is in simplest form. Write yes or no.

Question 10.
\(\frac{2}{8}\)
______

Answer:
No

Explanation:
2/8 in simplest form
Divide the 2/8 with 2
(2/2)/(8/2) = 1/4
The simplest form of 2/8 is 1/4
So, 2/8 is not the simplest form

Question 11.
\(\frac{9}{12}\)
______

Answer:
No

Explanation:
9/12 in simplest form
Divide the 9/12 with 3
(9/3)/(12/3) = 3/4
The simplest form of 9/12 is 3/4
So, 9/12 is not the simplest form

Question 12.
\(\frac{5}{6}\)
______

Answer:
Yes

Explanation:
5/6 is not divided by any number
Yes, 5/6 is the simplest form

Question 13.
\(\frac{4}{10}\)
______

Answer:
No

Explanation:
4/10 in simplest form
Divide the 4/10 with 2
(4/2)/(10/2) = 2/5
So, 4/10 is not the simplest form

Question 14.
There are 18 students in Jacob’s homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In simplest form, what fraction of students eat lunch in the cafeteria?
\(\frac{□}{□}\) of students

Answer:
\(\frac{2}{3}\) of students

Explanation:
As per the given data,
There are 18 students in Jacob’s homeroom
6 students bring their lunch to school = 6/18 = 1/3
The rest eat lunch in the cafeteria = 18 – 6 = 12/18
Divide the numerator and denominator of 12/18 with 6
(12/6) x (18/6) = 2/3
So, 2/3 of students eat lunch in the cafeteria

Page No. 342

Use the map for 15−16.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 6

Question 15.
Identify Relationships What fraction of the states in the southwest region share a border with Mexico? Is this fraction in simplest form?
\(\frac{□}{□}\)

Answer:
Yes, \(\frac{3}{4}\)

Explanation:
As per the given data,
Southwest region states = 4
Number of states in the southwest region shares a border with Mexico out of total southwest region states = 3/4
Yes, 3/4 is the simplest form

Question 16.
What’s the Question? \(\frac{1}{3}\) of the states in this region are on the Gulf of Mexico.
Type below:
_________

Answer:
In the simplest form, what fraction of the states in the southeast area on the Gulf of Mexico.

Question 17.
Pete says that to write \(\frac{4}{6}\) as \(\frac{2}{3}\), you combine pieces, but to write \(\frac{4}{6}\) as \(\frac{8}{12}\), you break apart pieces. Does this make sense? Explain.
______

Answer:
As per the given data,
Yes, it makes sense,
To write 4/6 as 2/3 combine sixth size pieces into equal groups of 2
Then (4/2)/(6/2) = 2/3
To write 4/6 as 8/12, break each sixth piece into 2 pieces
Then, 4/6 = (4 x 2)/(6 x 2) = 8/12

Question 18.
In Michelle’s homeroom, \(\frac{9}{15}\) of the students ride the bus to school, \(\frac{4}{12}\) get a car ride, and \(\frac{2}{30}\) walk to school.
For numbers 18a–18c, select True or False for each statement.
a. In simplest form, \(\frac{3}{5}\) of the students ride the bus to school.
i. True
ii. False

Answer:
i. True

Explanation:
9/15 of the students ride the bus to school
By dividing the numerator and denominator of 9/15 with 3
(9/3)/(15/3) =3/5
So, 3/5 of the students ride the bus to school
True

Question 18.
b. In simplest form, \(\frac{1}{4}\) of the students get a car ride to school.
i. True
ii. False

Answer:
ii. False

Explanation:
a. 4/12 of the students get a car ride
The simplest form of 4/12 = 1/3
So, 1/4 of the students get a car ride to school is a False statement

Question 18.
c. In simplest form, \(\frac{1}{15}\) of the students walk to school.
i. True
ii. False

Answer:
i. True

Explanation:
a. 2/30 of the students walk to school
By dividing the 2/30 with 2
(2/2)/(30/2) = 1/15
So, 1/15 of the students walk to school is a true statement

Common Core – Simplest Form – Page No. 343

Write the fraction in simplest form.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Simplest Form img 7

Answer:
\(\frac{3}{5}\)

Explanation:
To write the 6/10 in a simplest form
Divide the numerator and denominator of 6/10 with 2
(6 ÷2)/(10 ÷2) = 3/5
So, the simplest form of 6/10 = 3/5

Question 2.
\(\frac{6}{8}\) = \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
To write the 6/8in a simplest form
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, the simplest form of 6/8 = 3/4

Question 3.
\(\frac{5}{5}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{1}\) = 1

Explanation:
To write the 5/5in a simplest form
Divide the numerator and denominator of 5/5 with 5
(5 ÷5)/(5 ÷5) = 1/1
So, the simplest form of 5/5 = 1

Question 4.
\(\frac{8}{12}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
To write the 8/12in a simplest form
Divide the numerator and denominator of 8/12 with 4
(8 ÷4)/(12 ÷4) = 2/3
So, the simplest form of 8/12 = 2/3

Question 5.
\(\frac{100}{100}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{1}\) = 1

Explanation:
The simplest form of 100/100 = 1

Question 6.
\(\frac{2}{6}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{3}\)

Explanation:
To write the 2/6in a simplest form
Divide the numerator and denominator of 2/6 with 2
(2 ÷2)/(6 ÷2) = 1/3
So, the simplest form of 2/6 = 1/3

Question 7.
\(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:
\(\frac{1}{4}\)

Explanation:
To write the 2/8in a simplest form
Divide the numerator and denominator of 2/8 with 2
(2 ÷2)/(8 ÷2) = 1/4
So, the simplest form of 2/8 = 1/4

Question 8.
\(\frac{4}{10}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{5}\)

Explanation:
To write the 4/10 in a simplest form
Divide the numerator and denominator of 4 /10 with 2
(4 ÷2)/(10 ÷2) = 2/5
So, the simplest form of 4/10 = 2/5

Tell whether the fractions are equivalent. Write = or ≠. (if you dont have ≠on your keybord, copy and paste this one: ≠ )

Question 9.
\(\frac{6}{12}\) _______ \(\frac{1}{12}\)

Answer:
\(\frac{6}{12}\) ≠ \(\frac{1}{12}\)

Explanation:
6/12 ≠ 1/12

Question 10.
\(\frac{3}{4}\) _______ \(\frac{5}{6}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) _______ \(\frac{3}{5}\)

Answer:
\(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/( 10 ÷ 2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{3}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{3}{12}\) ≠ \(\frac{1}{3}\)

Explanation:
3/12 ≠ 1/3

Question 13.
\(\frac{6}{10}\) _______ \(\frac{60}{100}\)

Answer:
\(\frac{6}{10}\) = \(\frac{60}{100}\)

Explanation:
6/10
Multiply the numerator and denominator of 6/10 with 10
(6 x 10)/(10 x 10) = 60/100
So, 6/10 = 60/100

Question 14.
\(\frac{11}{12}\) _______ \(\frac{9}{10}\)

Answer:
\(\frac{11}{12}\) ≠ \(\frac{9}{10}\)

Explanation:
11/12 ≠ 9/10

Question 15.
\(\frac{2}{5}\) _______ \(\frac{8}{20}\)

Answer:
\(\frac{2}{5}\) = \(\frac{8}{20}\)

Explanation:
2/5
Multiply the numerator and denominator of 2/5 with 4
(2 x 4)/(5 x 4) = 8/20
So, 2/5 = 8/20

Question 16.
\(\frac{4}{8}\) _______ \(\frac{1}{2}\)

Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)

Explanation:
4/8
Divide the numerator and denominator of 4/8 with 4
(4 x 4)/(8 x 4) = 1/2
So, 4/8 = 1/2

Question 17.
At Memorial Hospital, 9 of the 12 babies born on Tuesday were boys. In simplest form, what fraction of the babies born on Tuesday were boys?
_______

Answer:
\(\frac{3}{4}\)

Explanation:
As per the given data,
At memorial hospital, 9 of the 12 babies born on Tuesday were boys = 9/12
Divide the numerator and denominator of 9/12 with 3
(9 ÷ 3)/(12 ÷ 3) = 3/4
So, in the simplest form
3/4 of the babies born on Tuesday were boys

Question 18.
Cristina uses a ruler to measure the length of her math textbook. She says that the book is \(\frac{4}{10}\) meter long. Is her measurement in simplest form? If not, what is the length of the book in simplest form?
\(\frac{□}{□}\)

Answer:
\(\frac{2}{5}\)

Explanation:
As per the given data,
Cristiana uses a ruler to measure the length of her math textbook
She says that the book is 4/10meter long
It is not in simplest form
Divide the numerator and denominator of 4/10 with 2
(4÷ 2)/( 10 ÷ 2) = 2/5
The length of the book in the simplest form = 2/5

Common Core – Simplest Form – Page No. 344

Question 1.
Six out of the 12 members of the school choir are boys. In simplest form, what fraction of the choir is boys?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{6}{12}\)
c. \(\frac{1}{2}\)
d. \(\frac{12}{6}\)

Answer:
c. \(\frac{1}{2}\)

Explanation:
As per the given data,
Six out of the 12 members of the school choir are boys = 6/12
To write the simplest form of 6/12, divide the numerator and denominator with 6
Then, (6 ÷ 6)/(12 ÷ 6) = 1/2
In simplest form, 1/2 of the choir is boys

Question 2.
Which of the following fractions is in simplest form?
Options:
a. \(\frac{5}{6}\)
b. \(\frac{6}{8}\)
c. \(\frac{8}{10}\)
d. \(\frac{2}{12}\)

Answer:
a. \(\frac{5}{6}\)

Explanation:
5/6 is in the simplest form
6/8 simplest form = 3/4
8/10 simplest form = 4/5
2/12 simplest form = 1/6

Question 3.
Each of the 23 students in Ms. Evans’ class raised $45 for the school by selling coupon books. How much money did the class raise in all?
Options:
a. $207
b. $225
c. $1,025
d. $1,035

Answer:
d. $1,035

Explanation:
As per the given data,
Each of the 23 students in Ms. Evan’s class raised $45 for the school by selling coupon books
= 23 x $45
= $1,035

Question 4.
Which pair of numbers below have 4 and 6 as common factors?
Options:
a. 12, 18
b. 20, 24
c. 28, 30
d. 36, 48

Answer:
d. 36, 48

Explanation:
36, 48
Here, 36 = 4 x 9
= 2 x 2 x 3 x 3
48 = 6 x 8
= 2 x 3 x 4 x 2

Question 5.
Bart uses \(\frac{3}{12}\) cup milk to make muffins. Which fraction is equivalent to \(\frac{3}{12}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{1}{2}\)
d. \(\frac{2}{3}\)

Answer:
a. \(\frac{1}{4}\)

Explanation:
As per the given data,
Bart uses 3/12 cup milk to make muffins
Divide the fraction with 3
(3 ÷ 3)/(12 ÷ 3) = 1/4
So, the equivalent fraction for 3/12 = 1/4

Question 6.
Ashley bought 4 packages of juice boxes. There are 6 juice boxes in each package. She gave 2 juice boxes to each of 3 friends. How many juice boxes does Ashley have left?
Options:
a. 24
b. 22
c. 18
d. 12

Answer:
c. 18

Explanation:
As per the given data,
Ashley bought 4 packages of juice boxes
There are 6 juice boxes in each package = 6 x 4 = 24
She gave 2 juice boxes to each of 3 friends = 2 x 3 = 6 juice boxes
So, 24 – 6 = 18
Total number of juice boxes left with Ashley = 18

Page No. 347

Question 1.
Find a common denominator for \(\frac{1}{3}\) and \(\frac{1}{12}\) by dividing each whole into the same number of equal parts. Use the models to help.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 8
common denominator:

Answer:
common denominator: 12

Explanation:
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, ….
List the multiples of 12 = 12, 24, 36, 48, ….
So, common denominators of 1/3 and 1/ 12 is 12

Write the pair of fractions as a pair of fractions with a common denominator.

Question 2.
\(\frac{1}{2}\) and \(\frac{1}{4}\)
Type below:
_________

Answer:
\(\frac{4}{8}\) and \(\frac{2}{8}\)

Explanation:
Common denominator of 1/2 and 1/4
List the multiples of 2 = 2, 4, 6, 8, 10, …
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of 1/2 and 1/4 is 4
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 4) ÷( 2 x 4) and ( 1 x 4 ) ÷ ( 4 x 4)
So, the common pair of fractions = 4/8 and 2/8

Question 3.
\(\frac{3}{4}\) and \(\frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{6}{8}\) and \(\frac{5}{8}\)

Explanation:
Common denominator of 3/4 and 5/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 8 = 8, 16, 24, 32, . . . .
Then, the common denominator of 3/4 and 5/8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 8) ÷( 4 x 8) and ( 5 x 8 ) ÷ ( 8 x 8)
So, the common pair of fractions = 6/8 and 5/8

Question 4.
\(\frac{1}{3}\) and \(\frac{1}{4}\)
Type below:
_________

Answer:
\(\frac{4}{12}\) and \(\frac{3}{12}\)

Explanation:
The common denominator of 1/3 and 1/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
Then, the common denominator of 1 /3 and 1/4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 3 x 12) and ( 1 x 12 ) ÷ ( 4 x 12)
So, the common pair of fractions = 4/12 and 3/12

Question 5.
\(\frac{4}{12}\) and \(\frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{8}{24}\) and \(\frac{15}{24}\)

Explanation:
Common denominator of 4/12 and 5/8
List the multiples of 12 = 12, 24, 36, 48, 60, …..
List the multiples of 8 = 8, 16, 24, 32, 40, 48, …
Then, the common denominator of 4/12 and 5/8 is 24
For the Common pair of fractions, multiply the common denominator with fractions
That is, (4 x 24) ÷( 12 x 24) and ( 5 x 24 ) ÷ ( 8 x 24)
So, the common pair of fractions = 8/24 and 15/24

Write the pair of fractions as a pair of fractions with a common denominator.

Question 6.
\(\frac{1}{4}\) and \(\frac{5}{6}\)
Type below:
_________

Answer:
\(\frac{3}{12}\) and \(\frac{10}{12}\)

Explanation:
The common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, . . .
List the multiples of 6 = 6, 12, 18, 24, 30, 36, ….
Then, the common denominator of 1/4 and 5/6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 5 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 10/12

Question 7.
\(\frac{3}{5}\) and \(\frac{4}{10}\)
Type below:
_________

Answer:
\(\frac{6}{10}\) and \(\frac{4}{10}\)

Explanation:
Common denominator of 3/5 and 4/10
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …..
List the multiples of 10 = 10, 20, 30, 40, 50 ….
Then, the common denominator of 3/5 and 4/10 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 5 x 10) and ( 4 x 10 ) ÷ ( 10 x 10)
So, the common pair of fractions = 6/10 and 4/10

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{3}{4}\) ______ \(\frac{1}{2}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{1}{2}\)

Explanation:
3/4 ≠ 1/2

Question 9.
\(\frac{3}{4}\) ______ \(\frac{6}{8}\)

Answer:
\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation:
3/4
Multiply the numerator and denominator of 3/4 with 2
(3 x 2) ÷ ( 4 x 2 ) = 6/8
So, 3/4 = 6/8

Question 10.
\(\frac{1}{2}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{1}{2}\) = \(\frac{4}{8}\)

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 4
(1 x 4) ÷ ( 2 x 4 ) = 4/8
So, 1/2 = 4/8

Question 11.
\(\frac{6}{8}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{6}{8}\) ≠ \(\frac{4}{8}\)

Explanation:
6/8 ≠ 4/8

Question 12.
Jerry has two same-size circles divided into the same number of equal parts. One circle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{2}{3}\) of the parts shaded. His sister says the least number of pieces each circle could be divided into is 7. Is his sister correct? Explain.
______

Answer:
As per the given data,
Jerry has two same size circles divided into the same number of equal parts
One circle has 3/4 of the parts shaded
So, non- shaded parts of one circle = 1 – 3/4 = 1/4
Another circle has 2/3 of the parts shaded
Non – shaded parts = 1 – 2/3 = 1/3
We can’t draw a conclusion that in how many parts or pieces a circle can be divided
So, his sister is incorrect

Page No. 348

Question 13.
Carrie has a red streamer that is \(\frac{3}{4}\) yard long and a blue streamer that is \(\frac{5}{6}\) yard long. She says the streamers are the same length. Does this make sense? Explain.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 9
______

Answer:
Carrie has a red streamer that is 3/4 yard long
The blue streamer that is 5/6 yard long
3/4 ≠ 5/6
She says the streamers are the same length, it doesn’t make any sense.

Question 14.
Leah has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{1}{3}\) of the parts shaded, and the other has \(\frac{2}{5}\) of the parts shaded. What is the least number of parts into which both rectangles could be divided?
______ parts

Answer:
15 parts

Explanation:
As per the given data,
Leah has two same size rectangles divided into the same number of equal parts
One rectangle has 1/3 of the parts shaded
Other rectangle has 2/5 of the parts shaded
15 parts

Question 15.
Julian says a common denominator for \(\frac{3}{4}\) and \(\frac{2}{5}\) is 9. What is Julian’s error? Explain.
Type below:
___________

Answer:
As per the given data,
Julian says a common denominator for 3/4 and 2/5 is 9
To find the common denominator for 3/4 and 2/5
List the multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, …..
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
So, the common denominator for 3/4 and 2/5 is 20
Julian says 9 in place of 20 and it is wrong.

Question 16.
Miguel has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{5}{8}\) of the parts shaded.
Into how many parts could each rectangle be divided? Show your work by sketching the rectangles.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 10
______ parts

Answer:
chapter 6 - simplest form - image 1. jpg
8 parts

Explanation:
As per the given data,
Miguel has two same – size rectangles divided into the same number of equal parts.
One rectangle has 3/4 of the parts shaded.
Another has 5/8 of the parts shaded.
The possible parts are 8.

Common Core – Common Denominators – Page No. 349

Write the pair of fractions as a pair of fractions with a common denominator.

Question 1.
\(\frac{2}{3} \text { and } \frac{3}{4}\)
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Common Denominators img 11

Answer:
\(\frac{8}{12} \text { and } \frac{9}{12}\)

Explanation:
2/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
Common multiple of 3 and 4 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 3 x 12 ) ÷ ( 4 x 12)
So, common pair of fractions = 8/12 and 9/12

Question 2.
\(\frac{1}{4} \text { and } \frac{2}{3}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{8}{12}\)

Explanation:
1/4 and 2/3
List the multiples of 4 = 4, 8, 12, 16, 20, …
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
Common multiple of 4 and 3 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 2 x 12 ) ÷ ( 3 x 12)
So, common pair of fractions = 3/12 and 8/12

Question 3.
\(\frac{3}{10} \text { and } \frac{1}{2}\)
Type below:
_________

Answer:
\(\frac{3}{10} \text { and } \frac{5}{10}\)

Explanation:
3/10 and 1/2
List the multiples of 10 = 10, 20, 30, 40, 50, ….
List the multiples of 2 = 2, 4, 6, 8, 10, 12, 14, ….
Common multiple of 10 and 2 is 10
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 10) ÷( 10 x 10) and ( 1 x 10 ) ÷ ( 2 x 10)
So, common pair of fractions = 3/10 and 5/10

Question 4.
\(\frac{3}{5} \text { and } \frac{3}{4}\)
Type below:
_________

Answer:
\(\frac{12}{20} \text { and } \frac{15}{20}\)

Explanation:
3/5 and 3/4
List the multiples of 5 = 5, 10, 15, 20, 25, 30, ….
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
Common multiple of 5 and 4 is 20
For the Common pair of fractions, multiply the common denominator with fractions
That is, (3 x 20) ÷( 5 x 20) and ( 3 x 20 ) ÷ ( 4 x 20)
So, common pair of fractions = 12/20 and 15/20

Question 5.
\(\frac{2}{4} \text { and } \frac{7}{8}\)
Type below:
_________

Answer:
\(\frac{4}{8} \text { and } \frac{7}{8}\)

Explanation:
2/4 and 7/8
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 8 = 8, 16, 24, 32, 40, ….
Common multiple of 4 and 8 is 8
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 8) ÷( 4 x 8) and ( 7 x 8 ) ÷ ( 8 x 8)
So, common pair of fractions = 4/8 and 7/8

Question 6.
\(\frac{2}{3} \text { and } \frac{5}{12}\)
Type below:
_________

Answer:
\(\frac{8}{12} \text { and } \frac{5}{12}\)

Explanation:
2/3 and 5/12
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 12 = 12, 24, 36, 48, 60, …
Common multiple of 3 and 12 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (2 x 12) ÷( 3 x 12) and ( 5 x 12 ) ÷ ( 12 x 12)
So, common pair of fractions = 8/12 and 5/12

Question 7.
\(\frac{1}{4} \text { and } \frac{1}{6}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{2}{12}\)

Explanation:
1/4 and 1/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, …
Common multiple of 4 and 6 is 12
For the Common pair of fractions, multiply the common denominator with fractions
That is, (1 x 12) ÷( 4 x 12) and ( 1 x 12 ) ÷ ( 6 x 12)
So, common pair of fractions = 3/12 and 2/12

Tell whether the fractions are equivalent. Write = or ≠.

Question 8.
\(\frac{1}{2}\) ______ \(\frac{2}{5}\)

Answer:
\(\frac{1}{2}\) ≠ \(\frac{2}{5}\)

Explanation:
Multiply the numerator and denominator of 1/2 with 2
(1 x 2) ÷ (2 x 2) = 2/4
So, 1/2 ≠ 2/5

Question 9.
\(\frac{1}{2}\) ______ \(\frac{3}{6}\)

Answer:
\(\frac{1}{2}\) = \(\frac{3}{6}\)

Explanation:
1/2
Multiply the numerator and denominator of 1/2 with 3
(1 x 3) ÷ (2 x 3) = 3/6
So, 1/2 = 3/6

Question 10.
\(\frac{3}{4}\) ______ \(\frac{5}{6}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{5}{6}\)

Explanation:
3/4 ≠ 5/6

Question 11.
\(\frac{6}{10}\) ______ \(\frac{3}{5}\)

Answer:
\(\frac{6}{10}\) = \(\frac{3}{5}\)

Explanation:
6/10
Divide the numerator and denominator of 6/10 with 2
(6 ÷ 2)/(10 ÷2) = 3/5
So, 6/10 = 3/5

Question 12.
\(\frac{6}{8}\) ______ \(\frac{3}{4}\)

Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷2)/(8 ÷2) = 3/4
So, 6/8 = 3/4

Question 13.
\(\frac{3}{4}\) ______ \(\frac{2}{3}\)

Answer:
\(\frac{3}{4}\) ≠ \(\frac{2}{3}\)

Explanation:
3/4 ≠ 2/3

Question 14.
\(\frac{2}{10}\) ______ \(\frac{4}{5}\)

Answer:
\(\frac{2}{10}\) ≠ \(\frac{4}{5}\)

Explanation:
2/10
Divide the numerator and denominator of 2/10 with 2
(2 ÷ 2)/(10 ÷ 2) = 1/5
So, 2/10 ≠ 1/5

Question 15.
\(\frac{1}{4}\) ______ \(\frac{3}{12}\)

Answer:
\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 3
(1 x 3)/(4 x 3) = 3/12
So, 1/4 = 3/12

Question 16.
Adam drew two same size rectangles and divided them into the same number of equal parts. He shaded \(\frac{1}{3}\) of one rectangle and \(\frac{1}{4}\) of other rectangle. What is the least number of parts into which both rectangles could be divided?
_________

Answer:
12 parts

Explanation:
As per the given data,
Adam drew two same size rectangles and divided them into the same number of equal parts
He shaded 1/3 of one rectangle
1/4 of another rectangle
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, …
A common multiple of 3 and 4 is 12
So, the least number of parts which rectangles could be divided = 12 parts

Question 17.
Mera painted equal sections of her bedroom wall to make a pattern. She painted \(\frac{2}{5}\) of the wall white and \(\frac{1}{2}\) of the wall lavender. Write an equivalent fraction for each using a common denominator.
Type below:
_________

Answer:
1/2 are 4/10 and 5/10

Explanation:
As per the given data,
Mera painted equal sections of her bedroom wall to make a pattern
She painted 2/5 of the wall white and 1/2 of the wall lavender
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
List the multiples of 2 = 2 ,4, 6, 8, 10, 12, 14, …
The common denominator of 2/5 and 1/2 = 10
Multiply the 2/5 and 1/2 with 10
(2 x 10)/(5 x 10) and (1 x 10)/(2 x 10)
4/10 and 5/10
So, common fractions of 2/5 and 1/2 are 4/10 and 5/10

Common Core – Common Denominators – Page No. 350

Question 1.
Which of the following is a common denominator of \(\frac{1}{4}\) and \(\frac{5}{6}\)?
Options:
a. 8
b. 9
c. 12
d. 15

Answer:
c. 12

Explanation:
Common denominator of 1/4 and 5/6
List the multiples of 4 = 4, 8, 12, 16, 20, 24, …
List the multiples of 6 = 6, 12, 18, 24, 30, ….
So, the common denominator of 1/4 and 5/6 is 12

Question 2.
Two fractions have a common denominator of 8. Which of the following could be the two fractions?
Options:
a. \(\frac{1}{2} \text { and } \frac{2}{3}\)
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)
c. \(\frac{3}{4} \text { and } \frac{1}{6}\)
d. \(\frac{1}{2} \text { and } \frac{4}{5}\)

Answer:
b. \(\frac{1}{4} \text { and } \frac{1}{2}\)

Explanation:
As per the given data,
Two fractions have a common denominator of 8
a. 1/2 and 2/3
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 3 = 3, 6, 9, 12, …
There is no common denominator of 8 for 1/2 and 2/3
b. 1/4 and 1 /2
List the multiples of 2 = 2, 4, 6, 8,10, ….
List the multiples of 4 = 4, 8, 12, 16, …
Here, the common denominator of 1 /4 and 1 /2 is 8
So, the answer is 1/4 and 1/2

Question 3.
Which number is 100,000 more than seven hundred two thousand, eighty-three?
Options:
a. 703,083
b. 712,083
c. 730,083
d. 802,083

Answer:
d. 802,083

Explanation:
802,083

Question 4.
Aiden baked 8 dozen muffins. How many total muffins did he bake?
Options:
a. 64
b. 80
c. 96
d. 104

Answer:
c. 96

Explanation:
As per the given data,
Aiden baked 8 dozen muffins
1 dozen = 12
then, 8 dozens = 12 x 8 = 96
So, Aiden baked totally 96 muffins

Question 5.
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourthgrade students in her school. She put the photos in 5 equal rows. How many photos did she put in each row?
Options:
a. 21
b. 23
c. 25
d. 32

Answer:
b. 23

Explanation:
As per the given data,
On a bulletin board, the principal, Ms. Gomez, put 115 photos of the fourth-grade students in her school
She put the photos in 5 equal rows
Then, number of photos in each row = 115/5 = 23
So, Ms. Gomez put photos in each row = 23

Question 6.
Judy uses 12 tiles to make a mosaic. Eight of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{4}\)
d. \(\frac{12}{18}\)

Answer:
a. \(\frac{2}{3}\)

Explanation:
As per the given data,
Judy uses 12 tiles to make a mosaic
Eight of the tiles are blue = 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
The simplest form of 8/12 is 2/3

Page No. 353

Question 1.
Keisha is helping plan a race route for a 10-kilometer charity run. The committee wants to set up the following things along the course.
Viewing areas: At the end of each half of the course
Water stations: At the end of each fifth of the course
Distance markers: At the end of each tenth of the course
Which locations have more than one thing located there?
First, make a table to organize the information.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 12
Next, identify a relationship. Use a common denominator, and find equivalent fractions.
Finally, identify the locations at which more than one thing will be set up. Circle the locations.
Type below:
___________

Answer:
Keisha is helping plan a race route for a 10-kilometer charity run.

Question 2.
What if distance markers will also be placed at the end of every fourth of the course? Will any of those markers be set up at the same location as another distance marker, a water station, or a viewing area? Explain.
Type below:
___________

Answer:
It really depends on where you place the other markers.

Question 3.
Fifty-six students signed up to volunteer for the race. There were 4 equal groups of students, and each group had a different task.
How many students were in each group?
_____ students

Answer:
14 students

Explanation:
As per the given data,
Fifty-six students signed up to volunteer for the race
There are four groups of students
Number of students in each group = 56/4 = 14
Total number of students in each group = 14

Page No. 354

Question 4.
A baker cut a pie in half. He cut each half into 3 equal pieces and each piece into 2 equal slices. He sold 6 slices. What fraction of the pie did the baker sell?
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}\)

Explanation:
A baker cut a pie in half. He cut each half into 3 equal pieces and each piece into 2 equal slices. He sold 6 slices. So, the remaining part is 1/2 of the pie.

Question 5.
Andy cut a tuna sandwich and a chicken sandwich into a total of 15 same-size pieces. He cut the tuna sandwich into 9 more pieces than the chicken sandwich. Andy ate 8 pieces of the tuna sandwich. What fraction of the tuna sandwich did he eat?
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\)

Explanation:
Let x be the number of pieces of the chicken sandwich so that x + 9 is the number of pieces of a tuna sandwich.
There is a total of 15 same-size pieces. So, we can write as
x + (x + 9) = 15
2x + 9 = 15
2x = 6
x = 3.
This means that there ate 3 + 9 = 12 pieces of a tuna sandwich. Since Andy ate 8, then this corresponds to a fraction of 8/12 = 2/3.

Question 6.
Luke threw balls into these buckets at a carnival. The number on the bucket gives the number of points for each throw. What is the least number of throws needed to score exactly 100 points? Explain.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 13
_____ throws

Answer:
13 throws

Explanation:
Take the maximum number to get the minimum throws = 9 X 10 = 90.
6 X 1 = 6; 2 X 2 = 4.
Add 90 + 6 + 4 = 100;
So, the least number of throws needed to score exactly 100 points = 10 + 1 + 2 = 13.

Question 7.
Victoria arranges flowers in vases at her restaurant. In each arrangement, \(\frac{2}{3}\) of the flowers are yellow. What other fractions can represent the part of the flowers that are yellow? Shade the models to show your work.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 14
\(\frac{□}{□}\)

Answer:
chapter 6
\(\frac{2}{3}\), \(\frac{8}{12}\), \(\frac{40}{60}\)

Explanation:
Basically, any fraction obtained by multiplying both the numerator and denominator by the same value would be an equivalent fraction:
2/3 = 2/3 * 4/4 = 8/12
8/12 = 8/12 * 5/5 = 40/60
etc.

Common Core – Find Equivalent Fractions – Page No. 355

Question 1.
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12, what other fractions could represent the part of the beads that are red?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Find Equivalent Fractions img 15

Answer:
\(\frac{2}{6}\), \(\frac{3}{9}\), \(\frac{4}{12}\)

Explanation:
Miranda is braiding her hair. Then she will attach beads to the braid. She wants \(\frac{1}{3}\) of the beads to be red. If the greatest number of beads that will fit on the braid is 12.
\(\frac{1}{3}\) X \(\frac{2}{2}\) = \(\frac{2}{6}\)
\(\frac{1}{3}\) X \(\frac{3}{3}\) = \(\frac{3}{9}\)
\(\frac{1}{3}\) X \(\frac{4}{4}\) = \(\frac{4}{12}\)

Question 2.
Ms. Groves has trays of paints for students in her art class. Each tray has 5 colors. One of the colors is purple. What fraction of the colors in 20 trays is purple?
\(\frac{□}{□}\)

Answer:
\(\frac{20}{100}\) or \(\frac{1}{5}\)

Explanation:
If you have 20 trays that are 100 colors with 20 being purple. 20/ 100 is 1/5

Question 3.
Miguel is making an obstacle course for field day. At the end of every sixth of the course, there is a tire. At the end of every third of the course, there is a cone. At the end of every half of the course, there is a hurdle. At which locations of the course will people need to go through more than one obstacle?
Type below:
_________

Answer:
\(\frac{1}{3}\), \(\frac{1}{2}\), \(\frac{2}{3}\) and final locations

Explanation:
We have three fractions with different denominators: sixths, thirds, and halves.
The first step is to make all the denominators equal for 1/6, 1/3, 1/2.
In this case, we want sixths since LCM(2, 3, 6) = 6
since 1/3 = 2/6, and 1/2 = 3/6. Now we can start solving.
1. There are six tires at the following: 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6.
2. There are three cones at the following (G.C.F.): 2/6 (or 1/3), 4/6 (or 2/3), and 6/6 (or 3/3).
3. There are two hurdles at the following (G.C.F.): 3/6 (or 1/2) and 6/6 (or 2/2).
We look for common numbers.
1. On 2/6, there are two obstacles: a tire and a cone.
2. On 3/6, there are two obstacles: a tire and a hurdle.
3. On 4/6, there are two obstacles: a tire and a cone.
4. At 6/6, there are three obstacles: a tire, cone, and a hurdle.
2/6 = 1/3
3/6 = 1/2
4/6 = 2/3
6/6 = 1
The answers are 1/3, 1/2, 2/3, and 1.

Question 4.
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Find Equivalent Fractions img 16
How many blueberry muffins should Preston put in a box with 36 muffins?
_________

Answer:
12 blueberry muffins

Explanation:
Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muffins should go in each box.
So, he had 2 blueberry muffins out of 6 muffins.
2/6 X 2/2 = 4/12. 4 blueberry muffins out of 12 muffins.
2/6 X 4/4 = 8/24. 8 blueberry muffins out of 24 muffins.
2/6 X 6/6 = 12/36. 12 blueberry muffins out of 36 muffins.

Common Core – Find Equivalent Fractions – Page No. 356

Question 1.
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade, how many books can she get from the store?
Options:
a. 9
b. 12
c. 18
d. 27

Answer:
b. 12

Explanation:
A used bookstore will trade 2 of its books for 3 of yours. If Val brings in 18 books to trade 2/3 X 6/6 = 12/18, she get 12 books

Question 2.
Every \(\frac{1}{2}\) hour Naomi stretches her neck; every \(\frac{1}{3}\) hour she stretches her legs; and every \(\frac{1}{6}\) hour she stretches her arms. Which parts of her body will Naomi stretch when \(\frac{2}{3}\) of an hour has passed?
Options:
a. neck and legs
b. neck and arms
c. legs and arms
d. none

Answer:
c. legs and arms

Explanation:
Summing \(\frac{1}{2}\)‘s only gives integer values giving 1, 2, 3, 4…or
integer values +\(\frac{1}{2}\) and 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\), 1 \(\frac{1}{2}\), 2 \(\frac{1}{2}\)…
So neck is excluded
Every \(\frac{1}{3}\): \(\frac{1}{3}\) + \(\frac{1}{2}\) = \(\frac{2}{3}\)
Legs will be stretched at \(\frac{2}{3}\) hour
Every \(\frac{1}{6}\): \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{4}{6}\)
Divide top and bottom by 2 giving:
(4 ÷ 2)/(6 ÷ 2) = \(\frac{2}{3}\)
Arms will be stretched at latex]\frac{2}{3}[/latex] hour

Question 3.
At the beginning of the year, the Wong family car had been driven 14,539 miles. At the end of the year, their car had been driven 21,844 miles. How many miles did the Wong family drive their car during that year?
Options:
a. 6,315 miles
b. 7,295 miles
c. 7,305 miles
d. 36,383 miles

Answer:
c. 7,305 miles

Explanation:
If at the beginning of the year, the Wong family’s car had driven 14539 miles and at the end of the year, it had driven 21844 miles, then subtract 14539 from 21844 to determine the difference between the two values, which will tell you how many miles the Wong family drove their car for during the year.
21844 – 14539 = 7305 miles

Question 4.
Widget Company made 3,600 widgets in 4 hours. They made the same number of widgets each hour. How many widgets did the company make in one hour?
Options:
a. 80
b. 90
c. 800
d. 900

Answer:
d. 900

Explanation:

3,600 widgets in 4 hours therefore 3,600 / 4 for one hour = 900 widgets 900 widgets in one hour.

Question 5.
Tyler is thinking of a number that is divisible by 2 and by 3. By which of the following numbers must Tyler’s number also be divisible?
Options:
a. 6
b. 8
c. 9
d. 12

Answer:
a. 6

Explanation:
The number 6 is divisible by 2 and by 3.

Question 6.
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. Which fraction is equivalent to the part of the circle that is shaded?
Options:
a. \(\frac{2}{3}\)
b. \(\frac{3}{4}\)
c. \(\frac{10}{16}\)
d. \(\frac{12}{18}\)

Answer:
b. \(\frac{3}{4}\)

Explanation:
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts.
6/8 = 3/4

Page No. 357

Choose the best term from the box.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 17

Question 1.
________ name the same amount.
________

Answer:
Equivalent Fractions

Question 2.
A _________ is a common multiple of two or more denominators
________

Answer:
Common Denominator

Write two equivalent fractions.

Question 3.
\(\frac{2}{5}\)
Type below:
________

Answer:
\(\frac{4}{10}\) and \(\frac{6}{15}\)

Explanation:
Two equivalent fractions of 2/5
Multiply the 2/5 with 2
(2 x 2)/(5 x 2) = 4/10
Multiply the 2/5 with 3
(2 x 3)/(5 x 3) = 6/15
So, the equivalent fractions of 2/5 are 4/10 and 6/15

Question 4.
\(\frac{1}{3}\)
Type below:
________

Answer:
\(\frac{2}{6}\) and \(\frac{3}{9}\)

Explanation:
Two equivalent fractions of 1/3
Multiply the 1/3 with 2
(1 x 2)/(3 x 2) = 2/6
Multiply the 1/3 with 3
(1 x 3)/(3 x 3) = 3/9
So, the equivalent fractions of 1/3 are 2/6 and 3/9

Question 5.
\(\frac{3}{4}\)
Type below:
________

Answer:
\(\frac{6}{8}\) and \(\frac{9}{12}\)

Explanation:
Two equivalent fractions of 3/4
Multiply the 3/4 with 2
(3 x 2)/(4 x 2) = 6/8
Multiply the 3/4 with 3
(3 x 3)/(4 x 3) = 9/12
So, the equivalent fractions of 3/4 are 6/8 and 9/12

Tell whether the fractions are equivalent. Write = or ≠.

Question 6.
\(\frac{2}{3}\) ______ \(\frac{4}{12}\)

Answer:
\(\frac{2}{3}\) ≠ \(\frac{4}{12}\)

Explanation:
2/ 3
Multiply the numerator and denominator of 2/3 with 2
(2 x 2)/(3 x 2) = 4/6
So, 2/3 ≠ 4/12

Question 7.
\(\frac{5}{6}\) ______ \(\frac{10}{12}\)

Answer:
\(\frac{5}{6}\) =_ \(\frac{10}{12}\)

Explanation:
5/6
Multiply the 5/6 with 2
(5 x 2)/(6 x 2) = 10/12
So, 5/6 = 10/12

Question 8.
\(\frac{1}{4}\) ______ \(\frac{4}{8}\)

Answer:
\(\frac{1}{4}\) ≠ \(\frac{4}{8}\)

Explanation:
1/4
Multiply the numerator and denominator of 1/4 with 4
(1 x 4)/(4 x 4) = 4/16
So, 1/4 ≠ 4/8

Write the fraction in simplest form.

Question 9.
\(\frac{6}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}\)

Explanation:
6/8
Divide the numerator and denominator of 6/8 with 2
(6 ÷ 2)/( 8 ÷ 2) = 3/4
The simplest form of 6/8 is 3/4

Question 10.
\(\frac{25}{100}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{4}\)

Explanation:
25/100
Divide the numerator and denominator of 25/100 with 25
(25 ÷ 25)/( 100 ÷ 25) = 1/4
The simplest form of 25/100 is 1/4

Question 11.
\(\frac{8}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{4}{5}\)

Explanation:
8/10
Divide the numerator and denominator of 8/10 with 2
(8 ÷ 2)/( 10 ÷ 2) = 4/5
The simplest form of 8/10 is 4/5

Write the pair of fractions as a pair of fractions with a common denominator.

Question 12.
\(\frac{3}{10} \text { and } \frac{2}{5}\)
Type below:
_________

Answer:
\(\frac{3}{10} \text { and } \frac{4}{10}\)

Explanation:
3/ 10 and 2/5
List the multiples of 10 = 10, 20, 30, 40, 50, …
List the multiples of 5 = 5, 10, 15, 20, 25, 30, …
Common denominator of 3/10 and 2/5 = 10
Multiply the 3/10 and 2/5 with 10
(3 x 10)/(10 x 10) and (2 x 10)/(5 x 10)
3/ 10 and 4/10
Pair of fractions of 3/10 and 2/5 are 3/10 and 4/10

Question 13.
\(\frac{1}{3} \text { and } \frac{3}{4}\)
Type below:
_________

Answer:
\(\frac{3}{12} \text { and } \frac{9}{12}\)

Explanation:
1/3 and 3/4
List the multiples of 3 = 3, 6, 9, 12, 15, 18, …
List the multiples of 4 = 4, 8, 12, 16, 20, ….
The common denominator of 1/3 and 3/4 are 12
Multiply the 1/3 and 3/4 with 12
(1 x 12)/(3 x 12) and (3 x 12)/(4 x 12)
3/ 12 and 9/12.
Pair of fractions of 1/3 and 3/4 are 3/12 and 9/12

Page No. 358

Question 14.
Sam needs \(\frac{5}{6}\) cup mashed bananas and \(\frac{3}{4}\) cup mashed strawberries for a recipe. He wants to find whether he needs more bananas or more strawberries. How can he write \(\frac{5}{6}\) and \(\frac{3}{4}\) as a pair of fractions with a common denominator?
Type below:
_________

Answer:
\(\frac{10}{12}\) and \(\frac{9}{12}\)

Explanation:
Sam needs 5/6 cup mashed bananas and 3/4 cup mashed strawberries for a recipe
He wants to find whether he needs more bananas or strawberries
List the multiples of 6 = 6, 12, 18, 24, 30, 36, 42,…..
List the multiples of 4 = 4, 8, 12, 16, 20, 24, ….
The common denominator of 6 and 4 is 12
Multiply the numerator and denominator of 5/6 and 3/4 with 12
(5 x 12)/(6 x 12) and (3 x 12)/(4 x 12)
10/12 and 9/12
Pair of fractions with a common denominator for 5/6 and 3/4 are 10/12 and 9/12

Question 15.
Karen will divide her garden into equal parts. She will plant corn in \(\frac{8}{12}\) of the garden. What is the fewest number of parts she can divide her garden into?
______ parts

Answer:
\(\frac{2}{3}\) parts

Explanation:
As per the given data,
Keren will divide her garden into equal parts
She will plant corn in 8/12 of the garden
To get the least number of parts she can divide her garden, simplify the 8/12
Divide the numerator and denominator of 8/12 with 4
(8 ÷ 4)/(12 ÷ 4) = 2/3
So, Karen can divide her garden into 2/3 of parts

Question 16.
Olivia is making scarves. Each scarf will have 5 rectangles, and \(\frac{2}{5}\) of the rectangles will be purple. How many purple rectangles does she need for 3 scarves?
______ purple rectangles

Answer:
6 purple rectangles

Explanation:
As per the given data,
Olivia is making scarves
Each scarf will have 5 rectangles and 2/5 of the rectangles will be purple = 5 x 2/5 = 2
That means each scarf will have 2 purple rectangles
For 3 scarves = 3 x 2 = 6
So, she needs 6 purple rectangles.

Question 17.
Paul needs to buy \(\frac{5}{8}\) pound of peanuts. The scale at the store measures parts of a pound in sixteenths. What measure is equivalent to \(\frac{5}{8}\) pound?
\(\frac{□}{□}\) pound of peanuts

Answer:
\(\frac{10}{16}\) pound of peanuts

Explanation:
As per the given data,
Paul needs to buy 5/8 pounds of peanuts
The scale at the store measures parts of a pound in sixteenths = 16 x 5/8 = 10
To find Equivalent fraction of 5/8
Multiply the numerator and denominator of 5/8 with 2
(5 x 2)/( 8 x 2) = 10/16
So, the equivalent fraction of 5/8 is 10/16

Page No. 361

Question 1.
Compare \(\frac{2}{5}\) and \(\frac{1}{8}\). Write < or >.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 18
\(\frac{2}{5}\) _____ \(\frac{1}{8}\)

Answer:
\(\frac{2}{5}\) > \(\frac{1}{8}\)

Explanation:
Least common denominator of 5 and 8 = 40
Multiply the numerator and denominator of 2/5 and 1/8 with 40
2/ 5 = (2 x 8)/(5 x 8) = 16/40
1/8 = (1 x 5)/(8 x 5) = 5/40
The denominators are same now
So, compare the numerator to find the greater number
16/40 > 5/40
So, 2/5 > 1/8

Compare. Write < or >.

Question 2.
\(\frac{1}{2}\) _____ \(\frac{4}{6}\)

Answer:
\(\frac{1}{2}\) < \(\frac{4}{6}\)

Explanation:
1/2 and 4/6
Least common denominator of 2 and 6 = 6
Multiply the numerator and denominator of 1/2 and 4/6 with 6
1/ 2 = (1 x 6)/(2 x 6) = 6/12
4/ 6 = (4x 2)/(6 x 2) = 8/12
The denominators are same now
So, compare the numerator to find the greater number.
6/12 < 8/12
So, 1/2 < 4/6

Question 3.
\(\frac{3}{10}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{3}{10}\) > \(\frac{1}{2}\)

Explanation:
1 / 10 and 1/2
Least common denominator of 10 and 2 = 10
Multiply the numerator and denominator of 3/10 and 1/2 with 10
3/ 10 = (3 x 2)/(10 x 2) = 6/20
1/2 = (1 x 10)/(2 x 10) = 10/20
The denominators are same now
So, compare the numerator to find the greater number.
6/20 < 10/20
So, 3/10 > 1/2

Question 4.
\(\frac{11}{12}\) _____ \(\frac{4}{8}\)

Answer:
\(\frac{11}{12}\) > \(\frac{4}{8}\)

Explanation:
11/12 and 4/8
Least common denominator of 12 and 8 = 24
Multiply the numerator and denominator of 11/12 and 4/8 with 24
11/ 12 = (11 x 8)/(12 x 8) = 88/96
4/8 = (4 x 12)/(8 x 12) = 48/96
The denominators are same now
So, compare the numerator to find the greater number
88/96 > 48/96
So, 11/12 > 4/8

Question 5.
\(\frac{5}{8}\) _____ \(\frac{2}{5}\)

Answer:
\(\frac{5}{8}\) > \(\frac{2}{5}\)

Explanation:
5/ 8 and 2/5
Least common denominator of 5 and 8 = 40
Multiply the numerator and denominator of 5/8 and 2/8 with 40
5/ 8 = (5 x 5)/(8 x 5) = 25/40
2/5 = (2 x 8)/(5 x 8) = 16/40
The denominators are same now
So, compare the numerator to find the greater number
25/ 40 > 16/40
So, 5/8 > 2/5

Question 6.
\(\frac{8}{10}\) _____ \(\frac{3}{8}\)

Answer:
\(\frac{8}{10}\) > \(\frac{3}{8}\)

Explanation:
8/10 and 3/8
Least common denominator of 10 and 8 = 40
Multiply the numerator and denominator of 8/10 and 3/8 with 40
8/ 10 = (8 x 8)/(10 x 8) = 64/80
3/8 = (3 x 10)/(8 x 10) = 30/80
The denominators are same now
So, compare the numerator to find the greater number
64/80 > 30/80
So, 8/10 > 3/8

Question 7.
\(\frac{1}{3}\) _____ \(\frac{7}{12}\)

Answer:
\(\frac{1}{3}\) < \(\frac{7}{12}\)

Explanation:
1/3 and 7/12
Least common denominator of 3 and 12 = 12
Multiply the numerator and denominator of 1/3 and 7/12 with 40.
1/ 3 = (1 x 12)/(3 x 12) = 12/36
7/12 = (7 x 3)/(12 x 3) = 21/36
The denominators are same now
So, compare the numerator to find the greater number
12/36 < 21/36
So, 1/3 < 7/12

Question 8.
\(\frac{2}{6}\) _____ \(\frac{7}{8}\)

Answer:
\(\frac{2}{6}\) < \(\frac{7}{8}\)

Explanation:
2/6 and 7/8
Least common denominator of 6 and 8 = 24
Multiply the numerator and denominator of 2/6 and 7/8 with 40
2/ 6 = (2 x 8)/(6 x 8) = 16/48
7/8 = (7 x 6)/(8 x 6) = 42/48
The denominators are same now
So, compare the numerator to find the greater number
16/48<42/48
So, 2/6 < 7/8

Question 9.
\(\frac{4}{8}\) _____ \(\frac{2}{10}\)

Answer:
\(\frac{4}{8}\) > \(\frac{2}{10}\)

Explanation:
4/8 and 2/10
Least common denominator of 8 and 10 = 40
Multiply the numerator and denominator of 4/8 and 2/10 with 40
4/ 8 = (4 x 10)/(8 x 10) = 40/80
2/10 = (2 x 8)/(10 x 8) = 16/80
The denominators are same now
So, compare the numerator to find the greater number
40/80 > 16/80
So, 4/8 > 2/10

Reason Quantitatively Algebra Find a numerator that makes the statement true.

Question 10.
\(\frac{2}{4}<\frac { □ }{ 6 } \)
□ = _____

Answer:
4

Explanation:
2/4 < x/6
Least common denominator of 4 and 6 = 12
Multiply the numerator and denominator of 2/4 < x/6 with 40
2/4 = (2 x 6)/(4 x 6) = 12/24
x/6 = (x x 4)/(6 x 4) = 4 x/24
The denominators are same now
So, compare the numerator to find the greater number
12/24 < 4 X 4/24

Question 11.
\(\frac{8}{10}>\frac { □ }{ 8 } \)
□ = _____

Answer:
1

Explanation:
8/10 < x/8
Least common denominator of 10 and 8 = 40
8/10 = (8 x 4)/(10 x 4) = 32/40
x/8 = (x X 5)/(8 x 5) = 5x/40
The denominators are same now
So, compare the numerator to find the greater number
8/10 < 5x/40. X will be 1

Question 12.
\(\frac{10}{12}>\frac { □ }{ 4 } \)
□ = _____

Answer:
1

Explanation:
10/12 < x/4
Least common denominator of 12 and 4 = 12
10/12 = (10 x 1)/(12 x 1) = 10/12
x/4 = (x X 3)/(4 x 3) = 3x/12
The denominators are same now
So, compare the numerator to find the greater number
10/12 < 3/12. X will be 1.

Question 13.
\(\frac{2}{5}<\frac { □ }{ 10 } \)
□ = _____

Answer:
5

Explanation:
2/5 < x/10
Least common denominator of 5 and 10 = 10
2/5 = (2x 2)/(5 x 2) = 4/10
x/10 = (x X 1)/(10 x 1) = x/10
The denominators are same now
So, compare the numerator to find the greater number
2/5 < 5/10. X will be 5.

Question 14.
When two fractions are between 0 and \(\frac{1}{2}\), how do you know which fraction is greater? Explain.
Type below:
_______

Answer:
When two fractions are between 0 and \(\frac{1}{2}\). \(\frac{1}{2}\) is greater. As the tenths place of 5 is greater than 0. \(\frac{1}{2}\) is greater.

Question 15.
If you know that \(\frac{2}{6}<\frac{1}{2}\) and \(\frac{3}{4}<\frac{1}{2}\), what do you know about \(\frac{2}{6} \text { and } \frac{3}{4}\)?
Type below:
_______

Answer:

Explanation:
As per the given data,
2/6 < 1/2 and 3/4 < 1/2
Then, 2/6 and 3/4 is
The least common denominator of 6 and 4 is 12
(2 x 4)/(6 x 4) and (3 x 6)/(4 x 6)
8/24 and 18/24
Now, the denominators are same, then compare the numerators
8/24 > 18/24
So, 2/6 > 3/4

Question 16.
Sandra has ribbons that are \(\frac{3}{4}\) yard, \(\frac{2}{6}\) yard, \(\frac{1}{5}\) yard, and \(\frac{4}{7}\) yard long. She needs to use the ribbon longer than \(\frac{2}{3}\) yard to make a bow. Which length of ribbon could she use for the bow?
\(\frac{□}{□}\) yard

Answer:

Explanation:

Page No. 362

Question 17.
Saundra ran \(\frac{7}{12}\) of a mile. Lamar ran \(\frac{3}{4}\) of a mile. Who ran farther? Explain.
_______

Answer:
As per the given data,
Saundra ran 7/12 of a mile
Lamar ran 3/4 of a mile
The least common denominator of 7/12 and 3/4 is 12
(7x 1)/( 12 x 1) and ( 3 x 3 )/( 4 x 3)
7/12 and 9/12
So, 7/12 < 9/12
So, 7/12 < 3/4
Lamar ran greater distance than Saundra

Question 18.
What’s the Question? Selena ran farther than Manny.
Type below:
_______

Answer:
Who ran farther? Selena or Manny

Question 19.
Chloe made a small pan of ziti and a small pan of lasagna. She cut the ziti into 8 equal parts and the lasagna into 9 equal parts. Her family ate \(\frac{2}{3}\) of the lasagna. If her family ate more lasagna than ziti, what fraction of the ziti could have been eaten?
Type below:
_______

Answer:
\(\frac{1}{4}\)

Explanation:
As per the given data,
Chloe made a small pan of ziti and a small pan of lasagna
She cut the ziti into 8 equal parts and the lasagna into 9 equal parts
Her family ate 2/3 of the lasagna = (2/3) x 9 = 6 parts
If her family ate more lasagna than ziti, then that is less than 6 parts
So, 1/4 of the ziti = (1/4) x 8 = 2 parts
So, 1/4 of ziti eaten by Chloe family

Question 20.
James, Ella, and Ryan biked around Eagle Lake. James biked \(\frac{2}{10}\) of the distance in an hour. Ella biked \(\frac{4}{8}\) of the distance in an hour. Ryan biked \(\frac{2}{5}\) of the distance in an hour. Compare the distances biked by each person by matching the statements to the correct symbol. Each symbol may be used more than once or not at all.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 19
Type below:
_______

Answer:
2/10 < 4/8
1 / 8 > 2/5
2/10 < 2/5

Explanation:
As per the given data,
James, Ella, and Ryan biked around eagle lake
James biked 2/10 of the distance in an hour
Ella biked 4/8 of the distance in an hour
Ryan biked 2/5 of the distance in an hour
Least common denominator of 2 /10, 4/8, and 2/5 is 40
(2x 4)/(10 x 4), (4 x 5)/(8 x 5), and (2 x 8)/(5 x 8)
8/40, 20/ 40, and 16/ 40
8/40 < 16/40 < 20/40
2/10 < 2/5 < 4/8
So, 2/10 < 4/8
1 / 8 > 2/5
2/10 < 2/5

Common Core – Compare Fractions Using Benchmarks – Page No. 363

Compare. Write < or > .

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions Using Benchmarks img 20

Answer:
\(\frac{1}{8}\) < \(\frac{6}{10}\)

Explanation:
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions Using Benchmarks img 20

Question 2.
\(\frac{4}{12}\) _______ \(\frac{4}{6}\)

Answer:
\(\frac{4}{12}\) < \(\frac{4}{6}\)

Explanation:
4/12 and 4/6
4/12 is less than 1/2
4/6 is greater than 1/2
So, 4/12 < 4/6

Question 3.
\(\frac{2}{8}\) _______ \(\frac{1}{2}\)

Answer:
\(\frac{2}{8}\) < \(\frac{1}{2}\)

Explanation:
2/8 and 1/2
2/8 is less than 1/2
1/2 is equal to 1/2
So, 2/8 < 1/2

Question 4.
\(\frac{3}{5}\) _______ \(\frac{3}{3}\)

Answer:
\(\frac{3}{5}\) < \(\frac{3}{3}\)

Explanation:
3/5 and 3/3
3/5 is greater than 1/2
3/3 is equal to 1
So, 3/5 < 3/3

Question 5.
\(\frac{7}{8}\) _______ \(\frac{5}{10}\)

Answer:
\(\frac{7}{8}\) > \(\frac{5}{10}\)

Explanation:
7/8 and 5/10
7/8 is greater than 1/2
5/10 is equal to 1/2
So, 5/10 < 7/8

Question 6.
\(\frac{9}{12}\) _______ \(\frac{1}{3}\)

Answer:
\(\frac{9}{12}\) > \(\frac{1}{3}\)

Explanation:
9/12 and 1/3
9/ 12 is greater than 1/2
1/3 is less than 1/2
1/3 < 9/12

Question 7.
\(\frac{4}{6}\) _______ \(\frac{7}{8}\)

Answer:
\(\frac{4}{6}\) < \(\frac{7}{8}\)

Explanation:
4/6 and 7/8
4/6 is greater than 1/2
7/8 is closer to 1
So, 4/6 < 7/8

Question 8.
\(\frac{2}{4}\) _______ \(\frac{2}{3}\)

Answer:
\(\frac{2}{4}\) < \(\frac{2}{3}\)

Explanation:
2/4 and 2/3
2/4 is equal to 1/2
2/3 is greater than 1/2
So, 2/4 < 2/3

Question 9.
\(\frac{3}{5}\) _______ \(\frac{1}{4}\)

Answer:
\(\frac{3}{5}\) > \(\frac{1}{4}\)

Explanation:
3/5 and 1/4
3/5 is greater than 1/2
1/4 is less than 1/2
So, 1/4 < 3/5

Question 10.
\(\frac{6}{10}\) _______ \(\frac{2}{5}\)

Answer:
\(\frac{6}{10}\) > \(\frac{2}{5}\)

Explanation:
6/10 and 2/5
6/10 is greater than 1/2
2/5 is less than 1/2
So, 2/5 < 6/10

Question 11.
\(\frac{1}{8}\) _______ \(\frac{2}{10}\)

Answer:
\(\frac{1}{8}\) < \(\frac{2}{10}\)

Explanation:
1/8 and 2/10
1/8 is less than 1/2
2/10 is less than 1/2 but greater than 1/8
So, 1/8 < 2/10

Question 12.
\(\frac{2}{3}\) _______ \(\frac{5}{12}\)

Answer:
\(\frac{2}{3}\) > \(\frac{5}{12}\)

Explanation:
2/3 and 5/12
2/3 is greater than 1/2
5/12 is less than 1/2
So, 5/12 < 2/3

Question 13.
\(\frac{4}{5}\) _______ \(\frac{5}{6}\)

Answer:
\(\frac{4}{5}\)< \(\frac{5}{6}\)

Explanation:
4/5 and 5/6
4/5 is greater than 1/2
5/6 is greater than 1/2
Common denominator is 30
(4×6)/(5×6) and (5×5)/(6×5)
24/30 and 25/30
24/30 < 25/30
So, 4/5 < 5/6

Question 14.
\(\frac{3}{5}\) _______ \(\frac{5}{8}\)

Answer:
\(\frac{3}{5}\) < \(\frac{5}{8}\)

Explanation:
3/5 and 5/8
3/5 is greater than 1/2
5/8 is greater than 1/2
Common denominator is 40
(3×8)/(5×8) and (5×5)/(8×5)
24/40 and 25/ 40
24/40 < 25/40
3/5 < 5/8

Question 15.
\(\frac{8}{8}\) _______ \(\frac{3}{4}\)

Answer:
\(\frac{8}{8}\) > \(\frac{3}{4}\)

Explanation:
8/8 and 3/4
8/8 is equal to 1
3/4 is less than 1
3/4 < 8/8

Question 16.
Erika ran \(\frac{3}{8}\) mile. Maria ran \(\frac{3}{4}\) mile. Who ran farther?
_________

Answer:
Maria

Explanation:
As per the data,
Erika ran 3/8 mile
Maria ran 3/4 mile
Multiply the numerator and denominator of 3/4 with 2
(3×2)/(4×2) = 6/8
3/8 < 6/8
So, 3/8 < 3/4
So, Maria ran faster than Erika

Question 17.
Carlos finished \(\frac{1}{3}\) of his art project on Monday. Tyler finished \(\frac{1}{2}\) of his art project on Monday. Who finished more of his art project on Monday?
_________

Answer:
Tyler

Explanation:
From the given data,
Carlos finished 1/3 of his art project on Monday
Tyler finished ½ of his art project on Monday
1/3 is less than 1/2
1/2 is equal to 1/2
So, 1/3 < 1/2
Then, Tyler finished more of his work on Monday

Common Core – Compare Fractions Using Benchmarks – Page No. 364

Question 1.
Which symbol makes the statement true?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions Using Benchmarks img 21
Options:
a. >
b.<
c. =
d. none

Answer:
a. >

Explanation:
4/6 ? 3/8
By comparing 4/6 with 1/2, 4/6 > 1/2
By comparing 3/8 with 1/2, 3/8 < 1/2
So, 4/6 > 3/8

Question 2.
Which of the following fractions is greater than \(\frac{3}{4}\)?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{5}{6}\)
c. \(\frac{3}{8}\)
d. \(\frac{2}{3}\)

Answer:
b. \(\frac{5}{6}\)

Explanation:
From the given data,
By comparing the 3/4 with 1/2, 3/4 > 1/2
Same as above, compare the options with ½
a. 1/4 < 1/2
b. 5/6 > 1/2
c. 3/8 < 1/2
d. 2/3 > 1/2
5/6 and 2/3 are greater than the 1/2
So, compare the 5/6 with 2/3
Then, 5/6 > 2/3
So, 5/6 > 3/4

Question 3.
Abigail is putting tiles on a table top. She needs 48 tiles for each of 8 rows. Each row will have 6 white tiles. The rest of the tiles will be purple. How many purple tiles will she need?
Options:
a. 432
b. 384
c. 336
d. 48

Answer:
c. 336

Explanation:
As per the given data
Abigail is putting tiles on a table top
Number of rows = 8
She needs 48 tiles for each of row = 48×8 = 384
Number of white tiles per row = 6×8 = 48
Rest of the tiles will be purple = 384 – 48 =336
So, the total number of purple color tiles = 336

Question 4.
Each school bus going on the field trip holds 36 students and 4 adults. There are 6 filled buses on the field trip. How many people are going on the field trip?
Options:
a. 216
b. 240
c. 256
d. 360

Answer:
b. 240

Explanation:
From the given data,
Each school bus going on the field trip holds 36 students and 4 adults
There are 6 filled buses on the field trip
6 x (36 + 4) = 6 x 40 = 240
So, the total number of people on the field trip = 240

Question 5.
Noah wants to display his 72 collector’s flags. He is going to put 6 flags in each row. How many rows of flags will he have in his display?
Options:
a. 12
b. 15
c. 18
d. 21

Answer:
a. 12

Explanation:
As mentioned in the data,
Noah wants to display his 72 collector’s flag
He is going to put 6 flags in each row = 6x = 72
X = 12
So, total 12 number of rows of flags will have in his display

Question 6.
Julian wrote this number pattern on the board:
3, 10, 17, 24, 31, 38.
Which of the numbers in Julian’s pattern are composite numbers?
Options:
a. 3, 17, 31
b. 10, 24, 38
c. 10, 17, 38
d. 17, 24, 38

Answer:
b. 10, 24, 38

Explanation:
As per the given information
Julian wrote his number pattern on the board =3, 10, 17, 24, 31, 38
Factors of 3 = 1,3
Factors of 10 = 1,2,5,10
Factors of 17 = 1, 17
Factors of 24 = 1, 2, 3, 4, 6
Factors of 31 = 1, 31
Factors of 38 = 1, 2, 19, 38
So, the composite number is 10, 24, and 38, which numbers have more than 2 factors

Page No. 367

Question 1.
Compare \(\frac{2}{5}\) and \(\frac{1}{10}\).
Think: Use ______ as a common denominator.
\(\frac{2}{5}=\frac { □×□ }{ □×□ } \) = \(\frac{□}{□}\)
\(\frac{1}{10}\)
Think: 4 tenth-size parts Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 22 1 tenth-size part.
\(\frac{2}{5}\) _____ \(\frac{1}{10}\)

Answer:
\(\frac{2}{5}\) > \(\frac{1}{10}\)

Explanation:
Compare 2/5 and 1/10
Think: 10 as common denominator
Multiply the numerator and denominator of 2/5 with 2
Then, (2×2) ÷ (5×2) = 4/10
Now, compare the 4/10 with 1/10
4/10 > 1/10
So, 2/5 > 1/10

Question 2.
Compare \(\frac{6}{10}\) and \(\frac{3}{4}\).
Think: Use ______ as a common denominator.
\(\frac{6}{10}\)
\(\frac{3}{4}=\frac { □×□ }{ □×□ } \) = \(\frac{□}{□}\)
Think: A tenth-size part Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 23 an eighth-size part.
\(\frac{6}{10}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{6}{10}\) < \(\frac{3}{4}\)

Explanation:
Compare 6/10 and 3/4
Think: Use 40 as a common denominator
So, multiply the denominator and numerator of 3/4 with 10
That is, (3×10) ÷ (4×10) = 30/40
Multiply the numerator and denominator of 6/10 with 4
That is, (6×4) ÷ (10×4) = 24/40
Denominators are same, compare the numerator values of 24/40 and 30/40
So, 24/40 < 30/40
Then, 6/10 < 3/4

Compare. Write <, >, or =.

Question 3.
\(\frac{7}{8}\) _____ \(\frac{2}{8}\)

Answer:
\(\frac{7}{8}\) > \(\frac{2}{8}\)

Explanation:
Compare 7/8 and 2/8
Denominator values are same but numerator values are different
Now, compare the numerator values of 7/8 and 2/8
Then, 7/8 > 2/8

Question 4.
\(\frac{5}{12}\) _____ \(\frac{3}{6}\)

Answer:
\(\frac{5}{12}\) < \(\frac{3}{6}\)

Explanation:
Compare 5/12 and 3/6
Multiply the numerator and denominator of 3/6 with 2
(3×2) ÷ (6×2) = 6/12
So, 5/12 < 6/12

Question 5.
\(\frac{4}{10}\) _____ \(\frac{4}{6}\)

Answer:
\(\frac{4}{10}\) < \(\frac{4}{6}\)

Explanation:
Compare 4/10 and 4/6
Multiply the numerator and denominator of 4/6 with 10
(4×10) ÷ (6×10) = 40/60
Multiply the numerator and denominator of 4/10 with 6
(4×6) ÷ (10×6) = 24/60
So, 24/60 < 40/60
Then, 4/10 < 4/6

Question 6.
\(\frac{6}{12}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{6}{12}\) = \(\frac{2}{4}\)

Explanation:
Compare 6/12 and 2/4
Multiply the numerator and denominator of 2/4 with 3
(2×3) ÷ (4×3) = 6/12
So, 6/12 = 6/12
Then, 6/12 = 2/4

Question 7.
\(\frac{1}{3}\) _____ \(\frac{1}{4}\)

Answer:
\(\frac{1}{3}\) < \(\frac{1}{4}\)

Explanation:
Compare 1/3 and 1/4
Multiply the numerator and denominator of 1/3 with 4
(1×4) ÷ (3×4) = 4/12
Multiply the numerator and denominator of 1/4 with 3
(1×3) ÷ (4×3) = 3/12
So, 4/12 < 3/12
Then, 1/3 < 1/4

Question 8.
\(\frac{4}{5}\) _____ \(\frac{8}{10}\)

Answer:
\(\frac{4}{5}\) = \(\frac{8}{10}\)

Explanation:
Compare 4/5 and 8/10
Multiply the numerator and denominator of 4/5 with 2
(4×2) ÷ (5×2) = 8/10
So, 8/10 = 8/10
Then, 4/5 = 8/10

Question 9.
\(\frac{3}{4}\) _____ \(\frac{2}{6}\)

Answer:
\(\frac{3}{4}\) < \(\frac{2}{6}\)

Explanation:
Compare 3/4 and 2/6
Multiply the numerator and denominator of 3/4 with 6
(3×6) ÷ (4×6) = 18/24
Multiply the numerator and denominator of 2/6 with 4
(2×4) ÷ (6×4) = 8/24
So, 18/24 < 8/24
Then, 3/4 < 2/6

Question 10.
\(\frac{1}{2}\) _____ \(\frac{5}{8}\)

Answer:
\(\frac{1}{2}\) < \(\frac{5}{8}\)

Explanation:
Compare 1/2 and 5/8
Multiply the numerator and denominator of 1/2 with 4
(1×4) ÷ (2×4) = 4/8
So, 4/8 < 5/8
Then, 1/2 < 5/8

Reason Quantitatively Algebra Find a number that makes the statement true.

Question 11.
\(\frac{1}{2}>\frac { □ }{ 3 } \)
□ = ______

Answer:
1

Explanation:
1/2 > x/3
Multiply the numerator and denominator of 1/2 with 3
(1×3) ÷ (2×3) = 3/6
Multiply the numerator and denominator of x/3 with 2
(Xx2) ÷ (3×2) = 2x/6
3/6 > 2x/6
So, x= 1
Then, 3/6 > 2/6
1/2 > 1/3

Question 12.
\(\frac{3}{10}>\frac { □ }{ 5 } \)
□ = ______

Answer:
1

Explanation:
3/10 > x/5
Multiply the numerator and denominator of x/5 with 2
(Xx2) ÷ (5×2) =2x/10
3/10 > 2x/10
So, x=1
3/10 > 2/10
3/10 > 1/5

Question 13.
\(\frac{5}{12}>\frac { □ }{ 3 } \)
□ = ______

Answer:
1

Explanation:
5/12 > x/3
Multiply numerator and denominator of x/3 with 4
(Xx4) ÷(3×4) = 4x/12
5/12 > 4x/12
So, x = 1
Then, 5/12 > 4/12
5/12 > 1/3

Question 14.
\(\frac{2}{3}>\frac { 4 }{ □ } \)
□ = ______

Answer:

Explanation:

Question 15.
Students cut a pepperoni pizza into 12 equal slices and ate 5 slices. They cut a veggie pizza into 6 equal slices and ate 4 slices. Use fractions to compare the amounts of each pizza that were eaten.
Type below:
_________

Answer:
\(\frac{5}{12}\) < \(\frac{4}{6}\)

Explanation:
As per the given data,
Students cut a pepperoni pizza into 12 equal slices and ate 5 slices
=5/12
They cut veggie pizza into 6 equal slices and ate 4 slices = 4/6
Compare 5/12 and 4/6
Multiply the numerator and denominator of 4/6 with 2
(4×2) ÷ (6×2) = 8/12
So, 5/12 < 8/12
Then, 5/12 < 4/6

Page No. 368

Question 16.
Jerry is making a strawberry smoothie. Which measure is greatest, the amount of milk, cottage cheese, or strawberries?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 24
a. What do you need to find?
Type below:
_________

Answer:
I need to find the greatest measure from milk, cottage cheese, or strawberries

Question 16.
b. How will you find the answer?
Type below:
_________

Answer:
Equal the denominators of 3/4, 2/6, and 8/12
Multiply the numerator and denominator of 3/4 with 3
(3×3) ÷ (4×3) = 9/12
Multiply the numerator and denominator of 2/6 with 2
(2×2) ÷ (6×2) = 4/12
Compare 4/12 < 8/12 < 9/12
So, 2/6 < 8/12 <3/4

Question 16.
c. Show your work.
Type below:
_________

Answer:
2/6 < 8/12 < 3/4

Question 16.
d. Jerry needs more ________ than the other two ingredients.
________

Answer:
Jerry needs more strawberries than the other two ingredients

Question 17.
Angie, Blake, Carlos, and Daisy went running. Angie ran \(\frac{1}{3}\) mile, Blake ran \(\frac{3}{5}\) mile, Carlos ran \(\frac{7}{10}\) mile, and Daisy ran \(\frac{1}{2}\) mile. Which runner ran the shortest distance? Who ran the greatest distance?
The shortest distance: ________
The greatest distance: ________

Answer:
The shortest distance: \(\frac{1}{3}\)
The greatest distance: \(\frac{7}{10}\)

Explanation:
As per the given data,
Angie, Blake, Carlos, and Daisy went running
Angie ran 1/3 mile, Blake ran 3/5 mile, Carlos ran 7/10 mile, and Daisy ran 1/2 mile
Least common denominator of 1/3, 3/5, 7/10, and 1/2 =30
(1x 10)/(3×10), (3×6)/(5×6), (7×3)/(10×3), (1×15)/(2×15)
10/30, 18/30, 21/30, 15/30
10/30 < 15/30 < 18/30 < 21/30
1/3 < 1/2 < 3/5 < 7/10
The shortest distance ran by Angie and that is 1/ 3
The greatest distance ran by Carlos and that is 7/10

Question 18.
Elaine bought \(\frac{5}{8}\) pound of potato salad and \(\frac{4}{6}\) pound of macaroni salad for a picnic. Use the numbers to compare the amounts of potato salad and macaroni salad Elaine bought.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 25
Type below:
_________

Answer:
As per the given data,
Elaine bought 5/8 pound of potato salad and 4/6 pound of macaroni salad for a picnic
Multiply the numerator and denominator of 5/8 with 6
(5×6) / (8×6) = 30/48
Multiply the numerator and denominator of 4/6 with 8
(4×8) / (6×8) = 32/48
30/48 < 32/48
So, 5/8 < 4/6
Elaine bought more macaroni salad than potato salad

Common Core – Compare Fractions – Page No. 369

Compare. Write <, >, or =

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions img 26

Answer:
\(\frac{1}{5}\) < \(\frac{2}{10}\)

Explanation:
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare Fractions img 26

Question 2.
\(\frac{1}{5}\) _____ \(\frac{2}{10}\)

Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation:
1/5 and 2/10
Think: 10 is a common denominator
1/5 = (1×2) / (5×2) = 2/10
2/10 = 2/10
So, 1/5 = 2/10

Question 3.
\(\frac{2}{4}\) _____ \(\frac{2}{5}\)

Answer:
\(\frac{2}{4}\) > \(\frac{2}{5}\)

Explanation:
2/4 and 2/5
20 is a common denominator
2/4 = (2×5)/(4×5) = 10/20
2/5 = (2×4)/(5×4) = 8/20
10/20 > 8/20
So, 2/4 > 2/5

Question 4.
\(\frac{3}{5}\) _____ \(\frac{7}{10}\)

Answer:
\(\frac{3}{5}\) < \(\frac{7}{10}\)

Explanation:
3/5 and 7/10
10 is a common denominator
3/5 = (3×2)/(5×2) = 6/10
7/10
6/10 < 7/10
So, 3/5 < 7/10

Question 5.
\(\frac{4}{12}\) _____ \(\frac{1}{6}\)

Answer:
\(\frac{4}{12}\) > \(\frac{1}{6}\)

Explanation:
4/12 and 1/6
12 is a common denominator
4/12
1/6 = (1×2)/(6×2) = 2/12
4/12 > 2/12
So, 4/12 > 1/6

Question 6.
\(\frac{2}{6}\) _____ \(\frac{1}{3}\)

Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)

Explanation:
2/6 and 1/3
6 is a common denominator
2/6
1/3 = (1×2)/(3×2) = 2/6
So, 2/6 =2/6
So, 2/6 = 1/3

Question 7.
\(\frac{1}{3}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{1}{3}\) < \(\frac{2}{4}\)

Explanation:
1/3 and 2/4
12 is a common denominator
1/3 = (1×4)/(3×4) = 4/12
2/4 = (2×3)/(4×3) = 6/12
4/12 < 6/12
So, 1/3 < 2/4

Question 8.
\(\frac{2}{5}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{2}{5}\) < \(\frac{1}{2}\)

Explanation:
2/5 and 1/2
10 is a common denominator
2/5 = (2×2)/(5×2) = 4/10
1/2 = (1×5)/(2×5) = 5/10
4/10 < 5/10
So, 2/5 < 1/2

Question 9.
\(\frac{4}{8}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{4}{8}\) = \(\frac{2}{4}\)

Explanation:
4/8 and 2/4
8 is a common denominator
4/8
2/4 = (2×2)/(4×2) = 4/8
2/4 = 4/8
So, 4/8 = 2/4

Question 10.
\(\frac{7}{12}\) _____ \(\frac{2}{4}\)

Answer:
\(\frac{7}{12}\) < \(\frac{2}{4}\)

Explanation:
7/12 and 2/4
12 is a common denominator
7/12
2/4 = (2×3)/(4×3) = 6/12
7/12 < 6/12
So, 7/12 < 2/4

Question 11.
\(\frac{1}{8}\) _____ \(\frac{3}{4}\)

Answer:
\(\frac{1}{8}\) <  \(\frac{3}{4}\)

Explanation:
1/8 and 3/4
8 is a common denominator
1/8
3/4 = (3×2)/(4×2) = 6/8
1/8 < 6/8
So, 1/8 < 3/4

Question 12.
A recipe uses \(\frac{2}{3}\) of flour and \(\frac{5}{8}\) cup of blueberries. Is there more flour or more blueberries in the recipe?
more _____

Answer:
flour

Explanation:
From the given data,
A recipe uses 2/3 of flour and 5/8 cup of blueberries
Common denominator is 24
2/3 = (2×8)/(3×8) = 16/24
5/8 = (5×3)/(8×3) = 15/24
16/24 > 15/24
So, 2/3 > 5/8
So, flour is more in the recipe

Question 13.
Peggy completed \(\frac{5}{6}\) of the math homework and Al completed \(\frac{4}{5}\) of the math homework. Did Peggy or Al complete more of the math homework?
_________

Answer:
Peggy completed more work than Al

Explanation:
As per the given data,
Peggy completed 5/6 of the math homework
A1 completed 4/5 of the math homework
30 is a common denominator
5/6 = (5×5)/(6×5) = 25/30
4/5 = (4×6)/(5×6) =24/30
25/30 > 24/30
So, 5/6 > 4/5
So, Peggy completed more work than Al

Common Core – Compare Fractions – Page No. 370

Question 1.
Pedro fills a glass \(\frac{2}{4}\) full with orange juice. Which of the following fractions is greater than \(\frac{2}{4}\)?
Options:
a. \(\frac{3}{8}\)
b. \(\frac{4}{6}\)
c. \(\frac{5}{12}\)
d. \(\frac{1}{3}\)

Answer:
b. \(\frac{4}{6}\)

Explanation:
\(\frac{4}{6}\) > \(\frac{2}{4}\)

Question 2.
Today Ian wants to run less than \(\frac{7}{12}\) mile. Which of the following distances is less than \(\frac{7}{12}\) mile?
Options:
a. \(\frac{3}{4}\) mile
b. \(\frac{2}{3}\) mile
c. \(\frac{5}{6}\) mile
d. \(\frac{2}{4}\) mile

Answer:
d. \(\frac{2}{4}\) mile

Explanation:
\(\frac{2}{4}\) is less than \(\frac{7}{12}\)

Question 3.
Ms. Davis traveled 372,645 miles last year on business. What is the value of 6 in 372,645?
Options:
a. 6
b. 60
c. 600
d. 6,000

Answer:
c. 600

Explanation:
Ms. Davis traveled 372, 645 miles last year on business
The value of 6 in 372,645 is 600

Question 4.
One section of an auditorium has 12 rows of seats. Each row has 13 seats. What is the total number of seats in that section?
Options:
a. 25
b. 144
c. 156
d. 169

Answer:
c. 156

Explanation:
From the given information
One section of an auditorium has 12 rows of seats
Each row has 13 seats = 13×12 = 156 seats
So, the total number of seats in the auditorium = 156 seats

Question 5.
Sam has 12 black-and-white photos and 18 color photos. He wants to put the photos in equal rows so each row has either black-and-white photos only or color photos only. In how many rows can Sam arrange the photos?
Options:
a. 1, 2, 3, or 6 rows
b. 1, 3, 6, or 9 rows
c. 1, 2, or 4 rows
d. 1, 2, 3, 4, 6, or 9 rows

Answer:
a. 1, 2, 3, or 6 rows

Explanation:
As per the given information
Sam has 12 black and white photos 18 color photos
He wants to put the photos in equal rows
So each row has either black and white photos only or color photos only
H.C.F of 12 and 18 is 6
Rows of 6.
2 rows of black equal 12.
3 rows of white equals 18.

Question 6.
The teacher writes \(\frac{10}{12}\) on the board. He asks students to write the fraction in simplest form. Who writes the correct answer?
Options:
a. JoAnn writes \(\frac{10}{12}\)
b. Karen writes \(\frac{5}{12}\)
c. Lynn writes \(\frac{6}{5}\)
d. Mark writes \(\frac{5}{6}\)

Answer:
d. Mark writes \(\frac{5}{6}\)

Explanation:
As per the given data,
The teacher writes 10/12 on the board
He asks students to write the fraction in simplest form
For the simplest form of 10/12, divide the 10/12 with 2
(10÷2)/(12÷2) = 5/6
5/6 is the simplest form of 10/12
So, Mark writes the correct answer

Page No. 373

Question 1.
Locate and label points on the number line to help you write \(\frac{3}{10}, \frac{11}{12}, \text { and } \frac{5}{8}\) in order from least to greatest.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 27
Type below:
___________

Answer:
chapter 6 - compare fractions and order fractions- image1

Explanation:
3/10, 11/12, 5/8
3/10 is closer to 0
11/12 is closer to 1
5/8 is closer to 1/2
So, 3/10 < 5/8 < 11/12

Write the fraction with the greatest value.

Question 2.
\(\frac{7}{10}, \frac{1}{5}, \frac{9}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{9}{10}\)

Explanation:
7/10, 1/5, and 9/10
7/10 is closer to 1/2
1/5 is closer to 0
9/10 is closer to 1
So, 9/10 > 7/10 > 1/5
Greatest value is 9/10

Question 3.
\(\frac{5}{6}, \frac{7}{12}, \frac{7}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}\)

Explanation:
7/12 is less than 1/2
7/10 and 5/6 are greater than 1/2
Compare 5/6 and 7/12
Multiply the numerator and denominator of 5/6 with 2
(5×2)/(6×2) = 10/12 > 7/12
So, 5/6 > 7/12
Compare 5/6 and 7/10
Multiply the 5/6 with 10
(5×10)/(6×10) = 50/60
Multiply the 7/10 with 6
(7×6)/(10×6) = 42/60
So, 5/6> 7/10
So, 7/12 <7/10<5/6

Question 4.
\(\frac{2}{8}, \frac{1}{8}, \frac{2}{4}, \frac{2}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{4}\)

Explanation:
2/8, 1/8, 2/4, 2/6
Common denominator of 4,6,8 = 24
(2×3)/(8×3), (1×3)/(8×3), (2×6)/(4×6), (2×4)/(6×4)
6/24, 3/24, 12/24, 8/24
Compare the numerator values
12/24 > 8/24 > 6/24 > 3/24
So, 2/4 > 2/6 > 2/8 >1/8

Write the fractions in order from least to greatest.

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{8}, \frac{3}{6}, \frac{1}{4}\)

Explanation:
1/4, 3/6, 1/8
1/ 4 is closer to 1/2
3/6 is equal to 1/2
1/8 is closer to 0
So, 1/8 < 3/6 < 1/4

Question 6.
\(\frac{3}{5}, \frac{2}{3}, \frac{3}{10}, \frac{4}{5}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{4}{5}, \frac{3}{10}, \frac{3}{5}, \frac{2}{3}\)

Explanation:
3/5, 2/3, 3/10, 4/5
3/5 is closer to 1/2
2/3 is greater than 1/2
3/10 is less than 1/2
4/5 is closer to 0
So, 4/5 < 3/10 < 3/5 < 2/3

Question 7.
\(\frac{3}{4}, \frac{7}{12}, \frac{5}{12}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{5}{12}, \frac{7}{12}, \frac{3}{4}\)

Explanation:
3/4, 7/12, 5/12
3/ 4 is closer to 1
7/12 is greater than 1/2
5/ 12 is closer to 1/2
So, 5/12 < 7/12 < 3/4

Write the fractions in order from least to greatest.

Question 8.
\(\frac{2}{5}, \frac{1}{3}, \frac{5}{6}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{3}, \frac{2}{5}, \frac{5}{6}\)

Explanation:
2/5, 1/3, 5/6
2/5 is closer to 1/2
1/3 is closer to 0
5/6 is closer to 1
So, 1/3 < 2/5 < 5/6

Question 9.
\(\frac{4}{8}, \frac{5}{12}, \frac{1}{6}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{1}{6}, \frac{5}{12}, \frac{4}{8}\)

Explanation:
4/8, 5/12, 1/6
4/8 is equal to1/2
5/12 is closer to 1/2
1/6 is closer to 0
So, 1/6 < 5/12 < 4/ 8

Question 10.
\(\frac{7}{100}, \frac{9}{10}, \frac{4}{5}\)
\(\frac{□}{□}\)
Type below:
________

Answer:
\(\frac{7}{100}, \frac{4}{5}, \frac{9}{10}\)

Explanation:
7/100, 9/10, 4/5
7/100 is closer to 0
9/10 is closer to 1
4/5 is greater than 1/2
So, 7/100 < 4/5 < 9/10

Reason Quantitatively Algebra Write a numerator that makes the statement true.

Question 11.
\(\frac{1}{2}<\frac { □ }{ 10 } <\frac{4}{5}\)
□ = _____

Answer:
6 or 7

Explanation:
1/2 < x/10 < 4/5
Common denominator is 10
(1×5)/(2×5) < x/10 < (4×2)/(5×2)
5/10 < x/10 < 8/10
Then, x = 6 or 7

Question 12.
\(\frac{1}{4}<\frac{5}{12}<\frac { □ }{ 6 } \)
□ = _____

Answer:
6

Explanation:
1/4 < 5/12 < x/6
Common denominator is 24
(1×6)/(4×6) < (5×2)/(12×2) < 4x/(6×4)
6/24 < 10/24 < 4x/24
If x = 6, then 4x = 24
So, 6/24 < 10/24 < 24/24

Question 13.
\(\frac { □ }{ 8 } <\frac{3}{4}<\frac{7}{8}\)
□ = _____

Answer:
1,2,3,4,5

Explanation:
x/8 < 3/4 < 7/8
Common denominator is 8
x/8 < (3×2)/(4×2) < 7/8
x/8 < 6/8 < 7/8
so x = 1,2,3,4,5

Page No. 374

Question 14.
Nancy, Lionel, and Mavis ran in a 5-kilometer race. The table shows their finish times. In what order did Nancy, Lionel, and Mavis finish the race?
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 28
a. What do you need to find?

Answer:
In which Nancy, Lionel, and Mavis finished the race?

Question 14.
b. What information do you need to solve the problem?
Type below:
_________

Answer:
the amount of time it took each runner to finish the race

Question 14.
c. What information is not necessary?
Type below:
_________

Answer:
the distance of the race

Question 14.
d. How will you solve the problem?
Type below:
_________

Answer:
By using the running race time of Nancy, Lionel, and Mavis

Question 14.
e. Show the steps to solve the problem.
Type below:
_________

Answer:
Common denominator of 2/3, 7/12, 3/4 is 12
(2×4)/(3×4), (7/12), (3×3)/(4×3)
8/12, 7/12, 9/12
7/12 < 8/12 < 9/12
7/12 < 2/3 < 3/4
Lionel < Nancy < Mavis

Question 14.
f. Complete the sentences.
The runner who finished first is _______.
The runner who finished second is _______.
The runner who finished third is _______.
The first: _______
The second: _______
The third: _______

Answer:
Lionel finished the race first
Nancy finished the race second
Mavis finished the race third
Lionel
Nancy
Mavis

Common Core – Compare and Order Fractions – Page No. 375

Write the fractions in order from least to greatest.

Question 1.
\(\frac{5}{8}, \frac{2}{12}, \frac{8}{10}\)
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare and Order Fractions img 29

Answer:
\(\frac{2}{12}, \frac{5}{8}, \frac{8}{10}\)

Explanation:
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison Common Core Compare and Order Fractions img 29

Question 2.
\(\frac{1}{5}, \frac{2}{3}, \frac{5}{8}\)
Type below:
_________

Answer:
\(\frac{1}{5}, \frac{5}{8}, \frac{2}{3}\)

Explanation:
chapter 6 - compare fractions and order fractions- image4
1/5, 2/3, 5/8
1/5 is closer to 0
2/3 is greater than 1/2
5/8 greater than 1/2
1/5 < 5/8 < 2/3

Question 3.
\(\frac{1}{2}, \frac{2}{5}, \frac{6}{10}\)
Type below:
_________

Answer:
\(\frac{2}{5}, \frac{1}{2}, \frac{6}{10}\)

Explanation:
chapter 6 - compare fractions and order fractions- image5
1/2, 2/5, 6/10
1/2 is equal to 1/2
2/5 is less than 1/2
6/10 is greater than 1/2

Question 4.
\(\frac{4}{6}, \frac{7}{12}, \frac{5}{10}\)
Type below:
_________

Answer:
\(\frac{5}{10}\) < \(\frac{7}{12}\) < \(\frac{4}{6}\)

Explanation:
chapter 6 - compare fractions and order fractions- image6
4/6, 7/12, 5/10
4/6 is closer to 1
7/12 is greater than 1/2
5/10 is equal to 1/2

Question 5.
\(\frac{1}{4}, \frac{3}{6}, \frac{1}{8}\)
Type below:
_________

Answer:
\(\frac{1}{8}\) < \(\frac{1}{4}\) < \(\frac{3}{6}\)

Explanation:
chapter 6 - compare fractions and order fractions- image7
1/4, 3/6, 1/8
1/4 is less than 1/2
3/6 is equal to 1/2
1/8 is closer to 0

Question 6.
\(\frac{1}{8}, \frac{3}{6}, \frac{7}{12}\)
Type below:
_________

Answer:
\(\frac{1}{8}\) < \(\frac{7}{12}\) < \(\frac{3}{6}\)

Explanation:
chapter 6 - compare fractions and order fractions- image8
1/8, 3/6, 7/12
1/8 is closer to 0
3/6 is equal to 1/2
7/12 is greater than 1/2

Question 7.
\(\frac{8}{100}, \frac{3}{5}, \frac{7}{10}\)
Type below:
_________

Answer:
\(\frac{8}{100}\) < \(\frac{3}{5}\) < \(\frac{7}{10}\)

Explanation:
chapter 6 - compare fractions and order fractions- image9
8/100, 3/5, 7/10
8/100 is closer to 0
3/5 is greater than 1/2
7/10 is closer to 1

Question 8.
\(\frac{3}{4}, \frac{7}{8}, \frac{1}{5}\)
Type below:
_________

Answer:
\(\frac{1}{5}\) < \(\frac{3}{4}\) < \(\frac{7}{8}\)

Explanation:
chapter 6 - compare fractions and order fractions- image10
3/4, 7/8, 1/5
3/4 is greater than 1/2
7/8 is closer to 1
1/5 is closer to 0

Question 9.
Amy’s math notebook weighs \(\frac{1}{2}\) pound, her science notebook weighs \(\frac{7}{8}\) pound, and her history notebook weighs \(\frac{3}{4}\) pound. What are the weights in order from lightest to heaviest?
Type below:
_________

Answer:
\(\frac{1}{2}\) pound, \(\frac{3}{4}\) pound, \(\frac{7}{8}\) pound

Explanation:
From the given data,
Amy’s math notebook weighs 1/2 pound
Science notebook weighs 7/8 pound
History notebook weighs 3/4 pound
7/8 is closer to 1
3/4 is greater than 1/2
1/2 < 3/4 < 7/8
So, Amy’s math notebook weight < history notebook weight < science notebook

Question 10.
Carl has three picture frames. The thicknesses of the frames are \(\frac{4}{5}\) inch, \(\frac{3}{12}\) inch, and \(\frac{5}{6}\) inch. What are the thicknesses in order from least to greatest?
Type below:
_________

Answer:
\(\frac{3}{12}\) inch, \(\frac{4}{5}\) inch, \(\frac{5}{6}\) inch

Explanation:
As per the given data,
Carl has three picture frames
The thickness of the frames are 4/5 inch, 3/12 inch, 5/6 inch
4/5 is greater than 1/2
3/12 is less than 1/2
5/6 is closer to 1
3/12 < 4/5 < 5/6

Common Core – Compare and Order Fractions – Page No. 376

Question 1.
Juan’s three math quizzes this week took him \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, and \(\frac{1}{5}\) hour to complete. Which list shows the lengths of time in order from least to greatest?
Options:
a. \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour, \(\frac{1}{5}\) hour
b. \(\frac{1}{5}\) hour, \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour
c. \(\frac{1}{3}\) hour, \(\frac{1}{5}\) hour, \(\frac{4}{6}\) hour
d. \(\frac{4}{6}\) hour, \(\frac{1}{3}\) hour, \(\frac{1}{5}\) hour

Answer:
b. \(\frac{1}{5}\) hour, \(\frac{1}{3}\) hour, \(\frac{4}{6}\) hour

Explanation:
From the given information
Juan’s three math quizzes this week took him 1/3 hour, 4/6 hour, and 1/5 hour
Compare 1/3 and 1/2
1/3 is less than 1/2
4/6 is greater than 1/2
1/5 is closer to 0
1/5 < 1/3 < 4/6
So, Juan’s math quizzes times from least to greatest is 1/5, 1/3, 4/6

Question 2.
On three days last week, Maria ran \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, and \(\frac{3}{5}\) mile. What are the distances in order from least to greatest?
Options:
a. \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile, \(\frac{3}{5}\) mile
b. \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile
c. \(\frac{7}{8}\) mile, \(\frac{3}{4}\) mile, \(\frac{3}{5}\) mile
d. \(\frac{7}{8}\) mile, \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile

Answer:
b. \(\frac{3}{5}\) mile, \(\frac{3}{4}\) mile, \(\frac{7}{8}\) mile

Explanation:
As per the information
On three days last week, Maria ran 3/4 mile, 7/8 mile, and 3/5 mile
3/4 is greater than 1/2
7/8 is closer to 1
3/5 is greater than 1/2
Compare 3/5 and 3/4
3/4 is greater than 3/5
So, 3/5 < 3/4 < 7/8
Distance from least to greatest is 3/5, 3/4 , 7/8

Question 3.
Santiago collects 435 cents in nickels. How many nickels does he collect?
Options:
a. 58
b. 78
c. 85
d. 87

Answer:
d. 87

Explanation:
As per the given data,
Santiago collects 435 cents in nickels
1 nickel worth is 5 cents
Then, nickels per 435 cents = 435/5 = 87
So, Santiago collects 87 nickels

Question 4.
Lisa has three classes that each last 50 minutes. What is the total number of minutes the three classes last?
Options:
a. 15 minutes
b. 150 minutes
c. 153 minutes
d. 156 minutes

Answer:
b. 150 minutes

Explanation:
From the given data,
Lisa has three classes that each last 50 minutes
The total number of minutes the three classes last = 3×50 =150 minutes

Question 5.
Some students were asked to write a composite number. Which student did NOT write a composite number?
Options:
a. Alicia wrote 2.
b. Bob wrote 9.
c. Arianna wrote 15.
d. Daniel wrote 21.

Answer:
a. Alicia wrote 2.

Explanation:
As per the information
Some students were asked to write a composite number
a. Alicia wrote 2
Factors of 2 is 1 and 2
b. Bob wrote 9
Factors of 9 is 1, 3, 9
c. Arianna wrote 15
Factors of 15 is 1, 3, 5, 15
d. Daniel wrote 21
Factors of 21 is 1,3,7,21
So, Alicia did not write a composite number

Question 6.
Mrs. Carmel serves \(\frac{6}{8}\) of a loaf of bread with dinner. Which fraction is equivalent to \(\frac{6}{8}\)?
Options:
a. \(\frac{2}{4}\)
b. \(\frac{9}{16}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer:
d. \(\frac{3}{4}\)

Explanation:
As per the given information
Mrs. Carmel serves 6/8 of a loaf of bread with dinner
To find the equivalent fraction of 6/8, simplify the 6/8 by dividing with the 2
(6÷2)/(8÷2) = ¾
So, the equivalent fraction of 6/8 is 3/4

Page No. 377

Question 1.
For numbers 1a–1d, tell whether the fractions are equivalent by selecting the correct symbol.
a. \(\frac{4}{16}\) _____ \(\frac{1}{4}\)

Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)

Explanation:
4/16 and 1/4
Divide the numerator and denominator of 4/16 with 4
(4÷4)/(16÷4) = 1/4
So, 4/16 = 1/4

Question 1.
b. \(\frac{3}{5}\) _____ \(\frac{12}{15}\)

Answer:
\(\frac{3}{5}\) ≠ \(\frac{12}{15}\)

Explanation:
3/5 and 12/15
Multiply the numerator and denominator of 3/5 with 3
(3×3)/(5×3) = 9/15
So, 3/5 ≠ 12/15

Question 1.
c. \(\frac{5}{6}\) _____ \(\frac{25}{30}\)

Answer:
\(\frac{5}{6}\) = \(\frac{25}{30}\)

Explanation:
c. 5/6 and 25/30
Multiply the numerator and denominator of 5/6 with 5
(5×5)/(6×5) = 25/30
So, 5/6 = 25/30

Question 1.
d. \(\frac{6}{10}\) _____ \(\frac{5}{8}\)

Answer:
\(\frac{6}{10}\) ≠ \(\frac{5}{8}\)

Explanation:
6/10 and 5/8
Divide the numerator and denominator of 6/10 with 2
(6÷2)/(10÷2) = 3/5
6/10 ≠5/8

Question 2.
Juan’s mother gave him a recipe for trail mix.
\(\frac{3}{4}\) cup cereal \(\frac{2}{3}\) cup almonds
\(\frac{1}{4}\) cup peanuts \(\frac{1}{2}\) cup raisins
Order the ingredients used in the recipe from least to greatest.
Type below:
_________

Answer:
As per the given data,
Juan’s mother gave him a recipe for trail mix
3/4 cup cereal and 2/3 cup almonds
1/4 cup peanuts and 1/2 cup raisins
3/4 is closer to 1
2/3 is greater than 1/2
1/4 is less than 1/2
1/2 is equal to 1/2
So, 1/4 < 1/2 <2/3 < 3/4
So, Jaun’s mother gave him a recipe for trail mix in order
1/4 cup of peanuts < 1/2 cup of raisins < 2/3 cup almonds < 3/4 cup of cereals

Question 3.
Taylor cuts \(\frac{1}{5}\) sheet of construction paper for an arts and crafts project. Write \(\frac{1}{5}\) as an equivalent fraction with the denominators shown.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 30
Type below:
_________

Answer:
From the given data,
Taylor cuts 1/5 sheet of construction paper for an arts and crafts project
So, the equivalent fractions of 1/5
Multiply the numerator and denominator of 1/5 with 2
(1×2)/(5×2) = 2/10
Multiply the numerator and denominator of 1/5 with 3
(1×3)/(5×3) = 3/15
Multiply the numerator and denominator of 1/5 with 5
(1×5)/(5×5) = 5/25
Multiply the numerator and denominator of 1/5 with 8
(1×8)/(5×8) = 8/40
So, the equivalent fractions of 1/5 are 2/10, 3/15, 5/25, 8/40

Question 4.
A mechanic has sockets with the sizes shown below. Write each fraction in the correct box.
\(\frac{7}{8} in. \frac{3}{16} in. \frac{1}{4} in. \frac{3}{8} in. \frac{4}{8} in. \frac{11}{16} in.\)
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 31
Type below:
_________

Answer:
chapter 6 - compare fractions and order fractions- image11

Explanation:
As per the given data,
A mechanic has sockets with the sizes 7/8 inch, 3/16 inch, 1/4 inch, 3/8 inch, 4/8 inch, 11/16 inch
7/8 is greater than 1/2
3/16 is less than 1/2
1/4 is less than 1/2
3/8 is less than 1/2
4/8 is equal to 1/2
11/16 is greater than 1/2

Page No. 378

Question 5.
Darcy bought \(\frac{1}{2}\) pound of cheese and \(\frac{3}{4}\) pound of hamburger for a barbecue. Use the numbers to compare the amounts of cheese and hamburger Darcy bought.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 32

Answer:
grade 4 chapter 6 image 3

Explanation:
From the given data,
Darcy bought 1/2 pound of cheese and 3/4 pound of hamburger for a barbecue
3/4 is greater than 1/2

Question 6.
Brad is practicing the piano. He spends \(\frac{1}{4}\) hour practicing scales and \(\frac{1}{3}\) hour practicing the song for his recital. For numbers 6a–6c, select Yes or No to tell whether each of the following is a true statement.
a. 12 is a common denominator of \(\frac{1}{4}\) and \(\frac{1}{3}\).
i. yes
ii. no

Answer:
i. yes

Explanation:
12 is a common denominator of 1/3 and 1/4

Question 6.
b. The amount of time spent practicing scales can be rewritten as \(\frac{3}{12}\).
i. yes
ii. no

Answer:
i. yes

Explanation:
b. The amount of time spent practicing scales can be rewritten as 3/12
Multiply the numerator and denominator of 1/4 with 3
(1×3)/(4×3) = 3/12
Yes, amount of time spent practicing scales can be rewritten as 3/12

Question 6.
c. The amount of time spent practicing the song for the recital can be rewritten as \(\frac{6}{12}\).
i. yes
ii. no

Answer:
ii. no

Explanation:
c. The amount of time spent practicing the song for the recital can be rewritten as 6/12
The amount of time spent practicing for the song for his recital = 1/3
Multiply the numerator and denominator of 1/3 with 4
(1×4)/(3×4) = 4/12
No, time spent practicing the song for the recital can not be written as 6/12

Question 7.
In the school chorus, \(\frac{4}{24}\) of the students are fourth graders. In simplest form, what fraction of the students in the school chorus are fourth graders?
\(\frac{□}{□}\)

Answer:
\(\frac{1}{6}\)

Explanation:
As per the given information,
In the school chorus,
4/24 of the students are fourth graders
For the simplest form of 4/24
Divide the numerator and denominator of 4/24 with 4
(4÷4)/(24÷4) =1/6
The simplest form of 4/24 is 1/6

Question 8.
Which pairs of fractions are equivalent? Mark all that apply.
a. \(\frac{8}{12} \text { and } \frac{2}{3}\)
b. \(\frac{3}{4} \text { and } \frac{20}{24}\)
c. \(\frac{4}{5} \text { and } \frac{12}{16}\)
d. \(\frac{7}{10} \text { and } \frac{21}{30}\)

Answer:
a. \(\frac{8}{12} \text { and } \frac{2}{3}\)

Explanation:
a. 8/12 and 2/3
Multiply the numerator and denominator of 2/3 with 4
(2×4)/(3×4) = 8/12
So, 8/12 = 2/3
b. 3/4 and 20/24
Multiply the numerator and denominator of 3/4 with 6
(3×6)/(4×6) = 18/24
c. 4/5 and 12/16
4/5 ≠ 12/16
d. 7/10 and 21/30
Multiply the numerator and denominator of 7/10 with 3
(7×3)/(10×3) =21/30
So, 7/10 = 21/30

Question 9.
Sam worked on his science fair project for \(\frac{1}{4}\) hour on Friday and \(\frac{1}{2}\) hour on Saturday. What are four common denominators for the fractions? Explain your reasoning.

Answer:
From the given data,
Sam worked on his science fair project for 1/4 hour on Friday and 1/2 hour on Saturday
4,8,12,16 are all common denominators because they all multiples of 2 and 4

Page No. 379

Question 10.
Morita works in a florist shop and makes flower arrangements. She puts 10 flowers in each vase, and \(\frac{2}{10}\) of the flowers are daisies.
Part A
If Morita makes 4 arrangements, how many daisies does she need? Show how you can check your answer.
_____ daisies

Answer:
8 daisies

Explanation:
If Morita makes 4 arrangements, 4 X 2 = 8.

Question 10.
Part B
Last weekend, Morita used 10 daisies to make flower arrangements. How many flowers other than daisies did she use to make the arrangements? Explain your reasoning.
_____ other flowers

Answer:
40 other flowers

Explanation:
If she used 10 daises, she must have made 5 arrangements. In each vase, she put \(\frac{2}{10}\) of the flowers are daisies. So, remaining flowers for each vase = 10 – 2 = 8. If she made 5 arrangements, 8 X 5 = 40 other flowers.

Question 11.
In Mary’s homeroom, \(\frac{10}{28}\) of the students have a cat, \(\frac{6}{12}\) have a dog, and \(\frac{2}{14}\) have a pet bird. For numbers 11a–11c, select True or False for each statement.
a. In simplest form, \(\frac{5}{14}\) of the students have a cat.
i. True
ii. False

Answer:
i. True

Explanation:
In simplest form 5/14 of the students have a cat
From the above, 10/28 of the students have a cat
Divide the numerator and denominator of 10/28 with 2
(10÷2)/(28÷2) = 5/14
True

Question 11.
b. In simplest form, \(\frac{2}{4}\) of the students have a dog.
i. True
ii. False

Answer:
i. True

Explanation:
In simplest form, 2/4 of the students have a dog
From the above, 6/12 of the students have a dog
Divide the 6/12 with 3
(6 = 2/4
True

Question 11.
c. In simplest form, \(\frac{1}{7}\) of the students have a pet bird.
i. True
ii. False

Answer:
i. True

Explanation:
In the simplest form, 1/7 of the students have a pet bird
From the data, 2/14 of the students have a pet bird
Divide the numerator and denominator of 2/14 with 2
(2÷2)/(14÷2) = 1/7
True

Page No. 380

Question 12.
Regina, Courtney, and Ellen hiked around Bear Pond. Regina hiked \(\frac{7}{10}\) of the distance in an hour. Courtney hiked \(\frac{3}{6}\) of the distance in an hour. Ellen hiked 38 of the distance in an hour. Compare the distances hiked by each person by matching the statements to the correct symbol. Each symbol may be used more
than once or not at all.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 33
Type below:
_________

Answer:
chapter 6 - compare fractions and order fractions- image13

Explanation:
From the given information
Regina, Courtney, and Ellen hiked around Bear Pond
Regina hiked 7/10 of the distance in an hour
Courtney hiked 3/6 of the distance in an hour
Ellen hiked 3 /8 of the distance in an hour
Compare 7/10 and 3/6
The common denominator of 7/10 and 3/6 is 30
(7×3)/(10×3) and (3×5)/(6×5)
21/30 and 15/30
So, 21/30 > 15/30
So, 7/10 > 15/30
Compare 3/8 and 3/6
The common denominator of 3/8 and 3/6 is 24
(3×3)/(8×3) and (3×4)/(6×4)
9/24 and 12/24 = 9/24 < 12/24 = 3/8 < 3/6
Compare 7/10 and 3/8
The common denominator of 7/10 and 3/8 is 40
(7×4)/(10×4) and (3×5)/(8×5)
28/40 >15/40 = 7/10 > 3/8

Question 13.
Ramon is having some friends over after a baseball game. Ramon’s job is to make a vegetable dip. The ingredients for the recipe are given.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 34
Part A
Which ingredient does Ramon use the greater amount of, buttermilk or cream cheese? Explain how you found your answer.
Type below:
_________

Answer:
Ramon use 5/8 cup of buttermilk and 1/2 cup cream cheese
By comparing these two ingredients
The common denominator of 5/8 and 1/2 are 8
(1×4)/(2×4) =4/8
So, 5/8 > 4/8
So, 5/8 cup buttermilk is > ½ cup cream cheese

Question 13.
Part B
Ramon says that he needs the same amount of two different ingredients. Is he correct? Support your answer with information from the problem.
______

Answer:
Ramon says that he needs the same amount of two ingredients
Yes, Ramon uses 3/4 cup parsley and 6/8 cup scallions
Multiply the 3/4 with 2
(3×2)/(4×2) = 6/8
So, Ramon uses the same amount that is 3/4 cup for parsley and scallions

Page No. 381

Question 14.
Sandy is ordering bread rolls for her party. She wants \(\frac{3}{5}\) of the rolls to be whole wheat. What other fractions can represent the part of the rolls that will be whole wheat? Shade the models to show your work.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 35
Type below:
_________

Answer:
chapter 6 - compare fractions and order fractions- image15

Explanation:
As per the information,
Sandy is ordering bread rolls for her party
She wants 3/5 of the rolls to be whole wheat
For an equivalent fraction of 3/5, multiply with 5
(3×5)/(5×5) = 15/25
Again multiply the 15/25 with 4
(15×4)/(25×4) = 60/100

Question 15.
Angel has \(\frac{4}{8}\) yard of ribbon and Lynn has \(\frac{3}{4}\) yard of ribbon. Do Angel and Lynn have the same amount of ribbon? Shade the model to show how you found your answer. Explain your reasoning.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 36
Type below:
_________

Answer:
grade 4 chapter 6 image 4
Angel and Lynn didn’t have the same amount of ribbon. 4/8 is a greater fraction compared to 3/4. So, Angel’s ribbon is long compared to Lynn’s ribbon.

Question 16.
Ella used \(\frac{1}{4}\) yard of red ribbon. Fill in each box with a number from the list to show equivalent fractions for \(\frac{1}{4}\). Not all numbers will be used.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 37
Type below:
_________

Answer:
grade 4 chapter 6 image 3

Explanation:
1/4 = 2/8 = 4/16 = 3/12

Page No. 382

Question 17.
Frank has two same-size rectangles divided into the same number of equal parts. One rectangle has \(\frac{3}{4}\) of the parts shaded, and the other has \(\frac{1}{3}\) of the parts shaded.
Part A
Into how many parts could each rectangle be divided? Show your work by drawing the parts of each rectangle.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 38
_____ parts

Answer:
grade 4 chapter 6 image 2
12 parts

Question 17.
Part B
Is there more than one possible answer to Part A? If so, did you find the least number of parts into which both rectangles could be divided? Explain your reasoning.
Type below:
_________

Answer:
Yes, as long it is a multiple of 12.
And yes,12 is the least in order to have 1 rectangle have 3/4 shaded and the other 1/3 shaded.

Question 18.
Suki rode her bike \(\frac{4}{5}\) mile. Claire rode her bike \(\frac{1}{3}\) mile. They want to compare how far they each rode their bikes using the benchmark \(\frac{1}{2}\). For numbers 18a–18c, select the correct answers to describe how to solve the problem.
a. Compare Suki’s distance to the benchmark:
\(\frac{4}{5}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{4}{5}\) ≠ \(\frac{1}{2}\)

Explanation:
The fraction \(\frac{4}{5}\) is not equal to \(\frac{1}{2}\).

Question 18.
b. Compare Claire’s distance to the benchmark:
\(\frac{1}{3}\) _____ \(\frac{1}{2}\)

Answer:
\(\frac{1}{3}\) ≠ \(\frac{1}{2}\)

Explanation:
The fraction \(\frac{1}{3}\) is not equal to \(\frac{1}{2}\)

Question 18.
c. Suki rode her bike _____ Claire.

Answer:
Suki rode her bike faster than Claire.

Page No. 387

Use the model to write an equation.

Question 1.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 39
Type below:
_________

Answer:
\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)

Question 2.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 40
Type below:
_________

Answer:
\(\frac{2}{3}\) – \(\frac{1}{3}\) = \(\frac{1}{3}\)

Question 3.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 41
Type below:
_________

Answer:
\(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\)

Question 4.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 42
Type below:
_________

Answer:
1 – \(\frac{5}{8}\) = \(\frac{8}{8}\) – \(\frac{5}{8}\) = \(\frac{3}{8}\)

Use the model to solve the equation.

Question 5.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 43
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer:
\(\frac{2}{4}\)

Question 6.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 44
\(\frac{5}{6}+\frac{1}{6}\) = \(\frac{□}{□}\)

Answer:
\(\frac{6}{6}\) = 1

Question 7.
Reason Abstractly Sean has \(\frac{1}{5}\) of a cupcake and \(\frac{1}{5}\) of a large cake.
a. Are the wholes the same? Explain.
______

Answer:
Yes; From the given information, the fraction of the cupcake and large cake are the same.

Explanation:

Question 7.
Does the sum \(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\) make sense in this situation? Explain.
______

Answer:
Yes; it makes sense. From the given data, 1 part is out of 5 parts. So, adding two fractions (1 part is out of 5 parts), the complete fraction becomes 2/5.

Question 8.
Carrie’s dance class learned \(\frac{1}{5}\) of a new dance on Monday, and \(\frac{2}{5}\) of the dance on Tuesday. What fraction of the dance is left for the class to learn on Wednesday?
\(\frac{□}{□}\)

Answer:
\(\frac{3}{5}\)

Explanation:
The fraction of left for the class to learn on Wednesday is \(\frac{3}{5}\).

Page No. 388

Question 9.
Samantha and Kim used different models to help find \(\frac{1}{3}+\frac{1}{6}\). Whose model makes sense? Whose model is nonsense? Explain your reasoning below each model.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 45

Answer:
Both Samantha and Kim’s statements make sense. Because both models have an equal number of fractions for each diagram.

Question 10.
Draw a model you could use to add \(\frac{1}{4}+\frac{1}{2}\).
Type below:
___________

Answer:
grade 4 chapter 6 image 1

Question 11.
Cindy has two jars of paint. One jar is \(\frac{3}{8}\) full. The other jar is \(\frac{2}{8}\) full. Use the fractions to write an equation that shows the amount of paint Cindy has.
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 46
Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison img 47
Type below:
___________

Answer:
\(\frac{3}{8}+\frac{2}{8}\) = \(\frac{5}{8}\)

Conclusion:

By downloading the Go Math Grade 4 Answer Key Chapter 6 Fraction Equivalence and Comparison PDF, students of grade 4 will aid you to understand different topics in Chapter 6 easily. Prepare well with the help of Go Math Grade 4 Answer Key PDFand solve each and every question properly. For more help utilize this Go Math Grade 4 Solution Key Chapter 6 Fraction Equivalence and Comparison PDF and gain what you require.

Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test

go-math-grade-4-chapter-13-algebra-perimeter-and-area-review-test-answer-key

Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test support students to improve their subject knowledge on the perimeter and area of the different shapes & gain maths skills. The answers provided in this chapter are designed by the math experts. Go ahead and download the Go Math Grade 4 Answer key pdf, to find out the Perimeter and Area of the rectangle, square, and etc. concepts easily.

Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test

Go Math Solution Key of grade 4 chapter 13 will provide perfect solutions in a step-by-step manner with a clear explanation of every question. Go Math taught explicitly about Perimeter and Area of different Shapes with the help of images, indicating images with arrows, and numbers. So, make use of this pdf formatted lesson-wise Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra: Perimeter and Area Review/Test & check your solutions within no time.

Chapter: 13 – Review/Test 

Review/Test – Page No. 519

Choose the best term from the box.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 1

Question 1.
The number of square units needed to cover a flat surface is the ______________.
_________

Answer: Area
The number of square units needed to cover a flat surface is the area.

Question 2.
The distance around a shape is the ____________.
_________

Answer: Perimeter
The distance around a shape is the Perimeter.

Find the area of the rectangle or combined rectangles.

Question 3.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 2
A = _____ square feet

Answer: 112 square feet

Explanation:
Given,
length = 14 ft
Width = 8 ft
Area of the rectangle = l × w
A = 14 ft × 8 ft
A = 112 square feet
Thus the area of the rectangle for the above figure is 112 square feet.

Question 4.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 3
A = _____ square centimeters

Answer: 65 square cm.

Explanation:
Figure 1:
S = 3 cm
Area of the square = s × s
A = 3 cm × 3 cm
A = 9 square cm
Figure 2:
b = 11 cm
h = 4 cm
Area of the rectangle = b × h
A = 11 cm × 4 cm
A = 44 square cm
Figure 3:
b = 2 cm
h = 6 cm
Area of the rectangle = b × h
A = 2 cm × 6 cm
A = 12 square cm
Area of the composite figure is 9 sq. cm + 44 sq. cm + 12 sq. cm = 65 square cm.

Find the unknown measure of the rectangle.

Question 5.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 4
A = _____ square yards

Answer: 136 square yard

Explanation:
Figure 1:
b = 12 yd
h = 8 yd
Area of the rectangle = b × h
A = 12 yd × 8 yd
A = 96 square yard.
Figure 2:
b = 16 yd
h = 1 yd
Area of the rectangle = b × h
A = 16 yd × 1 yd
A = 16 square yard.
Figure 3:
b = 4 yd
h = 6 yd
Area of the rectangle = b × h
A = 4 yd × 6 yd
A = 24 square yard.
The area of the composite figure is 96 square yard + 16 square yard + 24 square yard = 136 square yard.

Question 6.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 5
Perimeter = 60 meters
width = _____ m

Answer: 12 m

Explanation:
Given,
Perimeter = 60 meters
length = 18 m
width = _____ m
The perimeter of the rectangle = l + w + l + w
P = 2l + 2w
60 m = 2 × 18 m + 2w
60 m – 36 m = 2w
2w = 24
w = 24/2
w = 12 meters
Thus the width of the above rectangle is 12 meters.

Question 7.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 6
Area = 91 square feet
height = _____ feet

Answer: 13 ft

Explanation:
Given,
Area = 91 square feet
base = 7 ft
height = _____ feet
Area of the rectangle = b × h
91 sq ft = 7 ft × h
h = 91/7
h = 13 ft
Thus the height of the above rectangle is 13 ft.

Question 8.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 7
Area = 60 square inches
base = _____ in.

Answer: 10 inches

Explanation:
Given,
Area = 60 square inches
height = 6 in
base = _____ in.
Area of the rectangle = b × h
60 square inches = b × 6 in
b = 60/6
b = 10 inches
Thus the base of the above rectangle is 10 inches.

Question 9.
What is the perimeter of a rectangle with a length of 13 feet and a width of 9 feet?
P = _____ ft

Answer: 44 ft

Explanation:
Given,
l = 13 ft
w = 9 ft
The perimeter of the rectangle = l + w + l + w
P = 13 ft + 9 ft + 13 ft + 9 ft
P = 44 ft
Thus the perimeter of the rectangle is 44 ft.

Review/Test – Page No. 520

Fill in the bubble completely to show your answer.

Question 10.
Which pair of shapes has the same area?
Options:
a.Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 8
b. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 9
c. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 10
d. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 11

Answer: Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 10

Explanation:
a. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 8
4 × 2 = 8
3 × 3 = 9
8 ≠ 9
b. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 9
4 × 4 = 16
3 × 5 = 15
16 ≠ 15
c. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 10
3 × 4 = 12
2 × 6 = 12
12 = 12
Thus the correct answer is option c.

Question 11.
Jamie’s mom wants to enlarge her rectangular garden by adding a new rectangular section. The garden is now 96 square yards. What will the total area of the garden be after she adds the new section?
Options:
a. 84 square yards
b. 96 square yards
c. 180 square yards
d. 192 square yards

Answer: 192 square yards

Explanation:
Given that,
Jamie’s mom wants to enlarge her rectangular garden by adding a new rectangular section. The garden is now 96 square yards.
Add 96 square yards to the rectangular garden.
96 square yards + 96 square yards = 192 square yards
Thus the correct answer is option d.

Question 12.
A rectangular yoga studio has an area of 153 square feet. The width of the studio is 9 feet. What is the length of the studio?
lenght = _____ ft

Answer: 17 ft

Explanation:
Given,
A rectangular yoga studio has an area of 153 square feet.
The width of the studio is 9 feet.
Area of the rectangle = l × w
153 square feet = l × 9 ft
l = 153/9
l = 17 ft
Therefore the length of the studio is 17 feet.

Review/Test – Page No. 521

Fill in the bubble completely to show your answer.

Question 13.
Mr. Patterson had a rectangular deck with an area of 112 square feet built in his backyard. Which could be a diagram of Mr. Patterson’s deck?
Options:
a. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 12
b. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 13
c. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 14
d. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 15

Answer: c. Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 14

Explanation:
Given,
Mr. Patterson had a rectangular deck with an area of 112 square feet built in his backyard.
Area of the rectangle = l × w
A = 28 ft × 4 ft
A = 112 square feet
Thus the correct answer is option c.

Question 14.
The town indoor pool is in a rectangular building. Marco is laying tile around the rectangular pool. How many square meters of tile will Marco need?
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 16
Options:
a. 96 square meters
b. 252 square meters
c. 572 square meters
d. 892 square meters

Answer: 252 square meters

Explanation:
The outer rectangle is
l = 26 m
w = 22 m
Area of the rectangle = l × w
A = 26 m × 22 m
A = 572 square meters
The inner rectangle is
l = 20 m
w = 16 m
Area of the rectangle = l × w
A = 20 m × 16 m
A = 320 square meters
Thus the square meters of tile will Marco need is 572 – 320 = 252 square meters.

Review/Test – Page No. 522

Question 15.
A drawing of a high school pool is shown below.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 17
What is the area of the pool? Explain how you know.
_______ square yards

Answer:

Explanation:
Figure 1:
l = 10 yd
w = 15 yd
Area of the rectangle = l × w
A = 10 yd × 15 yd
A = 150 square yard
Figure 2:
l = 15 yd
w = 10 yd
Area of the rectangle = l × w
A = 15 yd × 10 yd
A = 150 square yard
Figure 3:
l = 10 yd
w = 5 yd
Area of the rectangle = l × w
A = 10 yd × 5 yd
A = 50 square yard
Area of the pool = 150 square yard + 150 square yard + 50 square yard = 350 square yard

Question 16.
Mr. Brown has 24 meters of fencing. He wants to build a rectangular pen for his rabbits.
Go Math Grade 4 Answer Key Homework FL Chapter 13 Algebra Perimeter and Area Review Test img 18
A. Draw two different rectangles that Mr. Brown could build. Use only whole numbers for the lengths of the sides of each rectangle. Label the length of each side.
Type below:
_________

Answer:
Go Math Grade 4 Answer Key Chapter 13 Review Test img-2

Question 16.
B. Find the area in square meters of each rabbit pen you made in Part A. Show your work.
Type below:
_________

Answer: 20 square meters

Explanation:
l = 10m
w = 2m
Area of the rectangle = l × w
A = 10 m × 2 m
A = 20 square meters
Therefore the area in square meters of each rabbit pen is 20 square meters.

Question 16.
C. If you were Mr. Brown, which of the two pens above would you construct for your rabbits? Explain why.
Type below:
_________

Answer: I would construct the second figure for the two rabbit pens.

Conclusion:

Once you go through the Go Math Grade 4 Review Test Solutions of ch 13, then students can immediately discover the perimeter and area of shapes. Stay Connected with us to get the Go Math Grade 4 Answer Key Chapter 13 Algebra: Perimeter and Area along with Go Math Grade 4 Answer Key Homework Practice FL Chapter 13 Algebra: Perimeter and Area pdf.

Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

go-math-grade-6-chapter-9-independent-and-dependent-variables-answer-key

Download Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables pdf for free of cost. It is very important for the students to learn the fundamentals at the secondary level. In order to help you guys, we are providing the answers to all the questions in HMH Go Math Grade 6 Chapter 9 Solution Key Independent and Dependent Variables.

Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

The Independent and Dependent Variables chapter consists of the topics like equations and tables, analyze relationships, graphs etc. It is essential for students to know the relationship between the graphs and tables in this chapter. You can know different methods of solving the problems by using Go Math Grade 6 Solution Key Chapter 9 Independent and Dependent Variables. All you have to do is to tap the below-given links.

Lesson 1: Independent and Dependent Variables

Lesson 2: Equations and Tables

Lesson 3: Problem Solving • Analyze Relationships

Mid-Chapter Checkpoint

Lesson 4: Graph Relationships

Lesson 5: Equations and Graphs

Chapter 9 Review/Test

Share and Show – Page No. 493

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 1.
An online store lets customers have their name printed on any item they buy. The total cost c in dollars is the price of the item p in dollars plus $3.99 for the name.
Type below:
________________

Answer: c = p + $3.99

Explanation:
The independent variable is c, the price of the item because it is not going to depend on anything else.
The dependent variable is p because the total cost depends on how many items there are, whether your name is marked on it, etc.
The equation would be:
c = p + $3.99

Question 2.
A raft travels downriver at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rate times the number of hours h.
Type below:
________________

Answer: d = 6 × h

Explanation:
Speed of the raft= 6 miles per hour
Total distance (d) of the raft = rate × number of hours h
The dependent variable is the number of hours h
The independent variable is distance d.
The equation would be:
d = 6 × h

Question 3.
Apples are on sale for $1.99 a pound. Sheila buys p pounds of apples for a total cost of c dollars.
Type below:
________________

Answer: c = p × $1.99

Explanation:
Apples are on sale for $1.99 a pound
p = pounds of apples
c = total cost of dollars
The equation would be:
c = p × $1.99
c is the independent variable.
p is the dependent variable.

On Your Own

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 4.
Sean can make 8 paper birds in an hour. The total number of birds b is equal to the number of birds he makes per hour times the number of hours h.
Type below:
________________

Answer: b = 8h

Explanation:
Given that,
Sean can make 8 paper birds in an hour.
The total number of birds b is equal to the number of birds he makes per hour times the number of hours h.
b = number of birds
h = number of hours
The equation would be:
b = 8 × h
b is the independent variable.
h is the dependent variable.

Question 5.
Billy has $25. His father is going to give him more money. The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.
Type below:
________________

Answer: t = m + $25

Explanation:
Billy has $25. His father is going to give him more money.
The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.
The equation would be:
t = m + $25
t is the independent variable
m is the dependent variable.

Question 6.
Connect Symbols and Words Describe a situation that can be represented by the equation c = 12b.
Type below:
________________

Answer:
Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the cost of the necklace c.
The equation is c = 12n

Question 7.
Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling. Write an equation and use it to find how much it will cost Belinda to buy 12 glasses.
Type below:
________________

Answer:
Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling.
The equation is: c = 4.25n + 9.95
Now we have to find the cost of 12 glasses.
c = 4.25(12) + 9.95
c = 60.95
It takes $60.95 to buy 12 glasses.

Unlock the Problem – Page No. 494

Question 8.
Benji decides to save $15 per week to buy a computer program. Write an equation that models the total amount t in dollars Benji will have saved in w weeks.
a. What does the variable t represent?
Type below:
________________

Answer: t represents the total amount in dollars Banji saved.

Question 8.
b. Which is the dependent variable? Which is the independent variable? How do you know?
Type below:
________________

Answer:
w is the dependent variable.
t is the independent variable.
w is dependent because it represents the number of weeks. So, we have to multiply 15 with w.
t is an independent variable because t determines the value of dependent variable.

Question 8.
c. How can you find the total amount saved in w weeks?
Type below:
________________

Answer: We can find the total amount saved in w weeks by multiplying 15 with w.

Question 8.
d. Write an equation for the total amount that Benji will have saved.
Type below:
________________

Answer: t = 15w

Question 9.
Coach Diaz is buying hats for the baseball team. The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it. Write an equation that can be used to find the cost of the hats.
Type below:
________________

Answer: c = n + 2h

Explanation:
Coach Diaz is buying hats for the baseball team.
The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it.
c represents the total cost.
n is the number of hats
h is the price per hat.
The equation is c is equal to the number of hats plus price per hat and $2.
c = n + 2h

Question 10.
A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot. The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable. Choose the letter or equation that makes each sentence true.
The independent variable is ______________ .
The dependent variable is ______________ .
The equation that represents the relationship between the variables is ______________ .

Answer:
A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot.
The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable.
The equation would be:
w = 0.2f
f is the dependent variable
w is the dependent variable.

Independent and Dependent Variables – Page No. 495

Identify the independent and dependent variables. Then write an equation to represent the relationship between them.

Question 1.
Sandra has a coupon to save $3 off her next purchase at a restaurant. The cost of her meal c will be the price of the food p that she orders, minus $3.
Type below:
________________

Answer: c = p – 3

Explanation:
Given,
Sandra has a coupon to save $3 off her next purchase at a restaurant.
The cost of her meal c will be the price of the food p that she orders, minus $3.
c is the independent variable
p is the dependent variable
The equation would be:
c = p – 3

Question 2.
An online clothing store charges $6 for shipping, no matter the price of the items. The total cost c in dollars is the price of the items ordered p plus $6 for shipping.
Type below:
________________

Answer: c = p + 6

Explanation:
Given,
An online clothing store charges $6 for shipping, no matter the price of the items.
The total cost c in dollars is the price of the items ordered p plus $6 for shipping.
The equation would be:
c = p + $6
where c = cost in dollars
p is the price of items
The independent variable is c.
The dependent variable is p

Question 3.
Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the number of necklaces n.
Type below:
________________

Answer: b = 12n

Explanation:
Melinda is making necklaces. She uses 12 beads for each necklace.
The total number of beads b depends on the number of necklaces n.
b = total number of beads
n = number of necklaces
The equation would be:
b = 12n
b is the independent variable
n is the dependent variable.

Problem Solving

Question 4.
Maria earns $45 for every lawn that she mows. Her earnings e in dollars depend on the number of lawns n that she mows. Write an equation that represents this situation.
Type below:
________________

Answer: e = 45n

Explanation:
Maria earns $45 for every lawn that she mows.
Her earnings e in dollars depend on the number of lawns n that she mows.
e = earnings in dollars
n = number of lawns
The equation would be:
e = 45n
e is the independent variable.
n is the dependent variable.

Question 5.
Martin sells cars. He earns $100 per day, plus any commission on his sales. His daily salary s in dollars depends on the amount of commission c. Write an equation to represent his daily salary.
Type below:
________________

Answer: s = 100 + c

Explanation:
Martin sells cars. He earns $100 per day, plus any commission on his sales. His daily salary s in dollars depends on the amount of commission c.
c = amount of commission
s = salary in dollars
The equation would be:
s = 100 + c
s is the independent variable.
c is the dependent variable.

Question 6.
Write a situation in which one unknown is dependent on another unknown. Write an equation for your situation and identify the dependent and independent variables.
Type below:
________________

Answer:
Byron is playing a game. He earns 10 points for each question he answers correctly. His total score s equals the number of correct answers a time a.
Answer:
Dependent variable: s
Independent variable: a
Equation: s = 10a

Lesson Check – Page No. 496

Question 1.
There are 12 boys in a math class. The total number of students s depends on the number of girls in the class g. Write an equation that represents this situation.
Type below:
________________

Answer: s = 12 + g

Explanation:
There are 12 boys in a math class.
The total number of students s depends on the number of girls in class g.
The equation would be:
s = 12 + g
s is the independent variable.
g is the dependent variable.

Question 2.
A store received a shipment of soup cans. The clerk put an equal number of cans on each of 4 shelves. Write an equation to represent the relationship between the total number of cans t and the number of cans on each shelf n.
Type below:
________________

Answer: n = t ÷ 4

Explanation:
A store received a shipment of soup cans. The clerk put an equal number of cans on each of 4 shelves.
t = number of cans.
n = number of cans on each shelf.
The equation would be:
n = t ÷ 4
n is the independent variable.
t is the dependent variable.

Spiral Review

Question 3.
The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees. Gwen measured a Celsius temperature of 35 degrees. What is this temperature in degrees Fahrenheit?
______ °F

Answer: 95 degrees

Explanation:
The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees.
C = 35
F = 9C ÷ 5 + 32
F = 9(35) ÷ 5 + 32
F = 315 ÷ 5 + 32
F = 63 + 32
F = 95 degrees

Question 4.
Write an equation to represent this sentence. The difference of a number n and 1.8 is 2.
Type below:
________________

Answer: n – 1.8 = 2

Explanation:
The difference of a number n and 1.8 is 2.
The phrase difference is nothing but subtraction.
The equation would be:
n – 1.8 = 2

Question 5.
Drew drank 4 cups of orange juice. This is \(\frac{2}{5}\) of the total amount of juice that was in the container. Solve \(\frac{2}{5}\)x = 4 to find the number of cups x of juice in the container. How much juice was in the container?
______ cups

Answer: 10 cups

Explanation:
Drew drank 4 cups of orange juice. This is \(\frac{2}{5}\) of the total amount of juice that was in the container.
\(\frac{2}{5}\)x = 4
2 × x = 4 × 5
2x = 20
x = 20/2
x = 10
Thus there are 10 cups of juice in the container.

Question 6.
Graph x ≤ 4.5 on a number line.
Type below:
________________

Answer:
GO Math Grade 6 Chapter 9 answer key img-1

Share and Show – Page No. 499

Use the equation to complete the table.

Question 1.
y = x + 3
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 1
Type below:
________________

Answer:
Substitute the value of x in the above equation.
The equation is x + 3.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-1

Question 2.
y = 2x + 1
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 2
Type below:
________________

Answer:
Substitute the value of x in the above equation.
The equation is y = 2x + 1
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-2

On Your Own

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 3.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 3
Type below:
________________

Answer:
The equation is y = 2x
The output is multiple of 2 and x
For x = 10
The output is y = 2x
y = 2 × 10 = 20

Question 4.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 4
Type below:
________________

Answer:
y = x ÷ 2
The output is the quotient of x and 2.
The output for x = 40 is
y = 40 ÷ 2
y = 20

Question 5.
The table shows the current cost of buying apps for a cell phone. Next month, the price of each app will double. Write an equation you can use to find the total cost y of buying x apps next month.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 5
Type below:
________________

Answer: y = 3x

Explanation:
The equation is multiple of 3 and x.
The equation is y = 3x

Question 6.
A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle. The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours. Use numbers and words to explain how to find the cost c of renting a bicycle for 6 hours.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 6
Type below:
________________

Answer:
A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle.
The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours.
For x = 1
c = 1.50(1) + 4.50
c = 1.50 + 4.50
c = $6.00
For x = 2
c = 1.50(2) + 4.50
c = 3.00 + 4.50
c = $7.50
For x = 3
c = 1.50(3) + 4.50
c = 4.50 + 4.50
c = $9.00
For x = 4
c = 1.50(4) + 4.50
c = 6.00 + 4.50
c = $10.50

</aCause and Effect – Page No. 500

The reading skill cause and effect can help you understand how a change in one variable may cause a change in another variable.

In karate, a person’s skill level is often shown by the color of his or her belt. At Sara’s karate school, students must pass a test to move from one belt level to the next. Each test costs $23. Sara hopes to move up 3 belt levels this year. How will this affect her karate expenses?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 7

Question 7.
Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.
Type below:
________________

Answer: y = 23x

Explanation:
Let x represent the number of belt levels Sara moves up and let y represent the increase in dollars in her karate expenses.
Write the equation:
y = 23x
Sara plans to move up 3 levels, so replace x with 3
y = 23 × 3
y = 69
So, if Sara moves up 3 belt levels this year, her karate expenses will increase by $69.

Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.

Question 8.
Classes at Tony’s karate school cost $29.50 per month. This year he plans to take 2 more months of classes than he did last year. How will this affect Tony’s karate expenses?
Type below:
________________

Answer:
The equation is y = 29.50x
where x is the number of additional classes
y is the increase in dollars in expenses.
Tony plans to take 2 more months of classes so his expenses will increase by y = 29.5 × 2 = $59

Question 9.
Write an Equation A sporting goods store regularly sells karate uniforms for $35.90 each. The store is putting karate uniforms on sale for 10% off. How will this affect the price of a karate uniform?
Type below:
________________

Answer:
The equation is y = 35.90x
where x is the percent of the discount and y is the decrease in dollars in the sales price.
For a 10% discount the price will decrease by y = 35.90 × 0.01 = $3.59

Equations and Tables – Page No. 501

Use the equation to complete the table.

Question 1.
y = 6x
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 8
Type below:
________________

Answer:
The equation is y = 6x
Substitute the value of x in the above equation.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-8

Question 2.
y = x − 7
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 9
Type below:
________________

Answer:
The equation is y = x – 7
Substitute the value of x in the equation.
Use the equation to get the output y.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-9

Question 3.
y = 3x + 4
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 10
Type below:
________________

Answer:
The equation is y = 3x + 4
Substitute the value of x in the above equation.
Use the equation to get the output y.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-10 (1)

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 4.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 11
Type below:
________________

Answer: y = 8x

Explanation:
The equation is the multiple of 8.
The equation is y = 8x
Substitute x = 3 in the equation.
y = 8(3) = 24
Thus the unknown value is 24.

Question 5.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 12
Type below:
________________

Answer: y = x ÷ 2

Explanation:
The equation is divisible by 2.
The equation is y = x ÷ 2
Substitute x = 22 in the equation.
y = x ÷ 2
y = 22 ÷ 2
y = 11
Therefore the unknown value is 11.

Problem Solving

Question 6.
Tickets to a play cost $11 each. There is also a service charge of $4 per order. Write an equation for the relationship that gives the total cost y in dollars for an order of x tickets.
Type below:
________________

Answer: 11x + 4

Explanation:
Given,
Tickets to a play cost $11 each.
There is also a service charge of $4 per order.
y represents the total cost in dollars.
x represents the order of tickets.
The equation is y = 11x + 4

Question 7.
Write an equation for the relationship shown in the table. Then use the equation to find the estimated number of shrimp in a 5-pound bag.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 13
Type below:
________________

Answer: y = 24x

Explanation:
The equation is the multiple of 24.
The equation is y = 24x

Question 8.
Write a word problem that can be represented by a table and equation. Solve your problem and include the table and equation.
Type below:
________________

Answer:
Susie ran a race. She ran 5 miles an hour and the race took her x hours to complete.
y = 5x
Use the equation to get the output y.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-10

Lesson Check – Page No. 502

Question 1.
Write an equation that represents the relationship shown in the table.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 14
Type below:
________________

Answer: y = x – 4

Explanation:
The relationship between x and y is y = x – 4.
We get the output when we subtract 4 from x.

Question 2.
There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18. Write an equation for the relationship that gives the total cost y in dollars of joining the gym and using it for x months.
Type below:
________________

Answer: y = 18x + 27

Explanation:
Given,
There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18.
Here y represents the total coast in dollars of joining the gym.
x represents months.
So, the equation would be: y = 18x + 27

Spiral Review

Question 3.
Mindy wants to buy several books that each cost $10. She has a coupon for $6 off her total cost. Write an expression to represent her total cost in dollars for b books.
Type below:
________________

Answer: 10b – 6

Explanation:
Given,
Mindy wants to buy several books that each cost $10.
She has a coupon for $6 off her total cost.
b represents the total cost in dollars for b books.
So, the equation to represent the total cost is 10b – 6.

Question 4.
When a coupon of $1.25 off is used, the cost of a taco meal is $4.85. The equation p – 1.25 = 4.85 can be used to find the regular price p in dollars of a taco meal. How much does a regular taco meal cost?
$ _______

Answer: 6.10

Explanation:
Given,
When a coupon of $1.25 off is used, the cost of a taco meal is $4.85.
The equation is p – 1.25 = 4.85
p = 4.85 + 1.25
p = 6.10
Therefore the taco meal cost $6.10.

Question 5.
Which of the following are solutions to the inequality n > 7?
n = 7 n = 6.9 n = 7.2 n = 6\(\frac{1}{2}\)
Type below:
________________

Answer: n = -7

Explanation:
Substitute the value of n in the inequality.
n > 7
n = -7
-7 > -7
Thus -7 is the solution.
n = 6.9
-6.9 > -7
-6.9 is not the solution.
n = 7.2
-7.2 > -7
-7.2 is less than – 7
Thus -7.2 is not the solution.
n = 6\(\frac{1}{2}\)
6\(\frac{1}{2}\) > -7
6\(\frac{1}{2}\) is not the solution.

Question 6.
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies. He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation.
Type below:
________________

Answer: p = d – 5.50

Explanation:
Marcus sold brownies at a bake sale. He sold d dollars worth of brownies.
He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings.
p represents the total profit in dollars.
d is the dollars worth of brownies.
The equation is p = d – 5.50

Share and Show – Page No. 505

Question 1.
A soccer coach is ordering shirts for the players. The table shows the total cost based on the number of shirts ordered. How much will it cost the coach to order 18 shirts?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 15
$ _______

Answer: 270

Explanation:
First, find a pattern and write an equation.
The cost is $15 multiplied by the number of shirts.
c = $15 × n
Next, use the equation to find the cost of 18 shirts.
c = $15 × n
c = $15 × 18
c = $270
So, the cost of 18 shirts is $270.

Question 2.
What if the coach spent $375 to purchase a number of shirts? Could you use the same equation to find how many shirts the coach bought? Explain.
Type below:
________________

Answer:
Yes, I could use the same equation.
I could substitute 375 for the variable c and solve for n.

Question 3.
The table shows the number of miles the Carter family drove over time. If the pattern continues, will the Carter family have driven more than 400 miles in 8 hours? Explain.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 16
Type below:
________________

Answer: 376 miles

Explanation:
First, find a pattern and write an equation.
The distance is 47 miles multiplied by the number of hours.
y = 47 × x
Next, use the equations to find the distance for 8 hours.
y = 47x
y = 47 × 8
y = 376
So, the family will have driven 376 miles in 8 hours, which is less than 400 miles.

Question 4.
Look for a Pattern The Carter family drove a total of 564 miles. Describe how to use the pattern in the table to find the number of hours they spent driving.
Type below:
________________

Answer: 12 hours

Explanation:
The equation is y = 47x
Next, use the equation to find the number of hours for 564 miles.
564 = 47 × x
x = 564/47
x = 12
So, the Carter family spent 12 hours driving for 564 miles.

On Your Own – Page No. 506

Question 5.
A group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June. If the pattern continues, how many hours will they practice in November?
_______ hours

Answer: 36 hours

Explanation:
Given that, a group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June.
The equation would be h = 4m
m = 9
h = 4 × 9 = 36
Thus the group practiced 36 hours in the month of November.

Question 6.
The table shows the number of hours Jacob worked and the amount he earned each day.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 17
At the end of the week, he used his earnings to buy a new pair of skis. He had $218 left over. How much did the skis cost?
$ _______

Answer: 142

Explanation:
First, add the total amount he earned.
60 + 84 + 72 + 96 + 48 = 360
Jacob earned $360 for the week.
If he has $218 leftover, this means that the cost of the skis is 360 – 218 = 14
Therefore the cost of the skis is $142.

Question 7.
Pose a Problem Look back at Problem 6. Use the data in the table to write a new problem in which you could use the strategy to find a pattern. Then solve the problem.
Type below:
________________

Answer:
How much money would Jacob earn if he worked for 10 hours?
From the table, we can see that the pattern is that Jacob earns $12 per hour.
The equation is s = 12h
Where s is the total pay and h is the number of hours worked.
s = 12h
s = 12 × 10
s = 120
Thus Jacob earned $120 for 10 hours.

Question 8.
Draw Conclusions Marlon rode his bicycle 9 miles the first week, 18 miles the second week, and 27 miles the third week. If the pattern continues, will Marlon ride exactly 100 miles in a week at some point? Explain how you determined your answer.
Type below:
________________

Answer: No, Marlon will not ride exactly 100 miles in a week at some point.
Each number in the pattern is a multiple of 9 and 100 is not a multiple of 9.

Question 9.
A diving instructor ordered snorkels. The table shows the cost based on the number of snorkels ordered.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 18
If the diving instructor spent $1,024, how many snorkels did he order? Use numbers and words to explain your answer.
_______ snorkels

Answer: 32

Explanation:
Use the table to find the equation.
c represents the cost based on the number of snorkels.
s represents the number of snorkels
The equation would be:
c = 32s
The diving instructor spent $1,024
c = 1024
1024 = 32s
s = 1024/32
s = 32
Thus the diving instructor gets 32 snorkels for $1024.

Problem Solving Analyze Relationships – Page No. 507

The table shows the number of cups of yogurt needed to make different amounts of a fruit smoothie. Use the table for 1–3.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 19

Question 1.
Write an equation to represent the relationship.
Type below:
________________

Answer: c = 3b

Explanation:
c represents number of cups of yogurt
b represents the batches
From the table, we can observe that b is multiplied with 3 to get cups of yogurt.
So, the equation to find the number of cups of yogurt is c = 3b

Question 2.
How much yogurt is needed for 9 batches of smoothie?
_______ cups

Answer: 27

Explanation:
Given that there are 9 batches of smoothie.
By using the above equation we can find the number of cups.
c = 3b
c = 3 × 9 = 27 cups
Thus 27 cups of yogurt is need to make 9 batches of smoothie.

Question 3.
Jerry used 33 cups of yogurt to make smoothies. How many batches did he make?
_______ batches

Answer: 11 batches

Explanation:
Jerry used 33 cups of yogurt to make smoothies.
Use the equation to find the batches.
c = 3b
33 = 3b
b = 33/3
b = 11
Therefore jerry made 11 batches of smoothie.

The table shows the relationship between Winn’s age and his sister’s age. Use the table for 4–5.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 20

Question 4.
Write an equation to represent the relationship.
Type below:
________________

Answer: s = w + 4

Explanation:
By using the table we can find the relationship between wine’s age and wine’s sister’s age.
Winn’s sister’s age will be the sum of Winn’s age and 4.
So, the equation is s = w + 4

Question 5.
When Winn is 14 years old, how old will his sister be?
_______ years old

Answer: 18

Explanation:
Use the equation s = w + 4
W = 14 years
s = 14 + 4
s = 18 years
Thus winn’s sister’s age is 18 years.

Question 6.
Write a problem for the table. Use a pattern and an equation to solve your problem.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 21
Type below:
________________

Answer: m = 16h

Explanation:
Jerry runs 16 miles per hour. How many miles he can run in 5 hours?
The equation is m = 16h
m = 16 × 5 = 80 miles
Therefore jerry runs 80 miles in 5 hours.

Lesson Check – Page No. 508

Question 1.
The table shows the total cost c in dollars of n gift baskets. What will be the cost of 9 gift baskets?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 22

Answer: $108

Explanation:
By seeing the above we can say that the equation is
c = 12n
n = 9
Use the equation to find the cost of 9 gift baskets.
c = 12 × 9
c = $108
Thus the cost of 9 gift baskets is $108.

Question 2.
The table shows the number of minutes m that Tara has practiced after d days. If Tara has practiced for 70 minutes, how many days has she practiced?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 23
_______ days

Answer: 2 days

Explanation:
The table shows the number of minutes m that Tara has practiced after d days.
The equation would be
m = 35d
If Tara has practiced for 70 minutes
m = 70
Use the equation to find the number of days she practiced.
70 = 35d
d = 70/35
d = 2 days
Thus Tara has practiced 2 days.

Spiral Review

Question 3.
Soccer shirts cost $15 each, and soccer shorts cost $18 each. The expression 15n + 18n represents the total cost in dollars of n uniforms. Simplify the expression by combining like terms.
Type below:
________________

Answer: 33n

Explanation:
Soccer shirts cost $15 each, and soccer shorts cost $18 each.
The expression 15n + 18n represents the total cost in dollars of n uniforms.
Now combine the like terms.
15n + 18n = 33n

Question 4.
What is an equation that represents the relationship in the table?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 24
Type below:
________________

Answer: y = x ÷ 2

Explanation:
By seeing the above table we can find the relationship between x and y.
y is the quotient of x and 2.
We get the value of y when you divide x by 2.
The equation is y = x ÷ 2

Question 5.
The lowest price of an MP3 of a song in an online store is $0.99. Write an inequality that represents the price p in dollars of any MP3 in the store.
Type below:
________________

Answer:
The lowest price of an MP3 of a song in an online store is $0.99.
p represents the price in dollars.
The inequality is p ≥ 0.99.

Question 6.
Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to Marisol’s ratio.
Type below:
________________

Answer: 9:2

Explanation:
Given that, Marisol plans to make 9 mini-sandwiches for every 2 people attending her party.
The ratio will be 9:2
Now we need to write the equivalent ratio for the 9 sandwiches for every 2 people i.e, 9:2
We know that the equivalent ratio can be written as
9/2 × 3/3 = 27/6
9/2 × 5/5 = 45/6
Thus the equivalent fractions are 27/6 and 45/6.

Mid-Chapter Checkpoint – Vocabulary – Page No. 509

Choose the best term from the box to complete the sentence.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 25

Question 1.
A(n) _____ has a value that determines the value of another quantity.
Type below:
________________

Answer: Independent variable
An Independent variable has a value that determines the value of another quantity.

Question 2.
A variable whose value is determined by the value of another quantity is called a(n) _____.
Type below:
________________

Answer: Dependent variable
A variable whose value is determined by the value of another quantity is called a Dependent variable.

Concepts and Skills

Identify the independent and dependent variables.

Question 3.
Marco spends a total of d dollars on postage to mail party invitations to each of g guests.
Type below:
________________

Answer:
dependent variable: d
independent variable: g

Question 4.
Sophie has a doll collection with 36 dolls. She decides to sell s dolls to a museum and has r dolls remaining.
Type below:
________________

Answer:
dependent variable: r
independent variable: s

Write an equation for the relationship shown in the table. Then find the unknown value in the table.

Question 5.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 26
Type below:
________________

Answer: 49

Explanation:
The equation is y = 7x
x = 7
y = 7 × 7 = 49
Thus the unknown value y is 49.

Question 6.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 27
Type below:
________________

Answer: 12

Explanation:
The equation for the above table is
y = x ÷ 5
Use the equation to find the value of y where x = 60
y = 60 ÷ 5
y = 12
Thus the unknown value is 12.

Write an equation that describes the pattern shown in the table.

Question 7.
The table shows how the number of pepperoni slices used depends on the number of pizzas made.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 28
Type below:
_______________

Answer: y = 17x

Explanation:
The table shows how the number of pepperoni slices used depends on the number of pizzas made.
y is 17 times of x.
The equation for the above table is y = 17x

Question 8.
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 29
Type below:
________________

Answer: m = w + 5

Explanation:
Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.
m is equal to the sum of w and 5.
Thus the equation is m = w + 5.

Page No. 510

Question 9.
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band. Write an equation that models how many marching band members m there are if there are c concert band members.
Type below:
________________

Answer: m = 152 – c

Explanation:
Given,
The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band.
m is equal to the difference of 152 and c.
The equation is m = 152 – c

Question 10.
A coach is ordering baseball jerseys from a website. The jerseys cost $15 each, and shipping is $8 per order. Write an equation that can be used to determine the total cost y, in dollars, for x jerseys.
Type below:
________________

Answer: y = 15x + 8

Explanation:
A coach is ordering baseball jerseys from a website.
The jerseys cost $15 each, and shipping is $8 per order.
y is equal to 15 times x plus 8
The equation is y = 15x + 8.

Question 11.
Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
_______ hours

Answer: 28 hours

Explanation:
Amy volunteers at an animal shelter.
She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June.
As she started working from the march. December will be the 10th month.
Keep on adding 2 hours for each month you get 28 hours for December.
Thus she worked 28 hours in December.

Question 12.
Aaron wants to buy a new snowboard. The table shows the amount that he has saved. If the pattern in the table continues, how much will he have saved after 1 year?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 30
$ _______

Answer: $540

Explanation:
Aaron wants to buy a new snowboard. The table shows the amount that he has saved.
The equation will be s = 45m
s is the money saved
m is the number of months
1 year = 12 months
s = 45 × 12
s = 540
Thus he saved $540 after 1 year.

Share and Show – Page No. 513

Graph the relationship represented by the table.

Question 1.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 31
Type below:
________________

Answer: y = 50x
Go Math Grade 6 Chapter 9 answer key img-19

Question 2.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 32
Type below:
________________

Answer: y = 5x
Go Math Grade 6 Chapter 9 answer key img-20

Graph the relationship represented by the table to find the unknown value of y.

Question 3.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 33
Type below:
________________

Answer: 3
Go Math Grade 6 Chapter 9 answer key img-15

Question 4.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 34
Type below:
________________

Answer: 6
Go Math Grade 6 Chapter 9 answer key img-16

On Your Own

Practice: Copy and Solve Graph the relationship represented by the table to find the unknown value of y.

Question 5.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 35
Type below:
________________

Answer: 5
Go Math Grade 6 Chapter 9 answer key img-17

Question 6.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 36
Type below:
________________

Answer: 7
Go Math Grade 6 Chapter 9 answer key img-18

Problem Solving + Applications – Page No. 514

The table at the right shows the typical price of a popular brand of corn cereal over time. Use the table for 7–8.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 37

Question 7.
Use Graphs Complete the table below to show the cost of buying 1 to 5 boxes of corn cereal in 1988. Then graph the relationship on the coordinate plane at right.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 38
Type below:
________________

Answer:
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-38
Go Math Grade 6 Chapter 9 answer key img-26

Question 8.
Suppose you graphed the cost of buying 1 to 5 boxes of corn cereal using the 1968 price and the 2008 price. Explain how those graphs would compare to the graph you made using the 1988 price.
Type below:
________________

Answer:
The points on both graphs would lie on a line, but the line for the 1968 costs would rise less steeply than the line for 1988 costs and the line for the 2008 costs would rise more steeply than the line for 1988 costs.

Question 9.
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for 1 to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain.
Type below:
________________

Answer: Yes her statement makes sense.
The points on the graph are (1,4), (2,4), (3,4), (4,4). These points lie on the horizontal line.

Question 10.
Graph the relationship represented by the table to find the unknown value of y.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 39
Type below:
________________

Answer: 3
Go Math Grade 6 Chapter 9 answer key img-25

Graph Relationships – Page No. 515

Graph the relationship represented by the table.

Question 1.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 40
Type below:
________________

Answer: y = 25x

Go Math Grade 6 Chapter 9 answer key img-10

Question 2.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 41
Type below:
________________

Answer:
Go Math Grade 6 Chapter 9 answer key img-11

Graph the relationship represented by the table to find the unknown value of y.

Question 3.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 42
Type below:
________________

Answer: 6

Go Math Grade 6 Chapter 9 answer key img-12

Question 4.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 43
Type below:
________________

Answer: 2

Go Math Grade 6 Chapter 9 answer key img-13

Problem Solving

Question 5.
Graph the relationship represented by the table.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 44
Type below:
________________

Answer: y = 15x

Go Math Grade 6 Chapter 9 answer key img-14

Question 6.
Use the graph to find the cost of purchasing 5 DVDs.
$ ______

Answer:
The above graph shows that the cost of 5 DVDs is $75.

Question 7.
Both tables and graphs can be used to represent relationships between two variables. Explain how tables and graphs are similar and how they are different.
Type below:
________________

Answer:
Tables and graphs can be useful tools for helping people make decisions. However, they only provide part of a story. Inferences often have to be made from the data shown. As well as being able to identify clearly what the graph or table is telling us, it is important to identify what parts of the story are missing.

Lesson Check – Page No. 516

Question 1.
Mei wants to graph the relationship represented by the table. Write an ordered pair that is a point on the graph of the relationship.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 45
Type below:
________________

Answer: y = 8x
Go Math Grade 6 Chapter 9 answer key img-27

Question 2.
An online bookstore charges $2 to ship any book. Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars. Name an ordered pair that is a point on the graph of the relationship.
Type below:
________________

Answer:
An online bookstore charges $2 to ship any book.
Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars.
y = x + 2
x = 4
y = 4 + 2
y = 6
The ordered pair is (4,6)

Spiral Review

Question 3.
Write an expression that is equivalent to 6(g + 4).
Type below:
________________

Answer:
6(g + 4)
6 × g + 6 × 4
6g + 24

Question 4.
There are 6 girls in a music class. This represents \(\frac{3}{7}\) of the entire class. Solve \(\frac{3}{7}\)s = 6 to find the number of students, s, in the class.
_____ students

Answer: 14

Explanation:
There are 6 girls in a music class. This represents \(\frac{3}{7}\) of the entire class.
\(\frac{3}{7}\)s = 6
3 × s = 6 × 7
3s = 42
s = 42/3
s = 14
There are 14 students in the class.

Question 5.
Graph n > 2 on a number line.
Type below:
________________

Answer:
HMH Go Math Grade 6 Key Chapter 9 img-28

Question 6.
Sam is ordering lunch for the people in his office. The table shows the cost of lunch based on the number of people. How much will lunch cost for 35 people?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 46
$ _____

Answer: 280

Explanation:
Sam is ordering lunch for the people in his office.
The table shows the cost of lunch based on the number of people.
The equation is c = 8n
c = 8 × 35
c = 280
Thus the lunch cost for 35 people is $280.

Share and Show – Page No. 519

Graph the linear equation.

Question 1.
y = x + 2
Type below:
________________

Answer:
Go math grade 6 chapter 9 answer key img-28

Question 2.
y = 3x
Type below:
________________

Answer:
Go math grade 6 chapter 9 answer key img-29

Write the linear equation for the relationship shown by the graph.

Question 3.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 47
Type below:
________________

Answer: y = x – 1

Question 4.
Type below:
________________

On Your Own

Graph the linear equation.

Question 5.
y = x + 1
Type below:
________________

Answer:
Go math grade 6 chapter 9 answer key img-30

Question 6.
y = 2x − 1
Type below:
________________

Answer:
Go math grade 6 chapter 9 answer key img-31

Question 7.
Identify Relationships The graph shows the number of loaves of bread y that Kareem bakes in x hours. Write the linear equation for the relationship shown by the graph.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 48
Type below:
________________

Answer:
The ordered pairs are (1,1), (2,2), (4,4), (5,5)
Look for a pattern among the pairs: each y value is the same as the corresponding x-value.
The equation is y = x
y = x

Problem Solving + Applications – Page No. 520

The graph shows the growth of a bamboo plant. Use the graph for 8–9.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 49

Question 8.
Write a linear equation for the relationship shown by the graph. Use your equation to predict the height of the bamboo plant after 7 days.
Type below:
________________

Answer:
Write the ordered pairs from the graph: (1,50), (2,100), (3,150), (4,200), (5,250).
Look for a pattern among the pairs: each y value is 50 times the corresponding x value.
The equation is y = 50x
For x = 7, the solution is y = 50 × 7 = 350.
So, the height of the bamboo plant after 7 days will be 350 centimeters.

Question 9.
The height y in centimeters of a second bamboo plant is given by the equation y = 30x, where x is the time in days. Describe how the graph showing the growth of this plant would compare to the graph showing the growth of the first plant.
Type below:
________________

Answer: The line of the graph for the second plant would be less steep than the line of the graph for the first plant.

Question 10.
Maria graphed the linear equation y = x + 3. Then she used her ruler to draw a vertical line through the point (4, 0). At what point do the two lines intersect?
Type below:
________________

Answer:
y = x + 3
y = 4 + 0 = 4
y = 4 + 3 = 7
The coordinate is (4, 7)
Go math grade 6 chapter 9 answer key img-32

Question 11.
Antonio claims the linear equation for the relationship shown by the graph is y = \(\frac{1}{2}\)x + 2. Use numbers and words to support Antonio’s claim.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 50
Type below:
________________

Answer:
The ordered pairs (2,3) and (6,5) on the line make the equation.
y = \(\frac{1}{2}\)x + 2
y = 1/2 × 2 + 2
y = 1 + 2 = 3
y = 1/2 × 6 + 2
y = 3 + 2 = 5

Equations and Graphs – Page No. 521

Graph the linear equation.

Question 1.
y = x − 3
Type below:
________________

Answer:
Go Math Grade 6 Chapter 9 answer key img-22

Question 2.
y = x ÷ 3
Type below:
________________

Answer:
Go Math Grade 6 Chapter 9 answer key img-23

Write a linear equation for the relationship shown by the graph.

Question 3.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 51
Type below:
________________

Answer:
By seeing the above graph we can say that the equation is
y = x + 1

Question 4.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 52
Type below:
________________

Answer:
The ordered pairs are (1,4), (1.5,6), (2,8)
By seeing the above pairs we can say that the equation is y = 4x

Problem Solving

Question 5.
Dee is driving at an average speed of 50 miles per hour. Write a linear equation for the relationship that gives the distance y in miles that Dee drives in x hours.
Type below:
________________

Answer: y = 50x

Explanation:
Dee is driving at an average speed of 50 miles per hour.
y represents the distance in miles
x is the number of hours.
y is equal to the product of 50 and x.
y = 50x

Question 6.
Graph the relationship from Exercise 5.
Type below:
________________

Answer:
Go Math Grade 6 Chapter 9 answer key img-24

Question 7.
Explain how to write a linear equation for a line on a graph.
Type below:
________________

Answer:
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope.

Lesson Check – Page No. 522

Question 1.
A balloon rises at a rate of 10 feet per second. What is the linear equation for the relationship that gives the height y in feet of the balloon after x seconds?
Type below:
________________

Answer: The linear equation for the relationship is y = 10x

Question 2.
Write the linear equation that is shown by the graph.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 53
Type below:
________________

Answer:
Write the ordered pairs from the graph: (3,3), (5,5), (8,8)
Look for a pattern among the pairs: each y value is the same as the corresponding x-value.
The equation is y = x

Spiral Review

Question 3.
Of the three expressions shown, which two are equivalent?
3 + 2(9 + 2n)     7(3 + 4n)         21 + 4n
Type below:
________________

Answer:
3 + 2(9 + 2n) = 3 + 18 + 4n = 21 + 4n
7(3 + 4n) = 21 + 28n
Thus  21 + 4n and 3 + 2(9 + 2n) are equivalent.

Question 4.
Which of the following are solutions of j ≥ 0.6?
j = 1      j = 0.6       j = \(\frac{3}{5}\)       j = 0.12        j = 0.08
Type below:
________________

Answer: j = \(\frac{3}{5}\)

Explanation:
Substitute the values of j in the inequality.
j = 1
1 ≥ 0.6
1 is greater than 0.6 but not equal.
Thus 1 is not the solution of j ≥ 0.6.
j = 0.6
-0.6 ≥ 0.6
-0.6 is less than 0.6
Thus -0.6 is not the solution of j ≥ 0.6.
j = \(\frac{3}{5}\)
\(\frac{3}{5}\) ≥ 0.6
\(\frac{3}{5}\) = 0.6
0.6 ≥ 0.6
Thus \(\frac{3}{5}\) is the solution.
j = 0.12
0.12 ≥ 0.6
0.12 is less than 0.6.
Thus 0.12 is not the solution of j ≥ 0.6.
j = 0.08
0.08 ≥ 0.6
0.08 is less than 0.6.
Thus 0.08 is not the solution of j ≥ 0.6.

Question 5.
Red grapes cost $2.49 per pound. Write an equation that shows the relationship between the cost c in dollars and the number of pounds of grapes p.
Type below:
________________

Answer: c = 2.49p

Explanation:
Given,
Red grapes cost $2.49 per pound.
c is the cost in dollars.
p is the number of pounds of grapes.
The equation c is equal to the product of the number of pounds of grapes and $2.49
c = 2.49p

Question 6.
It costs $8 per hour to rent a bike. Niko graphs this relationship using x for number of hours and y for total cost in dollars. Write an ordered pair that is a point on the graph of the relationship.
Type below:
________________

Answer: (5,40)

Explanation:
Given,
It costs $8 per hour to rent a bike.
Niko graphs this relationship using x for the number of hours and y for the total cost in dollars.
y = 8x

Chapter 9 Review/Test – Page No. 523

Question 1.
A box of peanut butter crackers contains 12 individual snacks. The total number of individual snacks s is equal to 12 times the number of boxes of crackers b.
The independent variable is _____.
The dependent variable is _____.
The equation that represents the relationship between the variables is _____.

Answer:
The independent variable is b.
The dependent variable is s.
The equation that represents the relationship between the variables is s = 12b.

Question 2.
A stationery store charges $8 to print logos on paper purchases. The total cost c is the price of the paper p plus $8 for printing the logo.
For numbers 2a–2d, select True or False for each statement.
2a. The total cost c depends on the price of the paper.
2b. c is the dependent variable.
2c. p is the independent variable.
2d. The equation that represents the relationship between the variables is c = 8p.
2a. ____________
2b. ____________
2c. ____________
2d. ____________

Answer:
2a. True
2b. True
2c. True
2d. False

Explanation:
2a. c represents the relationship between the two quantities.
So, the statement “The total cost c depends on the price of the paper” is true.
2b. c is the total cost so the statement “c is the dependent variable” is true.
2c. p represents the price to print logos
So, the statement “p is the independent variable” is true.
2d. The total cost c is the price of the paper p plus $8 for printing the logo.
The equation would be:
c = 8 + p
Thus the statement “The equation that represents the relationship between the variables is c = 8p” is false.

Question 3.
An electrician charges $75 an hour for labor and an initial fee of $65. The total cost c equals 75 times the number of hours x plus 65. Write an equation for the relationship and use the equation to complete the table.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 54
Type below:
________________

Answer: c = 75x + 65
Substitute the value of x in the equation.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-54

Page No. 524

Question 4.
The community center offers classes in arts and crafts. There is a registration fee of $125 and each class costs $79. The total cost c in dollars equals 79 times the number of classes n plus 125.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 55
For numbers 4a–4d, select True or False for each statement.
4a. The registration fee is $120.
4b. n is the independent variable.
4c. c is the dependent variable.
4d. The cost for 7 classes is $678.
4a. ____________
4b. ____________
4c. ____________
4d. ____________

Answer:
4a. False
4b. True
4c. True
4d. True

Explanation:
4a. The registration fee is $120.
The registration fee is $125, not $120.
So, the statement is false.
4b. n is the independent variable.
n represents the number of classes.
The statement is true.
4c. c is the dependent variable.
c depends on the registration fee.
Thus the statement is true.
4d. The cost for 7 classes is $678
79 × 7 + 125 = $678
Thus the statement is true.

Question 5.
Ms. Walsh is buying calculators for her class. The table shows the total cost based on the number of calculators purchased.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 56
If Ms. Walsh spent a total of $525, how many calculators did she buy? Use numbers and words to explain your answer.
Type below:
________________

Answer:
She bought 35 calculators. I found a pattern and wrote the equation c = 15n.
Since I know that Mrs.Walsh spent a total of $525, I can substitute 525 for c and solve for n
525 = 15n
n = 35

Chapter 9 Review/Test – Page No. 525

Question 6.
The table shows the number of cups of lemonade that can be made from cups of lemon juice.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 57
Mary Beth says the number of cups of lemon juice j depends on the number of cups of lemonade l. She says the equation j = 7l represents the relationship between the cups of lemon juice j and the cups of lemonade l. Is Mary Beth correct? Use words and numbers to explain why or why not.
Type below:
________________

Answer:
Mary Beth is not correct. The number of cups of lemonade l depends on the number of cups of lemon juice j.
So l is the dependent variable and j is the independent variable.
The equation showing the relationship is l = 7j

Question 7.
For numbers 7a–7d, choose Yes or No to indicate whether the points, when graphed, would lie on the same line.
7a. (1, 6), (2, 4), (3, 2), (4, 0)
7b. (1, 1), (2, 4), (3, 9), (4, 16)
7c. (1, 3), (2, 5), (3, 7), (4, 9)
7d. (1, 8), (2, 10), (3, 12), (4, 14)
7a. ____________
7b. ____________
7c. ____________
7d. ____________

Answer:
7a. Yes
Go Math Grade 6 Chapter 9 answer key img-2
7b. No
Go Math Grade 6 Chapter 9 answer key img-3
7c. Yes
Go Math Grade 6 Chapter 9 answer key img-4
7d. Yes
Go Math Grade 6 Chapter 9 answer key img-5

Question 8.
Graph the relationship represented by the table to find the unknown value.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 58
Type below:
________________

Answer: 10

Go Math Grade 6 Chapter 9 answer key img-6

Chapter 9 Review/Test – Page No. 526

Question 9.
Graph the relationship represented by the table.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 59
Type below:
________________

Answer:
Go Math Grade 6 Chapter 9 answer key img-7

Question 10.
Miranda’s wages are $15 per hour. Write a linear equation that gives the wages w in dollars that Miranda earns in h hours.
Type below:
________________

Answer: w = 15h
Go Math Grade 6 Chapter 9 answer key img-8

Question 11.
The table shows the number of miles m that Lucinda could walk in h hours.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 60
Graph the relationship between hours h and miles m. Then write the equation that shows the relationship.
Type below:
________________

Answer: m = 4h
Go Math Grade 6 Chapter 9 answer key img-9

Chapter 9 Review/Test – Page No. 527

Question 12.
Delonna walks 4 miles per day for exercise. The total number of miles m she walks equals 4 times the number of days d she walks.
What is the dependent variable?
What is the independent variable?
Write the equation that represents the relationship between the m and d.
Type below:
________________

Answer:
The equation is m = 4d
m is the dependent variable
d is the independent variable.

Question 13.
Lacy is staying at a hotel that costs $85 per night. The total cost c in dollars of Lacy’s stay is 85 times the number of nights n she stays.
For numbers 13a–13d, select True or False for each statement.
13a. The number of nights n is dependent on the cost c.
13b. n is the independent variable.
13c. c is the dependent variable.
13d. The equation that represents the total cost is c = 85n.
13a. ____________
13b. ____________
13c. ____________
13d. ____________

Answer:
13a. False
13b. True
13c. True
13d. True

Explanation:
13a. The number of nights n is dependent on the cost c.
n is independent on the cost c.
So, the statement is false.
13b. n is the independent variable.
The statement is true.
13c. c is the dependent variable.
c is dependent because it depends on the cost c.
So, the statement is true.
13d. The equation that represents the total cost is c = 85n.
The equation is true.

Question 14.
A taxi cab company charges an initial fee of $5 and then $4 per mile for a ride. Use the equation c = 4x + 5 to complete the table.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 61
Type below:
________________

Answer:
Substitute the value of x in the equation.
We get,
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-61

Chapter 9 Review/Test – Page No. 528

Question 15.
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row. The total number of cans c equals 2 times the row r minus 1. Use the equation c = 2r − 1 to complete the table.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 62
Type below:
________________

Answer:
A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row.
c = 2r − 1
Substitute r in the equation.
Go-Math-Grade-6-Answer-Key-Chapter-9-Independent-and-Dependent-Variables-img-62

Question 16.
The graph shows the number of words Mason read in a given amount of minutes. If Mason continues to read at the same rate, how many words will he have read in 5 minutes?
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 63
______ words

Answer: 1000 words
By seeing the above graph we can say that Mason can read 1000 words in 5 minutes.

Question 17.
Casey claims the linear equation for the relationship shown by the graph is c = 25j. Use numbers and words to support Casey’s claim.
Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables img 64
Type below:
________________

Answer: The ordered pairs (1,25), (3,75), (5,125) and (7,175) each make the equation c = 25j

Conclusion:

I wish the details prevailed in the Go Math Grade 6 Answer Key Chapter 9 is helpful for you. Share this pdf link with your friends and help them to overcome the difficulties. If you have any doubts regarding the solutions you can leave a comment in the comment section.

Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice

go-math-grade-3-chapter-10-time-length-liquid-volume-and-mass-extra-practice-answer-key

Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice helps you to test your preparation level. Solve as many questions in the 3rd Grade Go Math Answer Key Ch 10 Extra Practice and score better grades. We have provided detailed solutions for all the problems in Chapter Test, Practice Test, Assessment Tests in Go Math Grade 3 Answer Key making it easy for you to understand topics.

3d Grade Go Math Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice

Before you begin your practice sessions know the topics in Chapter 10 Time Length Liquid Volume and Mass through the quick links available. Assess your strengths and weaknesses using the 3rd Grade Go Math Answer Key Ch 10 Time Length Liquid Volume and Mass Extra Practice.

Common Core – Page No. 211000

Write the time. Write one way you can read the time.

Question 1.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 1
_______ : _______

Question 2.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 2
_______ : _______

Question 3.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 3
_______ : _______

Write the time. Use A.M. or P.M.

Question 4.
30 minutes past noon
_______ : _______ _______ (A.M. or P.M.)

Question 5.
14 minutes before 7:00 in the morning
_______ : _______ _______ (A.M. or P.M.)

Find the elapsed time.

Question 6.
Start: 10:10 P.M. End: 10:45 P.M.
________ minutes

Question 7.
Start: 7:05 A.M. End: 7:33 A.M.
________ minutes

Question 8.
Delia spent 45 minutes working on her book report. She finished the report at 6:10 P.M. At what time did Delia start working on her report?
_______ : _______ _______ (A.M. or P.M.)

Question 9.
Lucas leaves school at 3:05 P.M. The bus ride home takes 25 minutes. Then it takes Lucas 15 minutes to ride his bike to soccer practice. At what time does Lucas get to soccer practice?
_______ : _______ _______ (A.M. or P.M.)

Common Core – Page No. 212000

Measure the length to the nearest half inch.

Question 1.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 4
_____ inches

Question 2.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 5
_____ inches

Question 3.
Measure the length to the nearest fourth inch.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 6
_____ inches

Estimate how much liquid volume there will be when the container is filled. Write more than 1 liter, about 1 liter, or less than 1 liter.

Question 4.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 7
________

Question 5.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 8
________

Question 6.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 9
________

Choose the unit you would use to measure the mass.

Write gram or kilogram.

Question 7.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 10
________

Question 8.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 11
________

Question 9.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Extra Practice Common Core img 12
________

Write an equation and solve the problem.

Question 10.
Miles ate two hot dogs with buns. Each hot dog has a mass of 45 grams, and each hot dog bun has a mass of 33 grams. How many grams of hot dogs and buns id Miles eat in all?
________ grams

Question 11.
Celia’s famous raspberry limeade comes in 3-liter containers. Celia gets an order for 8 containers of raspberry limeade. How many liters of raspberry limeade were ordered?
________ liters

Final Words

We wish the info shared on Go Math Grade 3 Answer Key Ch 10 Extra Practice has helped you a lot. For any queries needed feel free to check Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass.

Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test

Improve student’s math skills by accessing our Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test. Get to know the areas you need to improve using the 3rd Grade Go Math Answer Key Ch 10 Time Liquid Volume and Mass Assessment Test. Check out the various models of Questions in Time Length Liquid Volume and Mass along with a detailed explanation on our page.

Go Math Answer Key Chapter 10 Time Liquid Volume and Mass Assessment Test includes all the topics you might need as a part of preparation. Practicing these Assessment Tests helps you to score better grades in exams. Get a good hold of the concepts and know how to solve Problems based on Time Liquid Volume and Mass from here.

Chapter 10: Time, Length, Liquid Volume, and Mass Assessment Test

Test – Page 1 – Page No. 101

Question 1.
Chris left to take his dog for a walk at 6:25 P.M. He returned home after 26 minutes. He talked to his neighbor for 10 minutes before going back into his house.
Write the time that Chris got home and the time he went back into the house. Explain how you found each time.

Answer: Chris got back home at 6:51 PM and he went into the house at 7:01 PM.

Explanation:

Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test

Question 2.
Kayla measured an object with an inch ruler. It was about 1 inch wide.
For numbers 2a–2d, choose Yes or No to tell whether the object could be the one Kayla measured.
a. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 1 img 1
i. yes
ii. no

Answer: Yes.

Explanation: It seems like a stamp that can be measured. 

Question 2.
b. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 1 img 2
i. yes
ii. no

Answer: Yes.

Explanation: It is a pin that is less than can be measured. 

Question 2.
c. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 1 img 3
i. yes
ii. no

Answer: No

Explanation: The pencil can be more than an inch.

Question 2.
d. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 1 img 4
i. yes
ii. no

Answer: No

Explanation: The rope can be more than an inch.

Test – Page 2 – Page No. 102

Question 3.
Luz left for the park at 2:27 P.M. She arrived at 3:09 P.M. How long did it take Luz to get to the park?
_____ minutes

Answer: 42 minutes.

Explanation: The time difference between 3:09 P.M and 2:27 P.M is 42 minutes.

Question 4.
Terry wakes up for school at five minutes before seven in the morning. At what time does Terry wake up?
Circle a time that makes the sentence true.
Terry wakes up at Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 2 img 5
__________

Answer: Terry wakes up at 6:55 A.M.

Explanation:

Terry wakes up at  Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test

Question 5.
Select the objects with a mass less than 1 kilogram.
Mark all that apply.
Options:
a. desk
b. eyeglasses
c. eraser
d. plastic fork

Answer: b,c,d

Explanation: Eyeglasses, eraser, plastic fork will be less than 1 kilogram.

Question 6.
A batch of muffins needs to bake in the oven for 22 minutes. They need to cool for at least 15 minutes before they should be eaten. Wade puts the muffins in the oven at 10:17 A.M.
For numbers 6a–6d, select True or False for each statement.
a. Wade can eat the muffins at 10:39 P.M.
i. True
ii. False

Answer: True.

Explanation: If Wade put a muffin in an oven at 10:17 A.M he has to take out then at 10:39 A.M (which is after 22mins), they should be cooled down at least for 15mins once they have taken out. So they can eat after 10:54 A.M.

Question 6.
b. Wade can eat the muffins at 10:44 A.M.
i. True
ii. False

Answer: False.

Explanation: The muffins are not cool, so Wade cannot eat.

Question 6.
c. Wade should take the muffins out of the oven at 10:39 P.M.
i. True
ii. False

Answer: False.

Explanation: No, Wade should take the muffins out of the oven at 10:39 A.M.

Question 6.
d. Wade should take the muffins out of the oven at 10:39 A.M.
i. True
ii. False

Answer: Yes.

Explanation: If Wade put a muffin in the oven at 10:17 A.M he has to take out then at 10:39 A.M which is after 22mins.

Test – Page 3 – Page No. 103

Question 7.
Kirk went to a friend’s house after dinner. He left his house at the time shown on the clock and returned home at 8:05 P.M.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 3 img 6
Part A
How long was Kirk gone?
______ minutes

Answer: 36 mins.

Explanation: Kirk left home at 7:29 PM and returned after 8:05 PM. Thus he has gone for 36 mins.

Question 7.
Part B
Explain how you found your answer.

Answer: Counted 31 mins from 7:29 to 8:00, 5 mins from 8:00 to 8:05. Then summing up all give 31 mins + 5 mins = 36 mins.

Question 8.
Brad looked at the clock on his way to the football game. What time is shown on Brad’s clock? Mark all that apply.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 3 img 7
Options:
a. thirteen minutes before ten
b. nine forty-seven
c. quarter to ten
d. nine forty

Answer: Options a and b.

Explanation: The time has shown on Brad’s clock is thirteen minutes before ten and nine forty-seven.

Question 9.
Andrea uses a balance scale to compare mass.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 3 img 8
Circle a symbol that makes the comparison true.
The mass of the erasers Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 3 img 9 the mass of the paper clips.
_____

Answer: >

Explanation:

The mass of the erasers Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test the mass of the paper clips.

Test – Page 4 – Page No. 104

Question 10.
A bucket of water holds about 19 liters.
For numbers 10a−10e, choose Yes or No to tell whether the container will hold all of the water.
a. bath tub
i. yes
ii. no

Answer: Yes.

Explanation: The bathtub can hold all of the water.

Question 10.
b. large water bottle
i. yes
ii. no

Answer: No.

Explanation: A large water bottle cannot hold all of the water.

Question 10.
c. soup bowl
i. yes
ii. no

Answer: No

Explanation: A soup bowl cannot hold all of the water.

Question 10.
d. large fish tank
i. yes
ii. no

Answer: Yes.

Explanation: A large fish tank can hold all of the water.

Question 10.
e. kitchen sink
i. yes
ii. no

Answer: Yes.

Explanation: A kitchen sink can hold all of the water.

Question 11.
Select the animals that would be best measured in kilograms. Mark all that apply.
Options:
a. dog
b. mouse
c. goat
d. sheep

Answer: a,c,d.

Explanation: Dog, Goat, Sheep are best measured in kilograms.

Question 12.
Luisa is planning her day on Saturday. Write the letter for each activity next to the time she plans to do it.
Options:
A. Wake up. ______ 3:30 P.M.
B. Play soccer game. ______ 8:30 P.M.
C. Eat lunch. ______ 7:30 A.M.
D. Go to a movie. ______ 12:30 P.M.
E. Go to bed. ______ 9:00 A.M.

Answer:

A. Wake up at 7:30 A.M.
B. Play soccer game 9:00 A.M.
C. Eat lunch at 12:30 P.M
D. Go to a movie at 3:30 P.M.
E. Go to bed at 8:30 P.M.

Test – Page 5 – Page No. 105

Question 13.
Stephen has 28 teaspoons of lemon juice. He uses 5 teaspoons of juice for each glass of lemonade he makes. He adds 2 teaspoons of juice to each glass of iced tea he makes.
Stephen makes 4 glasses of lemonade. Does he have enough lemon juice to make 4 glasses of iced tea?
Explain how you solved the problem.
______

Answer: Yes

Explanation:
How much lemon juice he used to make 4 glasses of lemonade = 4 x 5 = 20
Total no of teaspoons of lemon juice he had = 28
No of teaspoons of lemon juice needed to make iced tea = 4 x 2 = 8
Therefore total he needed = 20 + 8 = 28
Thus he has enough lemon juice to make 4 glasses of iced tea.

Question 14.
Use an inch ruler to measure.
Part A
What is the length of the flower to the nearest fourth-inch?
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 5 img 10
_____ \(\frac{□}{□}\)

Answer: 2 ¼ inches.

Explanation: The length of the rose diagram on the ruler is closest to 2.25 – inch mark (6 cm nearly). So taken as 2 ¼ inches which are nearest to the fourth inch.

Question 14.
Part B
Explain how your answer would change if you measured the length of the flower to the nearest inch instead of fourth-inch.

Answer: The length of the rose diagram on the ruler is closest to 2 – inch mark 6 cm nearly.

Question 15.
A football game begins at 11:32 A.M. The game lasts 3 hours 16 minutes. When does the game end?

Answer: The football game end at 2:48 P.M.

Explanation: As the football game begins at 11:32 A.M and the game lasts 3 hours 16 minutes. So the game ends at 2:48 P.M

Question 16.
Alicia buys two packets of flower seeds. She buys a total of 75 grams of seeds. Select the packets she buys.
Options:
a. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 5 img 11
b. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 5 img 12
c. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 5 img 13
d. Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 5 img 14

Answer: options b and d.

Explanation: As she buys a total of 75 grams, so 30g + 45g = 75g.

Test – Page 6 – Page No. 106

Question 17.
Mr. Barton measures the screws on his workbench. He records the measurements in a chart.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 6 img 15
Part A
Mr. Barton found another screw. Use an inch ruler to measure. Record the measurement in the chart.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 6 img 16
____ inches

Answer: 3 inches approx. (8 cm).

Explanation:

Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test

Question 17.
Part B
Complete the line plot to show the data in the chart. How many screws are longer than 2 inches? Tell how you know.
Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test Test - Page 6 img 17
_____ screws

Answer: 2 screws.

Explanation: Screw with 2 ½ inches and 3, thus two screws longer than 2 inches.

Question 18.
Abby fills a mug with hot cocoa. Is the amount of cocoa more than 1 liter, about 1 liter, or less than 1 liter? Explain how you know.

Explanation: A liter is about the amount in a medium bottle of water. The amount would not fit a mug, so the full mug has less than 1 liter.

Summary

Hoping the info shared above on Go Math Grade 3 Answer Key Chapter 10 Time Liquid Volume and Mass has helped you a lot. To resolve any queries related refer to Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass.

Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

go-math-grade-4-chapter-2-multiply-by-1-digit-numbers-answer-key

Go Math Solutions Resource is the best guide for students of 4th grade. In Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers you will find the questions and their detailed solutions in an easy manner. By using the 4th Standard Go Math solutions key everyone can prepare all chapter 2 topics easily & score well in the exams. This Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers will let students grasp the concepts properly & make them practice more regularly.

Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Practicing each and every step by step explained questions will provide immense results. Students can easily understand the topics of chapter 2 Multiply by 1-Digit Numbers via Go Math 4th Grade Answer Key. You will look up the concepts called Multiplication Comparisons, Multiplying using Distributive property and Expanded form, Estimate products, etc. clearly through this Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers for standard knowledge of the subject.

Lesson 1: Algebra • Multiplication Comparisons

Lesson 2: Algebra • Comparison Problems

Lesson 3: Multiply Tens, Hundreds, and Thousands

Lesson 4: Estimate Products

Lesson 5: Investigate • Multiply Using the Distributive Property

Lesson 6: Multiply Using Expanded Form

Lesson 7: Multiply Using Partial Products

Lesson 8: Multiply Using Mental Math

Lesson 9: Problem Solving • Multistep Multiplication Problems

Lesson 10: Multiply 2-Digit Numbers with Regrouping

Lesson 11: Multiply 3-Digit and 4-Digit Numbers with Regrouping

Lesson 12: Algebra • Solve Multistep Problems Using Equations

Chapter 2 Review/Test

Common Core – Multiplication Comparisons – Page No. 67

Write a comparison sentence.

Question 1.
6 × 3 = 18
6 times as many as 3 is 18.

Question 2.
63 = 7 × 9

Answer: 63 is 7 times as many as 9.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 3.
5 × 4 = 20

Answer: 5 times as many as 4 is 20.

Explanation:

Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 4.
48 = 8 × 6

Answer: 48 is 6 times as many as 8.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Write an equation.

Question 5.
2 times as many as 8 is 16.

Answer: 2 × 8 = 16

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 6.
42 is 6 times as many as 7.

Answer: 42 = 6 × 7

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 7.
3 times as many as 5 is 15.

Answer: 3 × 5 = 15

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 8.
36 is 9 times as many as 4.
Answer: 36 = 9 × 4

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 9.
72 is 8 times as many as 9.
Answer: 72 = 8 × 9

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 10.
5 times as many as 6 is 30.
Answer: 5 × 6 = 30

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Problem Solving

Question 11.
Alan is 14 years old. This is twice as old as his brother James is. How old is James?

Answer: 7 years old.

Explanation:
Alan’s age is 14 years old and his brother is James is twice younger than Alan, So James’s age is 14÷2= 7.

Question 12.
There are 27 campers. This is nine times as many as the number of counselors. How many counselors are there?

Answer: 3 counselors.

Explanation: 27 campers= 9× no.of counselors,
So no.of counselors are 27÷9= 3.

Question 13.

Draw a model, and write an equation to represent “4 times as many as 3 is 12.” Explain your work.

Answer: 4×3= 12.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Common Core – Multiplication Comparisons – Lesson Check – Page No. 68

Question 1.
Which equation best represents the comparison sentence?
24 is 4 times as many as 6.
Options:
a. 24 × 4 = 6
b. 24 = 4 × 6
c. 24 = 4 + 6
d. 4 + 6 = 24

Answer: b

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 2.
Which comparison sentence best represents the equation?
5 × 9 = 45
Options:
a. 5 more than 9 is 45.
b. 9 is 5 times as many as 45.
c. 5 is 9 times as many as 45.
d. 45 is 5 times as many as 9.

Answer: d

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Spiral Review

Question 3.
Which of the following statements correctly compares the numbers?
Options:
a. 273,915 > 274,951
b. 134,605 < 143,605
c. 529,058 > 530,037
d. 452,731 > 452,819

Answer: b

Explanation: 134,605 is lesser compared to 143,605.

Question 4.
What is the standard form for
200,000 + 80,000 + 700 + 6?
Options:
a. 2,876
b. 28,706
c. 208,706
d. 280,706

Answer: d

Explanation: 200,000+80,000+700+6= 280,706.

Question 5.
Sean and Leah are playing a computer game. Sean scored 72,491 points. Leah scored 19,326 points more than Sean. How many points did Leah score?
Options:
a. 53,615
b. 91,717
c. 91,815
d. 91,817

Answer: d

Explanation: Sean’s score is 72,491 and Leah’s score is 19,326 more than Sean’s score. So Sean score is 72,491+19,326 = 91,817.

Question 6.
A baseball stadium has 38,496 seats. Rounded to the nearest thousand, how many seats is this?
Options:
a. 38,000
b. 38,500
c. 39,000
d. 40,000

Answer: b

Explanation: Round off to nearest thousand is 38,000.

Multiplication Comparisons – Page No. 71

Question 1.
Maria’s dog weighs 6 times as much as her rabbit. Together the pets weigh 56 pounds. What does Maria’s dog weigh? Draw a model. Let n represent the unknown.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 1
Answer: 48 Pounds.

Explanation: Let the weight of the rabbit be X and the dog’s weight is 6X. Both pet’s weight is 56 pounds i.e 6X+X=56, 7X=56 then X is 8.
Rabbit’s weight is 8 and Dog’s weight is 6×8= 48.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Draw a model. Write an equation and solve.

Question 2.
Last month Kim trained 3 times as many dogs as cats. If the total number of cats and dogs she trained last month is 28, how many cats did Kim train?

Answer: 7

Explanation: Let the cats trained to be X and dogs trained to be 3X.
Total Cats and Dogs she trained are 28, then X+3X= 28 and X= 7.
Therefore Cats trained are 7.

Question 3.
How many more dogs than cats did Kim train?

Answer: 21 dogs

Explanation: 3×7= 21.

Practice: Copy and Solve Draw a model.
Write an equation and solve.

Question 4.
At the dog show, there are 4 times as many boxers as spaniels. If there are a total of 30 dogs, how many dogs are spaniels?

Answer: 24.

Explanation: Let spaniels be S and the boxers be 4S. As the total is 30, S+4S=30 then 5S=30.
Therefore S is 6. Spaniels are 6 and boxers are 4 times as many as spaniels. So boxers are 4×6=24.

Question 5.
There are 5 times as many yellow labs as terriers in the dog park. If there are a total of 18 dogs, how many dogs are terriers?

Answer: 3.

Explanation: Let the Terriers be T and yellow labs be 5T. As total dogs are 18, 5T+T=18, and therefore T=18/6 which is 3. Terriers are 3.

Question 6.
Ben has 3 times as many guppies as goldfish. If he has a total of 20 fish, how many guppies does he have?

Answer: 15.

Explanation: Let Goldfish be X and Guppies be 3X, So X+3X= 20.
Therefore X= 5. So guppies are 3×5= 15.

Question 7.
Carlita saw 5 times as many robins as cardinals while bird watching. She saw a total of 24 birds. How many more robins did she see than cardinals?

Answer: 4 cardinals and 20 robins.

Explanation: Let the cardinals be X and robins be 5X. Then the total is 5X+X=24 then X= 4. So Carlita saw 4 cardinals and 5×4= 20 robins.

Multiplication Comparisons – Page No. 72

Question 8.
To get to a dog show, Mr. Luna first drives 7 miles west from his home and then 3 miles north. Next, he turns east and drives 11 miles. Finally, he turns north and drives 4 miles to the dog show. How far north of Mr. Luna’s home is the dog show? To solve the problem, Dara and Cliff drew diagrams. Which diagram is correct? Explain.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 2

Answer: Cliff diagram is correct.

Explanation: Mr. Luna’s travels east and west are irrelevant to the question. As he drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.

Question 9.
Use Reasoning Valerie and Bret have a total of 24 dog show ribbons. Bret has twice as many ribbons as Valerie. How many ribbons does each have?
Valerie’s ribbons: ______          Bret’s ribbons: ______

Answer: Valerie has 8 and Bret has 16.

Explanation: Let the Valerie ribbons be X and Bret’s ribbons be 2X and the total be X+2X= 24. Therefore X= 8.
Valerie has 8 and Bret has 2×8= 16.

Question 10.
Noah built a fenced dog run that is 8 yards long and 6 yards wide. He placed posts at every corner and every yard along the length and width of the run. How many posts did he use?

Answer: 2×7+2×5+4(as he posted at every corner)= 14+10+4= 28 posts

Explanation: As there are 7 posts along one 8 yard side and 5 posts along one 6 yard side, so he used 2×7+2×5+4(as he posted at every corner)= 14+10+4= 28 posts

Question 11.
Last weekend, Mandy collected 4 times as many shells as Cameron. Together, they collected 40 shells. How many shells did Mandy collect? Complete the bar model. Then, write an equation and solve.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 3

 

Common Core – Comparison Problems – Page No. 73

Draw a model. Write an equation and solve.

Question 1.
Stacey made a necklace using 4 times as many blue beads as red beads. She used a total of 40 beads. How many blue beads did Stacey use?
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core - img 4

Question 2.
At the zoo, there were 3 times as many monkeys as lions. Tom counted a total of 24 monkeys and lions. How many monkeys were there?
______ monkeys

Answer: 18 monkeys.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 3.
Fred’s frog jumped 7 times as far as Al’s frog. The two frogs jumped a total of 56 inches. How far did Fred’s frog jump?

Answer: 49 inches.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 4.
Sheila has 5 times as many markers as Dave. Together, they have 18 markers. How many markers does Sheila have?

Answer:

Explanation: 15 markers.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Problem Solving

Question 5.
Rafael counted a total of 40 white cars and yellow cars. There were 9 times as many white cars as yellow cars. How many white cars did Rafael count?

Answer: 36 white cars.

Explanation: Let yellow cars be X, As white cars are 9 times as many as yellow cars, So white cars be 9X. Therefore 9X+X=40, X=4. So no.of white cars are 9×4= 36.

Question 6.
Sue scored a total of 35 points in two games. She scored 6 times as many points in the second game as in the first. How many more points did she score in the second game?

Answer: 30 points.

Explanation: Let the first game points be X and second game points be 6X. Sue’s total score is 35 points in two games so 6X+X= 35 then X is 5. Therefore the second game score is 6×5= 30.

Question 7.
Write a problem involving how much more than and solve it. Explain how drawing a diagram helped you solve the problem.

Answer: Mike has 10 chocolates and John has 5 chocolates. How many more chocolates does Chirs have?
5 chocolates more Chirs have.

Explanation: As Mike has 10 chocolates and john has 5 chocolates, Chirs has 5 more chocolates than John.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Common Core – Comparison Problems – Lesson Check – Page No. 74

Question 1.
Sari has 3 times as many pencil erasers as Sam. Together, they have 28 erasers. How many erasers does Sari have?
Options:
a. 7
b. 14
c. 18
d. 21

Answer: d

Explanation: Let the X be pencil erasers of Sam and Sari erasers be 3X. As Sari and Sam together have 28 erasers. So 3X+X= 28. And X is 7. Then Sari has 3×7= 21.

Question 2.
In Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies?
Options:
a. 5
b. 12
c. 15
d. 18

Answer: d

Explanation: Let Guppies be X and Goldfishes be 6X. And the total fishes are 21, So X+6X= 21 then X= 3.
So Goldfishes are 6×3= 18.

Spiral Review

Question 3.
Barbara has 9 stuffed animals. Trish has 3 times as many stuffed animals as Barbara. How many stuffed animals does Trish have?
Options:
a. 3
b. 12
c. 24
d. 27

Answer: d

Explanation: Barbara has 9 stuffed animals and Trish has 3 times as Barbara, So 9×3= 27.

Question 4.
There are 104 students in the fourth grade at Allison’s school. One day, 15 fourth-graders were absent. How many fourth-graders were at school that day?
Options:
a. 89
b. 91
c. 99
d. 119

Answer: a

Explanation: Total students in fourth grade are 104, as 15 students were absent 104-15= 89.

Question 5.
Joshua has 112 rocks. Jose has 98 rocks. Albert has 107 rocks. What is the correct order of the boys from the least to the greatest number of rocks owned?
Options:
a. Jose, Albert, Joshua
b. Jose, Joshua, Albert
c. Albert, Jose, Joshua
d. Joshua, Albert, Jose

Answer: a

Explanation: As 98<107<112. So Jose, Albert, Joshua.

Question 6.
Alicia has 32 stickers. This is 4 times as many stickers as Benita has. How many stickers does Benita have?
Options:
a. 6
b. 8
c. 9
d. 28

Answer: 8.

Explanation: Let Benita stickers be S and Alicia has 32 stickers, So 4×S= 32. Therefore Benita stickers are 8.

Comparison Problems – Page No. 77

Question 1.
Use the drawing to find 2 × 500.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 5

Answer: 2×= 1000.

Explanation: 2×500 is 2 times 5 hundreds, which is equal to 10 hundreds and 10 hundreds are equal to 1000.

Complete the pattern.

Question 2.
3 × 8 = 2
i. 3 × 80 = _____
ii. 3 × 800 = _____
iii. 3 × 8,000 = _____

Answer: 240, 2400, 24,000.

Explanation: 3×80= 240
3×800= 2400
3×8000= 24,000

Question 3.
6 × 2 = 12
i. 6 × 12 = _____
ii. 6 × 120 = _____
iii. 6 × 1,200 = _____

Answer: 72, 720, 7200.

Explanation: 6×12= 72
6×120= 720
6×1200= 7200.

Question 4.
i. 4 × 5 = _____
ii. 4 × 50 = _____
iii. 4 × 500 = _____
iv. 4 × 5,000 = _____

Answer: 20, 200, 2000, 20,000.

Explanation: 4×5= 20
4×50= 200
4×500= 2000
4×5,000= 20,000.

Find the product.

Question 5.
6 × 500 = 6 × _____ hundreds
= _____ hundreds
= _____

Answer: 6×5 hundreds = 30  hundreds.

Explanation: 6 × 500 = 6 × 5 hundreds = 30 hundreds = 3000

Question 6.
9 × 5,000 = 9 × _____ thousands
= _____ thousands
= _____

Answer: 9 × 5 thousands = 45 thousands.

Explanation: 9 × 5 thousands = 45 thousands. = 45,000.

Find the product.

Question 7.
7 × 6,000 = _____

Answer: 42,000.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 8.
4 × 80 = _____

Answer: 320

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 9.
3 × 500 = _____

Answer: 1500

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Use Reasoning Algebra Find the missing factor.

Question 10.
_____ × 9,000 = 63,000

Answer: 7

Explanation: As 7×9= 63

Question 11.
7 × _____ = 56,000

Answer: 8

Explanation: 7×8= 56.

Question 12.
8 × _____ = 3,200

Answer: 4

Explanation: 8×4= 32.

Question 13.
Communicate How does the number of zeros in the product of 8 and 5,000 compare to the number of zeros in the factors? Explain.

Answer: 8×5=40.

Explanation: There are 4 zeros in the product and 3 zeros only in the factors. Because there is a zero in basic fact as 8×5=40.

Comparison Problems – Page No. 78

Question 14.
Joe’s Fun and Sun rents beach chairs. The store rented 300 beach chairs each month in April and in May. The store rented 600 beach chairs each month from June through September. How many beach chairs did the store rent during the 6 months?
a. What do you need to know?

Answer: We need to know about the total number of beach chairs rented during the 6 months.

Question 14.
b. How will you find the number of beach chairs?

Answer: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000

Explanation: We will multiply 2 times 300 and 4 times 600 and the will add the product.

Question 14.
c. Show the steps you use to solve the problem.

Answer: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000.

Question 14.
d. Complete the sentences.
For April and May, a total of ______ beach chairs were rented.

Answer: 600

Explanation: As the store rented 300 beach chairs in April and May, So 300×2= 600.

Question 14.
For June through September, a total of _____ beach chairs were rented.

Answer: 2400

Explanation: As the store rented 600 beach chairs from June to September, So 600×4= 2400.

Question 14.
Joe’s Fun and Sun rented _____ beach chairs during the 6 months.

Answer: 3,000

Explanation: 300×2= 600 and 600×4= 2400. Total beach chairs are 3000.

Question 15.
Mariah makes bead necklaces. Beads are packaged in bags of 50 and bags of 200. Mariah bought 4 bags of 50 beads and 3 bags of 200 beads. How many beads did Mariah buy?

Answer: 800 beads.

Explanation: Mariah bought 4 bags of 50 beads which is 4×50= 200 beads. And 3 bags of 200 beads which is 3×200= 600. Total beads Mariah bought are 200+600= 800.

Question 16.
Carmen has three books of 20 stamps and five books of 10 stamps. How many stamps does Carmen have? Complete the equation using the numbers on the tiles.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 6
______ × 20 + ______ × 10 = ______

Answer: 3, 5, 110

Explanation: 3×20+5×10= 110.

Common Core – Multiply Tens, Hundreds, and Thousands – Page No. 79

Find the product.

Question 1.
4 × 7,000 = 28,000
Think: 4 × 7 = 28
So, 4 × 7,000 = 28,000

Question 2.
9 × 60 = _____

Answer: 540

Explanation: 9×6= 54.

Question 3.
8 × 200 = _____

Answer: 1600

Explanation: 8×2=16

Question 4.
5 × 6,000 = _____

Answer: 30,000.

Explanation: 5×6=30.

Question 5.
7 × 800 = _____

Answer: 5600

Explanation: 7×8= 56.

Question 6.
8 × 90 = _____

Answer: 720

Explanation: 8×9=72.

Question 7.
6 × 3,000 = _____

Answer: 18,000.

Explanation: 6×3= 18.

Question 8.
3 × 8,000 = _____

Answer: 24,000

Explanation: 3×8= 24.

Question 9.
5 × 500 = _____

Answer: 2500.

Explanation: 5×5= 25.

Question 10.
9 × 4,000 = _____

Answer: 36,000

Explanation: 9×4= 36.

Question 11.
7 × 7,000 = _____

Answer: 49,000.

Explanation: 7×7= 49.

Question 12.
3 × 40 = _____

Answer: 120.

Explanation: 3×4= 12.

Question 13.
4 × 5,000 = _____

Answer: 20,000.

Explanation: 4×5= 20.

Question 14.
2 × 9,000 = _____

Answer: 18,000

Explanation: 2×9= 18.

Problem Solving

Question 15.
A bank teller has 7 rolls of coins. Each roll has 40 coins. How many coins does the bank teller have?

Answer: 280 coins.

Explanation: Bank teller has 7 rolls of coins. As each roll has 40 coins, So total coins are 7×40= 280

Question 16.
Theo buys 5 packages of paper. There are 500 sheets of paper in each package. How many sheets of paper does Theo buy?

Answer: 2,500.

Explanation: Total no.of sheets of papers in each package are 500, And Theo buys 5 packages of papers. So total sheets of paper Theo bought are 500×5= 2,500.

Common Core – Multiply Tens, Hundreds, and Thousands Lesson CheckPage No. 80

Question 1.
A plane is traveling at a speed of 400 miles per hour. How far will the plane travel in 5 hours?
Options:
a. 200 miles
b. 2,000 miles
c. 20,000 miles
d. 200,000 miles

Answer: b

Explanation: The speed of the plane is 400 miles per hour. In 5 hours plane can travel 400×5= 2,000 miles.

Question 2.
One week, a clothing factory made 2,000 shirts in each of 6 different colors. How many shirts did the factory make in all?
Options:
a. 2,000
b. 12,000
c. 120,000
d. 200,000

Answer: b

Explanation: Shirts made in one week are 2000 in 6 different colors. So total shirts made in all are 2000×6= 12,000.

Spiral Review

Question 3.
Which comparison sentence best represents the equation?
6 × 7 = 42
Options:
a. 7 is 6 times as many as 42.
b. 6 is 7 times as many as 42.
c. 42 is 6 times as many as 7.
d. 6 more than 7 is 42.

Answer: c

Explanation: By comparing 42= 6×7 represents the equation.

Question 4.
The population of Middleton is six thousand, fifty-four people. Which of the following shows this number written in standard form?
Options:
a. 654
b. 6,054
c. 6,504
d. 6,540

Answer: b

Explanation: Six thousand fifty-four is equal to 6,054.

Question 5.
In an election for mayor, 85,034 people voted for Carl Green and 67,952 people voted for Maria Lewis. By how many votes did Carl Green win the election?
Options:
a. 17,082
b. 17,182
c. 22,922
d. 152,986

Answer: a

Explanation: Total votes Carl Green has got are 85,034and Maria Lewis got are 67,952. By 85,034-67,952= 17,082 votes Carl Green won the election.

Question 6.
Meredith picked 4 times as many green peppers as red peppers. If she picked a total of 20 peppers, how many green peppers did she pick?
Options:
a. 4
b. 5
c. 16
d. 24

Answer: c

Explanation: Let the red peppers be X and green peppers be 4X, And the total she picked is 20 peppers. So X+4X=20,
Then X=4. Green peppers she picked are 4×4= 16.

Multiply Tens, Hundreds, and Thousands – Page No. 83

Question 1.
Estimate the product by rounding.
5 × 2,213
_____ × _____ = _____

Answer: 5×2000= 10,000

Explanation: The rounding off for 2,213 is 2000. So 5×2000= 10,000.

Question 2.
Estimate the product by finding two numbers the exact answer is between.
5 × 2,213

Answer: 5×2000= 10,000 and 5×3000= 15,000.

Explanation: The rounding off for 2,213 is 2000 and 3000. So 5×2000= 10,000 and 5×3000= 15,000.

Tell whether the exact answer is reasonable.

Question 3.
Kira needs to make color copies of a horse show flyer. The printer can make 24 copies in 1 minute. Kira says the printer makes 114 copies in 6 minutes.

Answer: Kira is incorrect.

Explanation: As the printer can make 24 copies in 1 minute, So if we take 24 rounds off to 20 or 30 then the printer makes 120 or 180 copies. So Kira is incorrect.

Question 4.
Jones Elementary is having a car wash to raise money for a community horse trail. Each car wash ticket costs $8. Tiara says the school will receive $1,000 if 125 tickets are sold.

Answer: Tiara says correct.

Explanation: As 1000÷125= 8 which is each car wash ticket cost. So the answer is reasonable.

Tell whether the exact answer is reasonable.

Question 5.
Evaluate Reasonableness Mrs. Hense sells a roll of coastal Bermuda horse hay for $58. She says she will make $174 if she sells 3 rolls.

Answer: The answer is reasonable.

Explanation: As 174 is the nearest rounding off to 180. So the answer is reasonable.

Question 6.
Mr. Brown sells horse supplies. A pair of riding gloves sells for $16. He says he will make $144 if he sells 9 pairs.

Answer: The answer is reasonable

Explanation: As 144 is between 90 and 180, So the answer is reasonable. Here we will take rounding off for 9 as 10 and 20. So the answer must be between 90 and 180.

Question 7.
Path A and Path B are walking paths used for horses. Path A is 118 feet long. Path B is 180 feet long. Carlos walks his horse down each path 3 times. Which path did Carlos use to walk his horse about 500 feet? Explain.

Answer: Path B

Explanation: 118 is rounded off to 100 and then multiply with 3, 100  Then round off 180 to 200 and multiply with 3, 200  As 500 is closer to estimate of 600 compared to 300. So Path B is correct.

Question 8.
Students in the third grade sell 265 tickets to the school play. Students in the fourth grade sell 3 times as many tickets as the third-grade students. Estimate the number of tickets the fourth-grade students sold by finding the two numbers the exact answer is between.
The students sold between
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 8

Answer: 600 and 900.

Explanation: 1let 265 be rounded off 200 and 300. As fourth-grade students sell 3 times as many as third-grade students, So 200 and 300  So tickets sold between 600 and 900.

Multiply Tens, Hundreds, and Thousands – Page No. 84

Predict whether the exact answer will be less than or greater than the estimate. Explain your answer.

Question 9.
The food stand at the zoo sold 2,514 pounds of hamburger last month. The average cost of a pound of hamburger is $2. Jeremy estimates that about $6,000 worth of hamburger was sold last month.

Answer: Lesser than the actual amount of hamburger.

Explanation: As the amount of hamburger sold is 468 pounds less than the estimated amount of 3000 pounds. So, the answer will be less than estimated.

Question 10.
A zoo bought 2,240 pounds of fresh food for the bears this month. The average cost of a pound of food is $4. Jeremy estimates that about $8,000 was spent on fresh food for the bears this month.

Answer: Greater than the actual amount of food bought.

Explanation: As the actual amount of food bought for the bears this month was 240 pounds greater than the estimated amount of 2,000 pounds. So, the answer will be greater than the estimated amount.

Common Core – Estimate Products – Page No. 85

Estimate the product by rounding.

Question 1.
4 × 472
4 × 472

4 × 500 = 2,000

Question 2.
2 × 6,254

Answer: 12,000.

Explanation: The nearest rounding off for 6,254 is 6,000. So 2×6,000= 12,000.

Question 3.
9 × 54

Answer: 450

Explanation: The nearest rounding off for 54 is 50. So 9×50= 450.

Question 4.
5 × 5,503

Answer: 30,000.

Explanation: The nearest rounding off for 5,503 is 6,000. So 5×6,000= 30,000.

Question 5.
3 × 832

Answer: 2,400.

Explanation: The nearest rounding off for 832 is 800. So 3×800= 2,400.

Question 6.
6 × 98

Answer: The nearest rounding off for 98 is 100. So 6×100= 600.

Question 7.
8 × 3,250

Answer: The nearest rounding off for 3,250 is 3,000. So 8×3,000= 24,000.

Question 8.
7 × 777

Answer: 5,600.

Explanation: The nearest rounding off for 777 is 800. So 7×800= 5,600.

Find two numbers the exact answer is between.

Question 9.
3 × 567

Answer: 1500 and 1800.

Explanation: The rounding off for 567 is 500 and 600. So 3×500= 1500 and 3×600= 1800.

Question 10.
6 × 7,381

Answer: 42,000 and 48,000.

Explanation: The rounding off for 7,381 is 7,000 and 8,000. So 6×7000= 42,000 and 6×8000= 48,000.

Question 11.
4 × 94

Answer: 360 and 400.

Explanation: The rounding off for 94 is 90 and 100. So 4×90= 360 and 4×100= 400.

Question 12.
6 × 684

Answer: 3600 and 4200

Explanation: The rounding off for 684 is 600 and 700. So 6×600= 3600 and 6×700= 4200.

Problem Solving

Question 13.
Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable? Explain

Answer: Yes.

Explanation: As the round-off for 365 can be 300 or 400. So 8×300= 2,400 and 8×400= 3,200. The estimated answer can be between 2,400 to 3,200. So the answer is Yes.

Question 14.
Most Americans throw away about 1,365 pounds of trash each year. Is it reasonable to estimate that Americans throw away over 10,000 pounds of trash in 5 years? Explain.

Answer: No.

Explanation: As the round-off for 1,365 can be 1000 or 2000. So 5×1000= 5,000 and 5×2000= 10,000. The estimated answer can be between 5,000 to 10,000.

Common Core – Estimate Products – Lesson Check – Page No. 86

Question 1.
A theater has 4,650 seats. If the theater sells all the tickets for each of its 5 shows, about how many tickets will the theater sell in all?
Options:
a. 2,500
b. 10,000
c. 25,000
d. 30,000

Answer: c

Explanation: As the nearest round off for 4,650 is 5,000. So 5,000×5= 25,000.

Question 2.
Washington Elementary has 4,358 students. Jefferson High School has 3 times as many students as Washington Elementary. About how many students does Jefferson High School have?
Options:
a. 16,000
b. 12,000
c. 10,000
d. 1,200

Answer: b

Explanation: As the nearest round off for 4,358 is 4,000. So 4,000×3= 12,000.

Spiral Review

Question 3.
Diego has 4 times as many autographed baseballs as Melanie has. Diego has 24 autographed baseballs. How many autographed baseballs does Melanie have?
Options:
a. 28
b. 20
c. 8
d. 6

Answer: d

Explanation: Let the Melanie baseballs be S. As Diego has 4 times as many as Melanie and Diego has a total of 24 baseballs. So 4×S= 24, Then S= 24÷4 which is 6.

Question 4.
Mr. Turkowski bought 4 boxes of envelopes at the office supply store. Each box has 500 envelopes. How many envelopes did Mr. Turkowski buy?
Options:
a. 200
b. 504
c. 2,000
d. 20,000

Answer: c

Explanation: Turkowski has 4 boxes of envelopes and each box contains 500 envelopes, So total envelopes did Turkowski bought are 4×500= 2,000.

Question 5.
Pennsylvania has a land area of 44,816 square miles. Which of the following shows the land area of Pennsylvania rounded to the nearest hundred?
Options:
a. 44,000 square miles
b. 44,800 square miles
c. 44,900 square miles
d. 45,000 square miles

Answer: b.

Explanation: As the nearest round off for 44,816 is 44,800.

Question 6.
The table shows the types of DVDs customers rented from Sunshine Movie Rentals last year.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 9
How many comedy and action movies were rented in all last year?
Options:
a. 13,620
b. 13,000
c. 12,260
d. 10,752

Answer: c

Explanation: Comedy and action movies that are rented in last year are 6,720+5,540= 12,260.

Estimate Products – Page No. 89

Model the product on the grid. Record the product.

Question 1.
3 × 13
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 10
3 × 13 = _____

Answer: 39

Explanation: 3×13= 3 ×(10+3)
=(3×10)+ (3×3)
=30+9
=39

Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 2.
5 × 14
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 11
5 × 14 = _____

Answer: 70.

Explanation: 5×14 = 5×(10+4)
= (5×10)+(5×4)
= 50+20
= 70
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Find the product.

Question 3.
6 × 14
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 12
6 × 14 = ______

Answer: 84

Explanation: 6×14= 6×(10+4)
= (6×10)+(6×4)
= 60+24
= 84

Question 4.
5 × 18
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 13
5 × 18 = ______

Answer: 90

Explanation: 5 × 18 =5 ×(10+8)
= (5 × 10)+ (5 ×8)
= 50+40
= 90.

Question 5.
4 × 16
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 14
4 × 16 = ______

Answer: 64

Explanation: 4 × 16= (4 × 10)+( 4 ×6)
= 40+24
= 64.

Use grid paper or base-ten blocks to model the product.
Then record the product.

Question 6.
7 × 12 = ______

Answer: 84

Explanation: 7×12 = 7×(10+2)
=(7×10)+(7×2)
=70+14
84

Question 7.
5 × 16 = ______

Answer: 80

Explanation: 5×16= 5×(10+6)
=(5×10)+(5×6)
= 50+30
= 80

Question 8.
9 × 13 = ______

Answer: 117

Explanation: 9 × 13 = 9 ×(10+3)
=(9×10)+(9×3)
=90+27
=117

Question 9.
Explain how modeling partial products can be used to find the products of greater numbers.

Answer: 25 3= (20+5) 3
=(20×3)+(5×3)= 60+15=75

Explanation: The multiplication is easy. For example if we take 25 3= (20+5) 3
=(20×3)+(5×3)= 60+15=75

Question 10.
Use the Distributive Property to model the product on the grid. Record the product.
4 × 14 = _____

Answer: 56.

Explanation: 4×14= 4×(10+4)
=(4×10)+(4×4)
=40+16
=56

Estimate Products – Page No. 90

Question 11.
Kyle went to a fruit market. The market sells a wide variety of fruits and vegetables. The picture at the right shows a display of oranges. Write a problem that can be solved using the picture.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 15

Answer: A shopkeeper has oranges. He keeps his oranges in the basket having 6 rows and each row has 12 oranges. So how many oranges he owned.

Explanation: From the above picture we can see 6 rows and 12 columns of Oranges. So total
no. of Oranges are 6 12= 72 Oranges.

Question 12.
Describe how you could change the problem by changing the number of rows of oranges and the number of empty spaces in the picture. Then solve the problem.

Common Core – Multiply Using the Distributive Property – Page No. 91

Model the product on the grid. Record the product.

Question 1.
4 × 19 = 76
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 16
4 × 10 = 40 and 4 × 9 = 36
40 + 36 = 76

Question 2.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 17
5 × 13 = ______

Answer: 65.

Explanation:
5×10= 50 and 5×3= 15
50+15= 65.

Find the product.

Question 3.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 18
4 × 14 = ______

Answer: 56

Explanation:
4×10= 40 and 4×4= 16
40+16= 56.

Question 4.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 19
3 × 17 = ______

Answer: 51

Explanation:
3×10=30 and 3×7= 21
30+21= 51

Question 5.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 20
6 × 15 = ______

Answer: 90

Explanation:
6×10= 60 and 6×5= 30
60+30= 90

Problem Solving

Question 6.
Michael arranged his pennies in the following display.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 21
How many pennies does Michael have in all?

Answer: 91

Explanation: As there are 7 columns and 13 rows, So 13×7= 91.

Question 7.
A farmer has an apple orchard with the trees arranged as shown below.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 22
If the farmer wants to pick one apple from each tree, how many apples will he pick?

Answer: 70

Explanation: As there are 5 columns and 14 rows, So 5×14= 70.

Common Core – Multiply Using the Distributive Property – Lesson Check – Page No. 92

Question 1.
The model shows how Maya planted flowers in her garden.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 23
How many flowers did Maya plant?
Options:
a. 15
b. 18
c. 30
d. 45

Answer: d

Explanation: As 3×10= 30 and 3×5= 15
30+15= 45.

Question 2.
The model below represents the expression 5 x 18.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 24
How many tens will there be in the final product?
Options:
a. 5
b. 6
c. 8
d. 9

Answer: d

Explanation: As 5×18 is 90 and 90÷10= 9. So answer is 9.

Spiral Review

Question 3.
Center City has a population of twenty one thousand, seventy people. Which of the following shows the population written in standard form?
Options:
a. 21,007
b. 21,070
c. 21,077
d. 21,700

Answer: b

Explanation: Twenty-one thousand seventy is equal to 21,070.

Question 4.
Central School collected 12,516 pounds of newspaper to recycle. Eastland School collected 12,615 pounds of newspapers. How many more pounds of newspaper
did Eastland School collect than Central School?
Options:
a. 99 pounds
b. 101 pounds
c. 199 pounds
d. 1,099 pounds

Answer: a

Explanation: Central school has collected 12,516 pounds and Eastland school collected 12,615 pounds. So
12,615-12,516= 99.

Question 5.
Allison has 5 times as many baseball cards as football cards. In all, she has 120 baseball and football cards. How many baseball cards does Allison have?
Options:
a. 20
b. 24
c. 96
d. 100

Answer: d

Explanation: Let Football cards be X and baseball cards be 5X. So 5X+X= 120 in which X= 20. As Allison has 5 times as many baseball cards as football cards. So 5×20= 100.

Question 6.
A ruby-throated hummingbird beats its wings about 53 times each second. About how many times does a ruby throated hummingbird beat its wings in 5 seconds?
Options:
a. 25
b. 58
c. 250
d. 300

Answer: c

Explanation: As the nearest round-off for 53 is 50, So 50×5= 250.

Multiply Using the Distributive Property – Page No. 95

Question 1.
Find 4 × 213. Use expanded form.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 25
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 26
_____

Record the product. Use expanded form to help.

Question 2.
4 × 59 = _____

Answer: 236

Explanation: 4×(50+9)
= (4×50)+(4×9)
= 200+36
= 236.

Question 3.
3 × 288 = _____

Answer: 864

Explanation: 3×(200+80+8)
= (3×200)+(3×80)+(3×8)
= 600+240+24
= 864.

Record the product. Use expanded form to help.

Question 4.
4 × 21 = _____

Answer: 84

Explanation: 4×(20+1)
= (4×20)+(4×1)
= 80+4
= 84.

Question 5.
6 × 35 = _____

Answer: 210

Explanation: 6×(30+5)
= (6×30)+(6×5)
= 180+30
= 210.

Question 6.
A hotel has 128 rooms on each floor. There are 4 floors in all. If 334 of the rooms in the hotel have been cleaned, how many rooms still need to be cleaned?

Answer: 178.

Explanation: Total floors in a hotel are 4 and each floor has 128 rooms, So total rooms in the hotel are 128×4= 512.
In 512 rooms 334 were cleaned and the remaining rooms yet to be cleaned are 512-334= 178.

Question 7.
Ben wants to buy 2 blue sweaters for $119 each and 3 brown sweaters for $44 each. How much will Ben spend on the five sweaters?

Answer: $370.

Explanation: Ben wants to buy 2 blue sweaters for $119 each, So 119×2= 238. And 3 brown sweater for $44 each which means 44×3= 132. The total he spent on five sweaters is 238+132= 370.

Question 8.
A jeweler has 36 inches of silver chain. She needs 5 times that much to make some necklaces and 3 times that amount to make some bracelets. How much silver chain does the jeweler need to make her necklaces and bracelets?

Answer: 288 inches.

Explanation: As the jeweler has 36 inches of silver chain and she needs 5 times to make some necklaces which means 36×5= 180 and 3 times to make a bracelet which means 36×3= 108. So the total sliver she needs is 180+108= 288.

Question 9.
Gretchen walks her dog 3 times a day. Each time she walks the dog, she walks 1,760 yards. How many yards does she walk her dog in 3 days?

Answer: 15,840 yards.

Explanation: Gretchen walks 3 times a day which means for 3 days it will be 9 times. As she walks 1,760 yards, So 1760×9= 15,840.

Question 10.
Write an Expression Which expression could you write to show how to multiply 9 × 856 using place value and expanded form?

Answer: (9×800)+(9×50)+(9×6)

Explanation: Place value is the value of each digit in a number. So 856 can be expanded as 800+50+6.

Question 11.
Jennifer bought 4 packages of tacks. There are 48 tacks in a package. She used 160 of the tacks to put up posters. How many tacks does she have left? Explain.

Answer: 32.

Explanation: Jennifer bought 4 packages of tacks and each package contains 48 tacks. So total tacks are 48×4= 192.
As she used 160 tacks total tacks she left are 192-160= 32

Multiply Using the Distributive Property – Page No. 96

Use the table for 12–13.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 27

Question 12.
What is the total cost of 3 Italian cypress trees?

Answer: $237.

Explanation: The cost of each Italian cypress tree is $79.  The total cost of 3 Italian cypress tree is 79×3= 237.

Question 13.
What’s the Error? Tanya says that the difference in the cost of 4 flowering cherry trees and 4 Muskogee crape myrtles is $80. Is she correct? Explain.

Answer: No, Because she used a normal price instead of discounted price.

Explanation: For 4 and above trees, there is a discount price. So she is wrong.

Question 14.
What is the greatest possible product of a 2-digit number and a 1-digit number? Explain how you know.

Answer: 891.

Explanation: The greatest 2 digit number is 99 and the greatest single-digit number is 9. So the product is
99×9= 891.

Question 15.
Multiply 5 × 381 using place value and expanded form. Select a number from each box to complete the expression.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 28

Answer: (5×300)+(5×80)+(5×1).

Explanation: The expanded form of 381 is 300+80+1.

Common Core – Multiply Using Expanded Form – Page No. 97

Record the product. Use expanded form to help.

Question 1.
7 × 14 = 98
7 × 14 = 7 × (10 + 4)
= (7 × 10) + (7 × 4)
= 70 + 28
= 98

Question 2.
8 × 43 = _____

Answer: 344.

Explanation: 8×(40+3)
= (8×40)+(8×3)
= 320+24
= 344.

Question 3.
6 × 532 = _____

Answer: 3,192.

Explanation: 6×(500+30+2)
= (6×500)+(6×30)+(6×2)
= 3000+180+12
= 3,192.

Question 4.
5 × 923 = _____

Answer: 4,615

Explanation: 5×923= 5×(900+20+3)
=(5×900)+(5×20)+(5×3)
=4500+100+15
=4,615.

Question 5.
4 × 2,371 = _____

Answer: 9,484

Explanation: 4×2,371= 4×(2000+300+70+1)
= (4×2,000)+(4×300)+(4×70)+(4×1)
=8000+1200+280+4
=9,484

Question 6.
7 × 1,829 = _____

Answer: 12,803

Explanation: 7×1,829= 7×(1,000+800+20+9)
=(7×1,000)+( 7×800)+( 7×20)+( 7×9)
=7,000+5600+140+63
=12,803

Problem Solving

Question 7.
The fourth-grade students at Riverside School are going on a field trip. There are 68 students on each of the 4 buses. How many students are going on the field trip?

Answer: 272 students.

Explanation: No. of buses are 4 and on each bus, there are 68 students. So 68 4= 272.

Question 8.
There are 5,280 feet in one mile. Hannah likes to walk 5 miles each week for exercise. How many feet does Hannah walk each week?

Answer: 26,400 feet.

Explanation: There are 5,280 feet in one mile and Hannah walks 5 miles each week, So 5,280 5= 26,400.

Common Core – Multiply Using Expanded Form – Lesson Check – Page No. 98

Question 1.
Which expression shows how to multiply 7 × 256 by using expanded form and the Distributive Property?
Options:
a. (7 × 2) + (7 × 5) + (7 × 6)
b. (7 × 200) + (7 × 500) + (7 × 600)
c. (7 × 2) + (7 × 50) + (7 × 600)
d. (7 × 200) + (7 × 50) + (7 × 6)

Answer: d

Explanation: By Distributive property of multiplication 7×256=(7×200)+(7×50)+(7×6)

Question 2.
Sue uses the expression (8 × 3,000) + (8 × 200) + (8 × 9) to help solve a multiplication problem. Which is Sue’s multiplication problem?
Options:
a. 8 × 329
b. 8 × 3,029
c. 8 × 3,209
d. 8 × 3,290

Answer: b

Explanation: The expression (8×3,000)+(8×200)+(8×9) is written in the Distributive property of multiplication. So 8×3,029.

Spiral Review

Question 3.
What is another way to write 9 × 200?
Options:
a. 18 ones
b. 18 tens
c. 18 hundreds
d. 18 thousands

Answer: c

Explanation: 9×200= 1800

Question 4.
What is the value of the digit 4 in 46,000?
Options:
a. 4 ten thousands
b. 4 thousands
c. 4 hundreds
d. 4 tens

Answer: a

Explanation: The place value of 4 in 46,000 is 40,000.

Question 5.
Chris bought 6 packages of napkins for his restaurant. There were 200 napkins in each package. How many napkins did Chris buy?
Options:
a. 120
b. 1,200
c. 12,000
d. 120,000

Answer: b

Explanation: Total packages are 6 and each package contains 200 napkins. So 6 200=1,200.

Question 6.
Which of the following lists the numbers in order from least to greatest?
Options:
a. 8,512; 8,251; 8,125
b. 8,251; 8,125; 8,512
c. 8,125; 8,512; 8,251
d. 8,125; 8,251; 8,512

Answer: d

Explanation: 8,125>8,251>8,512.

Multiply Using Expanded Form – Page No. 101

Question 1.
Use the model to find 2 × 137.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 29
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 30

Answer: 274.

Explanation: 2×137= 2×(100+30+7)
=(2×100)+(2×30)+(2×7)
=200+60+14
=274.

Estimate. Then record the product.

Question 2.
1 9 0
×   3
———–
Estimate: ________
Product: ________

Answer:
Estimate: 600
Product: 570.

Explanation: Round off 190 to 200 and 200×3= 600. And the product is 190×3= 570.

Question 3.
4 7 1
×   4
———–
Estimate: ________
Product: ________

Answer:
Estimate: 2000
Product: 1884.

Explanation: Round off 471 to 500 and 500×4= 2000. And the product is 471×4= 1884.

Question 4.
3, 439
×     7
———–
Estimate: ________
Product: ________

Answer:
Estimate: 24,500
Product: 24,073.

Explanation: Round off 3,439 to 3500 and 3500×7= 24,500. And the product is 35000×7= 24,073.

Estimate. Then record the product.

Question 5.
$ 5 3
×   4
———–
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $ 240
Product: $ 212

Explanation: Round off 53 to 60 and 60×4= 240. And the product is 53×4= 212.

Question 6.
$ 4 7 3
×      4
———–
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $2,000
Product: $1,892.

Explanation: Round off 473 to 500 and 500×4= 2,000. And the product is 473×4= 1892.

Question 7.
6 0 8
×    6
———–
Estimate: ________
Product: ________

Answer:
Estimate: 4,200
Product: 3,648

Explanation: Round off 608 to 700 and 700×6= 4,200. And the product is 608×6= 3,648.

Practice: Copy and Solve Estimate. Then record the product.

Question 8.
2 × 78 =
Estimate: ________
Product: ________

Answer:
Estimate: 200
Product: 156

Explanation: Round off 78 to 100 and 100×2= 200. And the product is 78×2= 156.

Question 9.
2 × $210 =
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $600
Product: $420

Explanation: Round off 210 to 300 and 300×2= 600. And the product is 210×2= 420.

Question 10.
2 × $682 =
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $1,400.
Product: $1,364

Explanation: Round off 682 to 700 and 700×2= 1400. And the product is 682×2= 1364.

Question 11.
8 × 8,145 =
Estimate: ________
Product: ________

Answer:
Estimate: 68,000.
Product: 65,160.

Explanation: Round off 8,145 to 8,500 and 8,500×8= 68,000. And the product is 8145×8= 65,160.

Use Reasoning Algebra Find the missing digit.

Question 12.
■5
× 7
————-
455
■ = _____

Answer: 65

Explanation: 65×7= 455.

Question 13.
2 4 8
×   3
————-
■ 44
■ = _____

Answer: 744

Explanation: 248×3= 744

Question 14.
$3 9 5
×     ■
————
$2,370
■ = _____

Answer: 6

Explanation: 395×6= 2370

Question 15.
3,748
×    4
———-
1 ■,992
■ = _____

Answer: 14,992

Explanation: 3,748×4= 14,992

Question 16.
A store bought 9 cases of light bulbs in May and 8 cases in June. There are 48 light bulbs in a case. How many light bulbs did the store buy in May and June?

Answer: 816 bulbs.

Explanation: Light bulbs in May are 9 cases and in June are 8 cases. And each case have 48 light bulbs. So 9×48= 432 in May and 8×48= 384 in June. So total light bulbs in May and June are 384+432= 816.

Question 17.
Mr. Wilson saved $2,500 to buy airline tickets for his family. He bought 6 airline tickets for $372 each. How much of his savings does Mr. Wilson have after he buys the tickets?

Answer: $268.

Explanation: Mr. Wilson bought 6 tickets and each costs $372, So 372×6= 2,232. Total money Mr. Wilson saved is $2,500. Total Savings are 2500-2232=$268.

Question 18.
Coach Ramirez bought 8 cases of bottled water for a road race. There are 24 bottles in each case. After the race, 34 bottles of water were left. How many bottles were used at the race? Explain.

Answer: 158 bottles.

Explanation: Ramirez bought 8 cases of water and each case contains 24 bottles. So total bottles are 8×24=192 and 34 bottles left. Therefore used bottles are 192-34= 158.

Multiply Using Expanded Form – Page No. 102

Question 19.
Use Diagrams Look at the picture. Kylie has 832 songs on her portable media player. Lance has 3 times as many songs. How many fewer songs can Lance add to his player than Kylie can add to hers?
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 31

Answer: 1664.

Explanation: Total songs in portable media players are 9,000, And kylie has 832 songs. So Kylie can add 9000-832= 8,168 songs. Lance has 3 times as many songs as Kylie, So Lance has 832×3= 2,496. He can add 9000-2496= 6504 to his player. Therefore 8168-6504=1664 Lance can add 1664 fewer songs to his player than Kylie.

Question 20.
James wants to buy the new portable media player shown. He has 5 times as many songs as Susan. Susan has 1,146 songs. Will all of his songs fit on the portable media player? How many songs does James have?

Answer: 5,730 songs. Yes, will fit on the portable media player.

Explanation: Susan has 1,146 songs and James has 5 times as many songs as Susan, So 1,146 5= 5,730 songs will fit on the portable media player.

Question 21.
The sum of a 3-digit number and a 1-digit number is 217. The product of the numbers is 642. If one number is between 200 and 225, what are the numbers?

Answer: 3.

Explanation: As the given product is 642 and the 3 digit number is between 200 and 225, So the 1 digit number is 3 because if we multiply 200 and 225 by 3 we will get the product as 600 and 675 and 642 is in between them. So 642 3= 214. And the one-digit number is 3.

Question 22.
Mrs. Jackson bought 6 gallons of juice for a party. Each gallon has 16 cups. After the party, 3 cups of juice were left over. At the party, how many cups did people drink? Show your work and explain how you found your answer.

Answer: 93.

Explanation: Mrs. Jackson bought 6 gallons of juice and each gallon has 16 cups. So total cups of juice is 16 6= 96 cups. And in that 3 cups of juice was left after the party. So 96-3= 93 cups of juice people drank.

Common Core – Multiply Using Partial Products – Page No. 103

Estimate. Then record the product.

Question 1.
Estimate: 1,200
2 4 3
×   6
——————
1,200
2 4 0
+1 8
—————–
1,458

Question 2.
6 4 0
×   3
——————
Estimate: _________
Product: _________

Answer:
Estimate: 1800
Product: 1920.

Explanation: Rounding off 640 to 600 then estimated product is 600 3= 1800 and 640 3= 1920.
6 4 0
×   3
——————
1800
+120
+0
——————
1920

Question 3.
$ 1 4 9
×      5
——————
Estimate: $ _________
Product: $ _________

Answer:
Estimate: $500
Product: $745

Explanation: Rounding off 149 to 100 then estimated product is 100 5= 500 and 149 5= 745.
$ 1 4 9
×      5
——————
500
+200
+45
——————
745

Question 4.
7 2 1
×   8
——————
Estimate: _________
Product: _________

Answer:
Estimate: 5600
Product: 5768

Explanation: Rounding off 721 to 700 then estimated product is 700 8= 5600 and 721 8= 5,768.
7 2 1
×   8
——————
5600
+160
+8
——————
5,768

Question 5.
2 9 3
×   4
——————
Estimate: _________
Product: _________

Answer:
Estimate: 1,200
Product: 1,172

Explanation: Rounding off 293 to 300 then estimated product is 300 4= 1200 and 293 4=1,172.
2 9 3
×   4
——————
800
+360
+12
——————
1,172

Question 6.
$ 4 1 6
×      6
——————
Estimate: $ _________
Product: $ _________

Answer:
Estimate: $2400
Product: $2496

Explanation: Rounding off 293 to 300 then estimated product is 400 6= 2400 and
416 6= 2496.
$ 4 1 6
×      6
——————
2400
+60
+36
—————–
2,496

Question 7.
9 6 1
×    2
——————
Estimate: _________
Product: _________

Answer:
Estimate: 2000
Product: 1922

Explanation: Rounding off 961 to 1000 then estimated product is 1000 2= 2000 and
961 2= 1922.
9 6 1
×    2
——————
1800
+120
+2
——————-
1922

Question 8.
8 3 7
×   9
——————
Estimate: _________
Product: _________

Answer:
Estimate: 7,200
Product: 7,533

Explanation: Rounding off 837 to 800 then estimated product is 800 9= 7200 and
837 9= 7533.

8 3 7
×   9
——————
7200
+270
+63
—————–
7533

Question 9.
6 5 2
×   4
——————
Estimate: _________
Product: _________

Answer:
Estimate: 2,800
Product: 2,608

Explanation: Rounding off 652 to 700 then estimated product is 700 4= 2800 and
652 4= 2,608.
6 5 2
×   4
——————
2400
+200
+8
—————–
2608

Question 10.
3 0 7
×   3
——————
Estimate: _________
Product: _________

Answer:
Estimate: 900
Product: 921

Explanation: : Rounding off 307 to 300 then estimated product is 300 3= 900 and
307 3= 921.
3 0 7
×   3
——–
900
+21
——
921

Question 11.
5 4 3
×   7
——————
Estimate: _________
Product: _________

Answer:
Estimate: 3500
Product: 3,801

Explanation: : Rounding off 543 to 500 then estimated product is 500 7= 3500 and
543 7= 3801.
5 4 3
×   7
——————
3500
+280
+21
—————–
3801

Question 12.
$ 8 2 2
×      5
——————
Estimate: $ _________
Product: $ _________

Answer:
Estimate: $4,000.
Product: $4,110.

Explanation: Explanation: : Rounding off 822 to 800 then estimated product is 800 5= 4000 and
822 5= 4110.
$ 8 2 2
×      5
——————
4000
+100
+10
——————
4110

Problem Solving

Question 13.
A maze at a county fair is made from 275 bales of hay. The maze at the state fair is made from 4 times as many bales of hay. How many bales of hay are used for the maze at the state fair?

Answer: 1100 bales.

Explanation: No. of country fair bales are 275 and state fair bales are 4 times as many as country fair bales. So 275 4= 1100

Question 14.
Pedro gets 8 hours of sleep each night. How many hours does Pedro sleep in a year with 365 days?

Answer: 2,920 hours.

Explanation: Pedro sleeps 8 hours each night and 365 days Pedro sleeps 365 8= 2,920 hours.

Common Core – Multiply Using Partial Products – Lesson Check – Page No. 104

Question 1.
A passenger jet flies at an average speed of 548 miles per hour. At that speed, how many miles does the plane travel in 4 hours?
Options:
a. 2,092 miles
b. 2,112 miles
c. 2,192 miles
d. 2,480 miles

Answer: c

Explanation: Average speed of passenger jet is 548 miles per hour. And the plane travels in 4 hours is 548 4= 2,192 miles.

Question 2.
Use the model to find 3 x 157.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 32
Options:
a. 300,171
b. 300,157
c. 471
d. 451

Answer: c.

Explanation: By distributive property of multiplication 3 x 157= 3 x(100+50+7)
=(3 x100)+(3×50)+(3×7)
=300+150+21
=471

Spiral Review

Question 3.
The school fun fair made $1,768 on games and $978 on food sales. How much money did the fun fair make on games and food sales?
Options:
a. $2,636
b. $2,646
c. $2,736
d. $2,746

Answer: $2746.

Explanation: Money made on games is $1,768 and on food sale is $978. So total money make on games and food sales are 1768+978= 2746.

Question 4.
Use the table below.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 33
Which of the following lists the states from least to greatest population?
Options:
a. Alaska, North Dakota, Vermont
b. Vermont, Alaska, North Dakota
c. North Dakota, Vermont, Alaska
d. Vermont, North Dakota, Alaska

Answer: d.

Explanation: Vermont has 621,760, North Dakota has 646,844 and Alaska has 698,473.
So Vermont, North Dakota, Alaska.

Question 5.
A National Park covers 218,375 acres. What is this number written in expanded form?
Options:
a. 200,000 + 10,000 + 8,000 + 300 + 70 + 5
b. 20,000 + 1,000 + 800 + 30 + 75
c. 218 + 375
d. 218 thousand, 375

Answer: a.

Explanation: 218,375 is expanded as 200,000 + 10,000 + 8,000 + 300 + 70 + 5

Question 6.
Last year a business had profits of $8,000. This year its profits are 5 times as great. What are this year’s profits?
Options:
a. $4,000
b. $40,000
c. $44,000
d. $400,000

Answer: b

Explanation: Last year’s profit of $8,000 and this year 5 times more. So this year profit is 8000 5= 40,000.

Multiply Using Partial Products – Page No. 105

Choose the best term from the box to complete the sentence.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 34

Question 1.
To find the product of a two-digit number and a 1-digit number, you can multiply the tens, multiply the ones, and find the sum of each ________________.

Answer: Factor

Explanation: Factors are the numbers which divides the original number completely.

Question 2.
The _____________ states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Answer: Distributive Property

Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.

Write a comparison sentence.

Question 3.
5 × 9 = 45
______ times as many as ______ is ______ .

Answer: 5 times as many as 9 is 45

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 4.
24 = 6 × 4
______ is ______ times as many as ______ .

Answer: 24 is 6 times as many as 4.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 5.
54 = 6 × 9
______ is ______ times as many as ______ .

Answer: 54 is 6 times as many as 9

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Question 6.
8 × 6 = 48
______ times as many as ______ is ______ .

Answer: 48 is 8 times as many as 6.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers

Estimate. Then record the product.

Question 7.
7 5
× 5
—————
Estimate: ________
Product: ________

Answer:
Estimate: 500
Product: 375

Explanation: Rounding off 75 to 100 estimated value is 100×5= 500 and 75×5= 375

Question 8.
1 2
× 6
—————
Estimate: ________
Product: ________

Answer:
Estimate: 60
Product: 72

Explanation: Rounding off 12 to 10 estimated value is 10×6= 60 and 12×6= 72

Question 9.
2 8
× 3
—————

Answer:
Estimate: 90
Product: 84

Explanation: Rounding off 28 to 30 estimated value is 30×3= 90 and 28×3= 84

Question 10.
$4 3
× 6
—————
Estimate: $ ________
Product: $ ________

Answer:
Estimate: 300
Product: 258

Explanation: Rounding off 43 to 50 estimated value is 50×6= 300 and 43×6= 258

Record the product. Use expanded form to help.

Question 11.
5 × 64 = _____

Answer: 320

Explanation: 5 × 64= 5×(60+4)
=(5×60)+(5×4)
=300+20
=320

Question 12.
3 × 272 = _____

Answer: 812

Explanation: 3 × 272= 3×(200+70+2)
=(3×200)+(3×70)+(3×2)
=600+210+6
= 812

Multiply Using Partial Products – Page No. 106

Question 13.
There are 6 times as many dogs as cats. If the total number of dogs and cats is 21, how many dogs are there?

Answer: 18 dogs.

Explanation: Let cats be X and dogs are as many as 6 so dogs be 6X. As the total number of cats and dogs are X+6X=21, And X= 3 so dogs are 6×3= 18

Question 14.
The table below shows the number of calories in 1 cup of different kinds of berries. How many calories are in 4 cups of blackberries?
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 35

Answer: 248 Calories.

Explanation: The number of calories of blackberries in one cup are 62 and in 4 cups are 62×4= 248.

Question 15.
The skating rink rented 218 pairs of skates during the month of April and 3 times that many in May. How many pairs of skates did the skating rink rent during April and May?

Answer: 872 pairs.

Explanation: No. of pairs of skates in April are 218 and 3 times that many in May. So
3×218= 654. Total skates in April and May are 218+654= 872

Multiply Using Partial Products – Page No. 109

Question 1.
Break apart the factor 112 to find 7 × 112 by using mental math and addition.
7 × 112 = 7 × (_____ + 12)

Answer: 100

Explanation: 7 × 112 = 7 × (100 + 12)
= 7×(100+12)
= 700+84
= 784

Find the product. Tell which strategy you used.

Question 2.
4 × 6 × 50 = _____

Answer: 1200, Associative property.

Explanation:
4 × 6 × 50= 4 ×(6×50)
=4×(300)
=1200.

Question 3.
5 × 420 = _____

Answer: 2100, Use addition

Explanation: 420= 400+20
5×420= 5×(400+20)
=(5×400)+(5×20)
=2000+100
=2100.

Question 4.
6 × 298 = _____

Answer: 1788, Distributive property.

Explanation: 6×298 = 6×(200+90+8)
= (6×200)+( 6×90)+( 6×8)
= 1200+540+48
= 1788

Find the product. Tell which strategy you used.

Question 5.
14 × 50 = _____

Answer: 700, Halving and doubling.

Explanation: 14×50= (14×25)+(7×50)
= 350+350
= 700

Question 6.
32 × 25 = _____

Explanation: 32 × 25= 32× (20+5)
=(32×20)+(32×5)
=640+160
=800

Question 7.
8 × 25 × 23 = _____

Answer: 4,600, Associative property.

Explanation: 8×25×23=(8×25)× 23
=(200) ×23
4,600

Practice: Copy and Solve Use a strategy to find the product.

Question 8.
16 × 400 = _____

Answer: 6400, Distributive Property.

Explanation: 16×400= (8+8)×400
=(8×400)+ (8×400)
=3200+3200
=6400

Question 9.
3 × 31 × 10 = _____

Answer: 930, Associative property.

Explanation: 3×31×10= (3×31)×10
=(93) ×10
=930

Question 10.
3 × 199 = _____

Answer: 597, Distributive property.

Explanation: 3×199=3×(100+90+9)
=(3×100)+(3×90)+(3×9)
=300+270+27
= 597

Question 11.
3 × 1,021 = _____

Answer: 3063, Distributive Property.

Explanation: 3×1021= 3×(1000+20+1)
=(3×1000)+(3×20)+(3×1)
=3000+60+3
=3063

Identify Relationships Algebra Use mental math to find the unknown number.

Question 12.
21 × 40 = 840, so
21 × 42 = _____

Answer: 882

Explanation: By Distributive property 21 × 42= 21(40+2)
=(21×40)+(21×2)
=840+42
=882

Question 13.
9 × 60 = 540, so
18 × 30 = _____

Answer: 540

Explanation: As one factor is halved and the other one is doubled and the result is an equivalent expression.

Question 14.
The science museum sells dinosaur models to schools and libraries for $107 each. The town library buys 3 models. The town elementary school buys 5 models. What is the total cost of the models the town buys?

Answer: $856.

Explanation: The cost of each dinosaur model is $107, And the town library buys 3 models which cost 107×3= 321, and town elementary school buys 5 models which cost 107×5= 535. Total cost is 321+535= 856.

Question 15.
Kyle and Karen each bought 6 books of ride tickets at the fair. Each book has 15 tickets. How many tickets did they buy altogether?

Answer: 180 tickets

Explanation: Kyle and Karen each bought 6 books each that means total of 12 books and each book has 15 tickets. So total tickets both bought are 12×15= 180

Multiply Using Partial Products – Page No. 110

Use the table for 16–18.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 36

Question 16.
Three thousand, forty-three people buy tickets at the gate for Section N and one hundred people buy tickets at the gate for Section L. How much money is collected for Section N and Section L at the gate?

Answer: $79575.

Explanation: As 3043 people bought tickets at the gate for Section N, So 3043×25= $76075 and 100 people bought tickets at the gate for Section L, So 100×35= $3500. The total money collected by both sections is 76075+3500= 79575.

Question 17.
Use Diagrams Tina and 3 of her friends buy the full season plan for Section M. If there are 45 games in the full season, how much money do they spend?

Answer: $4500.

Explanation: Tina and 3 of her friends which means a total of 4 members bought full season for Section M which costs $25 for each, So total cost is 25×4= 100. If there are 45 games in full seasons then 45×100= $4500.

Question 18.
When the full season tickets first went on sale, 2,000 Full Season tickets sold for Section N. Two weeks after the tickets first went on sale, another 1,500 full season tickets were sold for Section N. How much money was spent on full season tickets for Section N in total? How much more money was spent when the tickets first went on sale than after the first two weeks?
$ _____ was spent on full season tickets for Section N in total;

Answer: $70,000. $10,000 more

Explanation: The first sale tickets sold are 2,000 for Section N which is 2,000×20= 40,000.
And in next sale 1500 tickets sold out which is 1500×20= 30,000. Total money spent are 40,000+30,000= 70,000.

Question 19.
Find 6 × 407. Show your work and explain why the strategy you chose works best with the factors.

Answer: 2,442

Explanation: By using Distributive property 6×407= 6×(400+7)
=(6×400)+(6×7)
=2400+42
=2,442.

Common Core – Multiply Using Mental Math – Page No. 111

Find the product. Tell which strategy you used.

Question 1.
6 × 297
Think: 297 = 300 – 3
6 × 297 = 6 × (300 – 3)
= (6 × 300) – (6 × 3)
= 1,800 – 18
= 1,782;
use subtraction

Question 2.
8 × 25 × 23 = _____

Answer: 4,600. Associative property.

Explanation: Associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same.
8 × 25 × 23= (8×25)×23
=200×23
=4600

Question 3.
8 × 604 = _____

Answer: 4832, Use Addition.

Explanation: 604= 600+4
8×604= 8×(600+4)
=(8×600)+(8×4)
=4800+32
=4832.

Question 4.
50 × 28 = _____

Answer: 1400, Halving and doubling.

Explanation: 50×28= (25×28)+(50×14)
=700+700
=1400

Question 5.
9 × 199 = _____

Answer: 1,791

Explanation: By Distributive property 9 × 199= 9 ×(100+90+9)
=(9×100)+(9×90)+(9×9)
=900+810+81
= 1791

Question 6.
20 × 72 × 5 = _____

Answer: 7,200.

Explanation: Associative property states that the terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same.
20 × 72 × 5= (20×72) ×5
=1440×5
=7,200.

Question 7.
32 × 25 = _____

Answer: 800.

Explanation: Multiplication.
32×25= 800.

Problem Solving

Question 8.
Section J in an arena has 20 rows. Each row has 15 seats. All tickets cost $18 each. If all the seats are sold, how much money will the arena collect for Section J?

Answer: $5400.

Explanation: Total rows in the arena are 20 rows and each row has 15 seats. So total seats are 20×15= 300 seats. And each ticket cost is $18, So the total ticket price is 300×15= 5400.

Question 9.
At a high-school gym, the bleachers are divided into 6 equal sections. Each section can seat 395 people. How many people can be seated in the gym?

Answer: 2,370 people.

Explanation: Total sections are 6 and each section contains 395 people. So total members can be seated in the gym are 395×6= 2,370 people.

Common Core – Multiply Using Mental Math – Lesson Check – Page No. 112

Question 1.
Pencils come in cartons of 24 boxes. A school bought 50 cartons of pencils for the start of school. Each box of pencils cost $2. How much did the school spend
on pencils?
Options:
a. $240
b. $1,200
c. $2,400
d. $4,800

Answer: c

Explanation: Total boxes of pencils are 24 and a school bought 50 cartons of pencils. So total no. of boxes are 24×50=1200 and each box of pencils cost $2. So 1200×2= 2400 school has spent.

Question 2.
The school also bought 195 packages of markers. There are 6 markers in a package. How many markers did the school buy?
Options:
a. 1,170
b. 1,195
c. 1,200
d. 1,230

Answer: a

Explanation: The school bought 195 packages of markers and each package contains 6 markers, So total markers are 195×6= 1170

Spiral Review

Question 3.
Alex has 175 baseball cards. Rodney has 3 times as many baseball cards as Alex. How many fewer cards does Alex have than Rodney?
Options:
a. 700
b. 525
c. 450
d. 350

Answer: d

Explanation: Alex has 175 baseball cards and Rodney has 3 times as many as Alex, So total no. of cards Rodney have are 175×3= 525. And Alex has 525-175= 350 fewer cards than Rodney.

Question 4.
A theater seats 1,860 people. The last 6 shows have been sold out. Which is the best estimate of the total number of people attending the last 6 shows?
Options:
a. fewer than 6,000
b. about 6,000
c. fewer than 12,000
d. more than 20,000

Answer: c

Explanation:  No. of seats in a theater are 1,860 people and last 6 shows have been sold out, So 1,860×6= 11,160 which are fewer than 12,000.

Question 5.
At one basketball game, there were 1,207 people watching. At the next game, there were 958 people. How many people in all were at the two games?
Options:
a. 2,155
b. 2,165
c. 2,265
d. 10,787

Answer: b

Explanation: There are 1207 people are watching basketball game and in the next game 958 people are there. So total no. of people are 1,207+958= 2165.

Question 6.
Bill bought 4 jigsaw puzzles. Each puzzle has 500 pieces. How many pieces are in all the puzzles altogether?
Options:
a. 200
b. 900
c. 2,000
d. 20,000

Answer: c

Explanation: Bill bought 4 jigsaw puzzle and each puzzle has 500 pieces. So altogether pieces are 500×4= 2000.

Multiply Using Mental Math – Page No. 115

Question 1.
The seats in Sections A and B of the stadium are all taken for the last show. Section A has 8 rows of 14 seats each. Section B has 6 rows of 16 seats each. How many people are seated in Sections A and B for the last show?
First, draw and label a diagram. Next, find the number of seats in each section.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 37
Last, find the total number of seats.
_____ + _____ = _____

Answer: 112+96= 208.

Explanation: As section A has 8 rows and 14 seats each, So 14×8= 112 and Section B has 6 rows and 16 seats each, So 16×6= 96. Total no. of people are seated in Section A and Section B are
112+96= 208.

Question 1.
There are _____________ people seated in Sections A and B for the last show.

Answer: 208.

Explanation: As Section A has 112 people and Section B has 96 people, So 112+96= 208.

Question 2.
What if Sections A and B each had 7 rows? How many people would have been seated in Sections A and B?

Answer: 210

Explanation: As section A has 7 rows and 14 seats each, So 14×7= 98 and Section B has 7 rows and 16 seats each, So 16×7= 112. Total no. of people are seated in Section A and Section B are
112+98= 210.

Question 3.
Brenda’s vegetable garden has 13 rows with 8 plants in each row. Brenda plans to plant peppers in the first 2 rows and the last 2 rows of the garden. The rest of the rows will be tomatoes. How many tomato plants will Brenda plant?

Answer: 72 tomato plants

Explanation: Brenda’s vegetable garden has 13 rows with 8 plants in each row as she plans to plant first 2 rows and last 2 rows with pepper, So 13-4= 9 rows contains tomato plants and each row contains 8 plants, So 9×8= 72 tomato plants.

Question 4.
There are 8 rows of 22 chairs set up for an awards ceremony at the school. In each row, the 2 chairs on each end are reserved for students receiving awards. The rest of the chairs are for guests. How many chairs are there for guests?

Answer: 144 Chairs.

Explanation: As there are 8 rows with 22 chairs in each row, So total no. of chairs is 22×8= 176 chairs. As 2 chairs at each end are reserved for students receiving the award, So total chairs reserved are 8×4=32. So remaining chairs are 176-32= 144.

Multiply Using Mental Math – Page No. 116

Use the graph for 5–6.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 38

Question 5.
Mr. Torres took his students to the dolphin show. Each row in the stadium had 11 seats. One adult sat at each end of a row, and each group of 4 students was seated between 2 adults. Mr. Torres sat by himself. How many adults were there?
_____ adults including Mr. Torres

Answer: 13 adults.

Explanation: First we must find total no. of rows, As there are 24 students each group contains 4 students, So 24 4= 6 rows. And one adult sat in each end of the row, So in 6 rows 2 people will sit. Therefore total adults are 6×2=12 adults+ Mr. Torres= 13 adults.

Question 6.
Another stadium section has 24 rows of 10 seats each. Describe at least two ways Mrs. Allen’s class can sit if an equal number of students sit in each row.

Answer: 9 rows of 4 students or 6 rows of 6 students.

Explanation: As there are 36 students in Mrs. Allen’s class. So students can sit in 6 rows of 6 students or 9 rows of 4 students.

Question 7.
Carol, Ann, and Liz each bought a toy fish. Carol’s fish is 10 inches longer than Ann’s fish. Liz’s fish is 2 inches longer than twice the length of Ann’s fish. Ann’s fish is 12 inches long. Find the length of each toy fish.
Carol’s: _____ in.         Liz’s: _____ in.

Answer: Carol’s: 22 in., Liz’s: 26in.

Explanation: Ann’s fish is 12 inches longer and Carol’s fish is 10 inches longer than Ann’s fish which means 10+12= 22 inches, So Carol’s fish is 22 inches. Liz’s fish is 2 inches longer than twice the length of Ann’s fish, which means (2×12) +2=24+2= 26 inches.

Question 8.
Evaluate Relationships Nell made a secret code. Each code word has 2 letters. Each word begins with a consonant and ends with a vowel. How many code words can Nell make with 3 consonants and 2 vowels?
_____ code words

Answer: 6 ways.

Explanation: As each word begins with a consonant and ends with a vowel, So the first letter can be any one of 3 consonants and the second letter can be either one of 2 vowels. So Nell can make 3×2= 6 ways.

Question 9.
Allie is building a patio. The patio will have 8 tiles in each of 13 rows. She has already built the center section with 4 tiles in each of 7 rows. How many more tiles are needed to complete the patio? Show your work.

Answer: 76 tiles.

Explanation: Allie had 8 tiles in each of 13 rows, which means 13×8= 104 tiles. And the center section was built by 4 tiles in each of 7 rows, which means 4×7= 28 tiles. So 104-28= 76 tiles more needed to complete the patio.

Common Core – Problem Solving Multistep Multiplication Problems – Page No. 117

Solve each problem.

Question 1.
A community park has 6 tables with a chessboard painted on top. Each board has 8 rows of 8 squares. When a game is set up, 4 rows of 8 squares on each board are covered with chess pieces. If a game is set up on each table, how many total squares are NOT covered by chess pieces?
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 39
4 × 8 = 32
32 × 6 = 192 squares

Question 2.
Jonah and his friends go apple picking. Jonah fills 5 baskets. Each basket holds 15 apples. If 4 of Jonah’s friends pick the same amount as Jonah, how many apples do Jonah and his friends pick in all? Draw a diagram to solve the problem.

Answer: 375 apples.

Explanation: As Jonah fills 5 baskets which holds 15 apples, So Jonah picked 15×5= 75 apples.
And 4 of his friends pick same amount of apples, which means 75×4=300. So total apples Jonah and his friends picked up are 300+75= 375 apples.

Question 3.
There are 6 rows of 16 chairs set up for the third-grade play. In the first 4 rows, 2 chairs on each end are reserved for teachers. The rest of the chairs are for students. How many chairs are there for students?

Answer: 80 chairs.

Explanation: As there are 6 rows of 16 chairs which means 16×6= 96 total chairs. And first 4 rows 2 chairs on each end are reserved for teachers, which means 4×4= 16 chairs are reserved for teachers. So 96-16= 80 chairs are left for the students.

Common Core – Problem Solving Multistep Multiplication Problems – Lesson Check – Page No. 118

Question 1.
At a tree farm, there are 9 rows of 36 spruce trees. In each row, 14 of the spruce trees are blue spruce. How many spruce trees are NOT blue spruce?
Options:
a. 126
b. 198
c. 310
d. 324

Answer: b

Explanation: There are 9 rows of 36 spruce trees which means 9×36= 324 spruce trees. And in that, each row has 14 blue spruce trees which mean 14×9= 126. So 324-126= 198 spruce trees are not blue.

Question 2.
Ron is tiling a countertop. He needs to place 54 square tiles in each of 8 rows to cover the counter. He wants to randomly place 8 groups of 4 blue tiles each and have the rest of the tiles be white. How many white tiles will Ron need?
Options:
a. 464
b. 432
c. 400
d. 32

Answer: c

Explanation: Ron places 54 square tiles in each of 8 rows which means 54×8=432 tiles. And he randomly places 8 groups of 4 blue tiles which means 8×4= 32 blue tiles are placed. So no. of white tiles are 432-32= 400.

Question 3.
Juan reads a book with 368 pages. Savannah reads a book with 172 fewer pages than Juan’s book. How many pages are in the book Savannah reads?
Options:
a. 196
b. 216
c. 296
d. 540

Answer: a

Explanation: Juan reads a book with 368 pages and Savannah reads a book with 172 fewer pages than Juan’s which means 368-172= 196 pages are in Savannah’s read.

Question 4.
Hailey has bottles that hold 678 pennies each. About how many pennies does she have if she has 6 bottles filled with pennies?
Options:
a. 3,600
b. 3,900
c. 4,200
d. 6,000

Answer: c

Explanation: Let’s round off 678 to 700 and Hailey has bottles that hold 700 pennies each and if she has 6 bottles filled with pennies which means 700×6= 4200.

Question 5.
Terrence plants a garden that has 8 rows of flowers, with 28 flowers in each row. How many flowers did Terrence plant?
Options:
a. 1,664
b. 224
c. 164
d. 36

Answer: b

Explanation: As the garden has 8 rows of flowers with 28 flowers in each row, So no. of flowers is 28×8= 224.

Question 6.
Kevin has 5 fish in his fish tank. Jasmine has 4 times as many fish as Kevin has. How many fish does Jasmine have?
Options:
a. 15
b. 20
c. 25
d. 30

Answer: b

Explanation: As Kevin has 5 fishes and Jasmine has 4 times as many as Kevin which means 5×4= 20 fishes Jasmine has.

Problem Solving Multistep Multiplication Problems – Page No. 121

Question 1.
Use the model to find the product.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 40
2 × 36 = _____

Answer: 72

Explanation: 2×36=2×(30+6)
=(2×30)+(2×6)
=60+12
=72

Estimate. Then record the product.

Question 2.
4 2
× 4
—————-
Estimate: _________
Product: _________

Answer:
Estimate: 160
Product: 168

Explanation: Round off 42 to 40 and estimated value is 40×4= 160 and 42×4= 168
4 2
× 4
——-
168

Question 3.
3 2
× 2
—————-
Estimate: _________
Product: _________

Answer:
Estimate: 60
Product: 64

Explanation: Round off 32 to 30 and the estimated value is 30×2= 60 and 32×2= 64.
3 2
× 2
——
64

Question 4.
8 1
× 5
—————-
Estimate: _________
Product: _________

Answer:
Estimate: 400
Product: 405

Explanation: Round off 81 to 80 and the estimated value is 80×5= 400 and 81×5= 405.
81
× 5
——
405

Question 5.
$6 3
× 7
—————-
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 420
Product: 441

Explanation: Round off 63 to 60 and the estimated value is 60×7= 420 and 63×7= 441.
$63
× 7
——
441

Estimate. Then record the product.

Question 6.
3 3
× 2
—————-
Estimate: _________
Product: _________

Answer:
Estimate: 60
Product: 66

Explanation: Round off 33 to 30 and the estimated value is 30×2= 60 and 33×2= 66.
3 3
× 2
——
66

Question 7.
$2 5
× 3
—————-
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 90
Product: 75

Explanation: Round off 25 to 30 and the estimated value is 30×3= 90 and 25×3= 75.
$25
× 3
——
75

Question 8.
3 6
× 8
—————-
Estimate: _________
Product: _________

Answer:
Estimate: 320
Product: 288

Explanation: Round off 36 to 40 and the estimated value is 40×8= 320 and 36×8= 288.
36
× 8
——
288

Question 9.
$9 4
× 5
—————-
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 450
Product: 470

Explanation: Round off 94 to 90 and the estimated value is 90×5= 450 and 94×5= 470.
$94
× 5
——
470

Practice: Copy and Solve Estimate. Then record the product.

Question 10.
3 × 82
Estimate: _________
Product: _________

Answer:
Estimate: 240
Product: 246

Explanation: Round off 82 to 80 and the estimated value is 80×3= 240 and 82×3= 246.
3 2
× 2
——
246

Question 11.
9 × 41
Estimate: _________
Product: _________

Answer:
Estimate: 360
Product: 369

Explanation: Round off 41 to 40 and the estimated value is 40×9= 360 and 41×9= 369.
41
×9
——
369

Question 12.
7 × $23
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 140
Product: 161

Explanation: Round off 23 to 20 and the estimated value is 20×7= 140 and 23×7= 161.
23
× 7
——
161

Question 13.
8 × $54
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 400
Product: 432

Explanation: Round off 54 to 50 and the estimated value is 50×8= 400 and 54×8= 432.
54
×8
——
432

Identify Relationships Algebra Write a rule. Find the unknown numbers.

Question 15.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 41

Answer: 36, 60

Explanation: If 1 carton contains 12 eggs then 3 cartons will have 3×12= 36 and 5 cartons contains 5×12= 60.

Question 16.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 42

Answer: 160, 192

Explanation: If 2 rows have 32 seats then 5 rows will have 5×32= 160 and 6 rows will have 6×32= 192 seats

Question 17.
It will cost $73 per hour to rent a sailboat and $88 per hour to rent a ski boat. How much more will it cost to rent a ski boat than a sailboat for 4 hours?

Answer: $60.

Explanation: Cost of sailboat to rent per hour is $73 and for 4 hours it costs $73×4= $292. And cost of Ski boat to rent per hour is $88 and for 4 hours it costs $88×4= $352. So $352-$292= $60 much more costs for a ski boat than a sailboat.Problem Solving Multistep Multiplication Problems – Page No. 122

Use the table for 18–19.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 43

Question 18.
At the speeds shown, how much farther could a black-tailed jackrabbit run than a desert cottontail in 7 seconds?

Answer: 203 ft.

Explanation: Black-tailed jackrabbit runs at a speed of 51 ft per sec, So in 7 seconds jackrabbit runs 51×7= 357 ft and Desert cottontail runs at a speed of 22 ft per sec, So in 7 seconds it runs 22×7= 154 ft. So 357-154= 203 ft could a black-tailed jackrabbit run than a desert cottontail in 7 seconds.

Question 19.
A black-tailed jackrabbit hops about 7 feet in a single hop. How far can it hop in 5 seconds?
about ______ hops

Answer: 35 hops.

Explanation: As black-tailed jackrabbit hops about 7 feet in a single hop, So in 5 seconds it hops 7×5= 35.

Question 20.
Mr. Wright bought a 3-pound bag of cat food and a 5-pound bag of dog food. There are 16 ounces in each pound. How many ounces of pet food did Mr. Wright buy?

Answer: 128 ounces.

Explanation: Mr. Wright bought a 3-pound bag of cat food and there are 16 ounces in each pound, So 3×16= 48 ounces and 5pound bag of dog food as 5×16= 80 ounces. So total ounces of pet food are 48+80= 128 ounces.

Question 21.
The sum of two numbers is 31. The product of the two numbers is 150. What are the numbers?

Answer: 6 and 25.

Explanation: Let the numbers be X and Y, So the sum of two numbers is 31 which means X+Y=31 and product of two numbers is 150 which means X×Y=150. So X=31-Y then replace X=31-Y, So (31-Y)×Y= 150, then 31Y-Y^2 = 150 which is Y^2 – 31Y+ 150 = 0. By factorization Y= 25 and X×25= 150 then X= 6. Therefore X= 6 and Y= 25.

Question 22.
Use Reasoning 6 × 87 is greater than 5 × 87. How much greater? Explain how you know without multiplying.

Answer: 6×87>5 × 87.

Explanation: As 6 is greater than 5, So 6×87 is greater than 5 × 87

Question 23.
Multiply 6 × 73. For 23a–23d, select True or False for each statement.
a. A reasonable estimate of the product is $420.
i. True
ii. False

Answer: False

Explanation: 6×73= 438

Question 23.
b. Using partial products, the products are 42 and 180.
i. True
ii. False

Answer: False

Explanation: The partial products are 420 and 18

Question 23.
c. Using regrouping, 18 ones are regrouped as 8 tens and 1 one.
i. True
ii. False

Answer: False.

Explanation: 8 tens and 1 one means 81.

Question 23.
d. The product is 438.
i. True
ii. False

Answer: True

Explanation: 6×73= 438


Common Core – Multiply 2-Digit Numbers with Regrouping – Page No. 123

Estimate. Then record the product.

Question 1.
Estimate: 150
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 44

Question 2.
3 2
× 8
Estimate: ________
Product: ________

Answer:
Estimate: 240
Product: 256

Explanation: Round off 32 to 30 and 30×8=240.
3 2
× 8
————
256

Answer:
Estimate: 240
Product: 256

Explanation: Round off 32 to 30 and 30×8=240.
3 2
× 8
————
256

Answer:
Estimate: 240
Product: 256

Explanation: Round off 32 to 30 and 30×8=240.
3 2
× 8
————
256

Question 3.
$5 5
× 2
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $120
Product: $110

Explanation: Round off 55 to 60 and 60×2= 120.
$5 5
× 2
————-
$110

Question 4.
6 1
× 8
Estimate: ________
Product: ________

Answer:
Estimate: 480
Product: 488

Explanation: Round off 61 to 60 and 60×8= 480.
6 1
× 8
———–
488

Question 5.
3 7
× 9
Estimate: ________
Product: ________

Answer:
Estimate: 360
Product: 333

Explanation: Round off 37 to 40 and 40×6= 360.
3 7
× 9
———–
333

Question 6.
$1 8
× 7
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $140
Product: $126

Explanation: Round off 18 to 20 and 20×7= 140.
$1 8
× 7
———-
$126

Question 7.
8 3
× 5
Estimate: ________
Product: ________

Answer:
Estimate: 400
Product: 415

Explanation: Round off 83 to 80 and 80×5= 400.
8 3
× 5
——-
415

Question 8.
9 5
× 8
Estimate: ________
Product: ________

Answer:
Estimate: 800
Product: 760

Explanation: Round off 95 to 100 and 100×8= 800.
9 5
× 8
——–
760

Question 9.
9 4
× 9
Estimate: ________
Product: ________

Answer:
Estimate: 810
Product: 846

Explanation: Round off 94 to 90 and 90×9= 810.
9 4
× 9
——-
846

Question 10.
5 7
× 6
Estimate: ________
Product: ________

Answer:
Estimate: 360
Product: 342

Explanation: Round off 57 to 60 and 60×6= 360.
5 7
× 6
——
342

Question 11.
7 2
× 3
Estimate: ________
Product: ________

Answer:
Estimate: 210
Product: 216

Explanation: Round off 72 to 70 and 70×3= 210.
7 2
× 3
——-
216

Question 12.
$7 9
× 8
Estimate: ________
Product: ________

Answer:
Estimate: $640
Product: $632

Explanation: Round off 79 to 80 and 80×8= 640.
$7 9
× 8
——-
$632

Problem Solving

Question 13.
Sharon is 54 inches tall. A tree in her backyard is 5 times as tall as she is. The floor of her treehouse is at a height that is twice as tall as she is. What is the difference, in inches, between the top of the tree and the floor of the treehouse?

Answer: 162 inches.

Explanation: Sharon is 54 inches tall and a tree in her backyard is 5 times as tall as she is which means 54×5= 270. And her treehouse is twice as tall as she is which means 54×2= 108 inches. So the difference between the top of the tree and the floor of the treehouse is 270-108= 162 inches.

Question 14.
Mr. Diaz’s class is taking a field trip to the science museum. There are 23 students in the class, and a student admission ticket is $8. How much will the student
tickets cost?

Answer: $184.

Explanation: Total no. of students are 23 and tickets cost is $8, So 23×8= $184.

Common Core – Multiply 2-Digit Numbers with Regrouping – Lesson Check – Page No. 124

Question 1.
A ferryboat makes four trips to an island each day. The ferry can hold 88 people. If the ferry is full on each trip, how many passengers are carried by the ferry
each day?
Options:
a. 176
b. 322
c. 332
d. 352

Answer: d

Explanation: Total trips made by the ferryboat each day are 4 and it can hold 88 people, So 88×4= 352 passengers are carried by ferryboat each day.

Question 2.
Julian counted the number of times he drove across the Seven Mile Bridge while vacationing in the Florida Keys. He crossed the bridge 34 times. How many miles in all did Julian drive crossing the bridge?
Options:
a. 328 miles
b. 248 miles
c. 238 miles
d. 218 miles

Answer: c

Explanation: No. of times Julian drive across the bridge is 7 miles and he crossed the bridge 34 times, So 34×7= 238 miles Julian drive crossing the bridge.

Spiral Review

Question 3.
Sebastian wrote the population of his city as 300,000 + 40,000 + 60 + 7. Which of the following shows the population of Sebastian’s city written in standard form?
Options:
a. 346,700
b. 340,670
c. 340,607
d. 340,067

Answer: d

Explanation: 300,000+40,000+60+7= 340,067.

Question 4.
A plane flew 2,190 kilometers from Chicago to Flagstaff. Another plane flew 2,910 kilometers from Chicago to Oakland. How much farther did the plane that flew to Oakland fly than the plane that flew to Flagstaff?
Options:
a. 720 kilometers
b. 820 kilometers
c. 5,000 kilometers
d. 5,100 kilometers

Answer: a

Explanation: Plane flew from Chicago to Flagstaff is 2,190 km and another plane flew from Chicago to Oakland is 2,910, So 2910-2190= 720 km.

Question 5.
Tori buys 27 packages of miniature racing cars. Each package contains 5 cars. About how many miniature racing cars does Tori buy?
Options:
a. 15
b. 32
c. 100
d. 150

Answer: d

Explanation: Let’s round off 27 packages to 30 and each package contains 5 cars, which means 30×5=150.

Question 6.
Which of the following equations represents the Distributive Property?
Options:
a. 3 × 4 = 4 × 3
b. 9 × 0 = 0
c. 5 × (3 + 4) = (5 × 3) + (5 × 4)
d. 6 × (3 × 2) = (6 × 3) × 2

Answer: c

Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.

Multiply 2-Digit Numbers with Regrouping – Page No. 127

Question 1.
Tell what is happening in Step 1 of the problem.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 45

Answer: Multiplying 4×6

Explanation: In step 1 Multiplying 4×6= 24.

Estimate. Then find the product.

Question 2.
6 0 3
×   4
————
2,400
Estimate: __________
Product: ___________

Answer:
Estimate: 2400
Product: 2412

Explanation: Rounding off 603 to 600 then 600×4= 2400.
6 0 3
×   4
——–
2412

Question 3.
1,935
×    7
————
Estimate: __________
Product: ___________

Answer:
Estimate: 14,000.
Product: 13,545.

Explanation: Rounding off 1935 to 2000 then 2000×7= 14,000.
1,935
×    7
———
13,545

Question 4.
$ 8,326
×       5
————
Estimate: $ __________
Product: $ ___________

Answer:
Estimate: 40,000
Product: 41,630

Explanation: Rounding off 8326 to 8000 then 8000×5= 40,000.
$ 8,326
×       5
———-
41,630

Estimate. Then find the product.

Question 5.
$ 3,316
×       8
—————-
Estimate: $ __________
Product: $ ___________

Answer:
Estimate: 24,000.
Product: 26,528.

Explanation: Rounding off 3316 to 3000 then 3000×8= 24,000.
$ 3,316
×       8
———
26,528

Question 6.
$ 2,900
×       7
—————–
Estimate: $ __________
Product: $ ___________

Answer:
Estimate: 21,000.
Product: 20,300

Explanation: Rounding off 2900 to 3000 then 3000×7= 21,000.
$ 2,900
×       7
———-
20,300

Question 7.
$ 4,123
×       6
—————–
Estimate: $ __________
Product: $ ___________

Answer:
Estimate: 24,000.
Product: 24,738

Explanation: Rounding off 4,123 to 4000 then 4000×6= 24,000.
$ 4,123
×       6
———–
24,738

Question 8.
Mr. Jackson has $5,400 to buy supplies for the school computer lab. He buys 8 boxes of printer ink that cost $149 each and 3 printers that cost $1,017 each. How much money will Mr. Jackson have left after he buys the printer ink and printers?

Answer: $1,157

Explanation: As 8 boxes of printer ink cost $149 each which is $149×8=$1,192 and 3 printers costs $1,017 which is $1,017×3=$3,051. So 3051+1192= 4,243 total spent by Mr. Jackson on Printer ink and printers. The money left are $5,400-$4,243= 1,157.

Practice: Copy and Solve Compare. Write <, >, or = .

Question 9.
5 × 352 _____ 4 × 440

Answer: 5 × 352  = 4 × 440

Explanation: As 5 × 352= 1,760 and 4 × 440= 1,760

Question 10.
6 × 8,167 _____ 9,834 × 5

Answer: 6 × 8,167 <  9,834 × 5

Explanation: As 6 × 8,167= 49,002 and 9,834 × 5= 49,170. So 6 × 8,167 <  9,834 × 5

Question 11.
3,956 × 4 _____ 5 × 7,692

Answer: 3,956 × 4 < 5 × 7,692

Explanation: As 3,956 × 4= 15,824 and 5 × 7,692= 38,460. So 3,956 × 4 < 5 × 7,692

Question 12.
740 × 7 _____ 8 × 658

Answer: 740 × 7 < 8 × 658

Explanation:  As 740 × 7 = 5180 and 8 × 658= 5264. So 740 × 7 < 8 × 658

Question 13.
4 × 3,645 _____ 5 × 2,834

Answer: 4 × 3,645 > 5 × 2,834

Explanation: As 4 × 3,645= 14580 and 5 × 2,834= 14,170. So 4 × 3,645 > 5 × 2,834.

Question 14.
6,573 × 2 _____ 4,365 × 3

Answer: 6,573 × 2 > 4,365 × 3

Explanation: As 6,573 ×2= 13,146 and 4,365 × 3= 13,095. So 6,573 × 2 > 4,365 × 3.

Multiply 2-Digit Numbers with Regrouping – Page No. 128

Question 15.
Airplane tickets to Fairbanks, Alaska, will cost $958 each. Airplane tickets to Vancouver, Canada, will cost $734. How much can the four members of the Harrison family save on airfare by vacationing in Vancouver?

Answer: $896.

Explanation: Airplane tickets cost for Alaska is $958 each. As Harrison family are 4 members so it will cost $958×4= $3,832 And for Vancouver it costs $734 each. So $734×4= $2,936 and Harrison family save $3832-$2936= $896.

Question 16.
Philadelphia, Pennsylvania, is 2,147 miles from Salt Lake City, Utah, and 2,868 miles from Portland, Oregon. What is the difference in the round-trip distances between Philadelphia and each of the other two cities? Explain whether you need an estimate or an exact answer.

Answer: 1,442 mi.

Explanation: The distance between Philadelphia and Salt Lake is 2,147 miles and round-trip distance is 2×2,147= 4,294 miles. And the distance between Philadelphia and Portland is 2,868 miles and the round-trip distance is 2×2868= 5736 miles. So the difference is
5,736-4,294= 1442 miles.

Question 17.
Verify the Reasoning of Others Joe says that the product of a 4-digit number and a 1-digit number is always a 4-digit number. Does Joe’s statement make sense? Explain.

Answer: No, Joe’s statement is incorrect.

Explanation: As there are regrouped thousands, the product of a 4-digit number and a 1-digit number can have 5 digits.

Question 18.
What number is 150 more than the product of 5 and 4,892? Explain how you found the answer.

Answer: 24,610.

Explanation: Let’s find the product of 5×4,892= 54,460 and then add 150 to the product, So 24,460+150= 24,610.

Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 129

Estimate. Then find the product.

Question 1.
Estimate: 4,000
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Common Core img 46

Question 2.
5,339
×    6
————-
Estimate: ________
Product: ________

Answer:
Estimate: 30,000
Product: 32,034

Explanation: Round off 5,339 to 5000 then 5000×6= 30,000.
5,339
×    6
———-
32,034

Question 3.
$879
×   8
————-
Estimate: $ ________
Product: $ ________

Answer:
Estimate: $7,200.
Product: $7,032.

Explanation: Round off 879 to 900 then 900×8= 7,200.
$879
×   8
——–
7,032

Question 4.
3,182
×    5
————-
Estimate: ________
Product: ________

Answer:
Estimate: 15,000
Product: 15,910

Explanation: Round off 3,182 to 3000 then 3000×5= 15,000.
3,182
×    5
———-
15,910

Question 5.
4,616
×    3
————-
Estimate: ________
Product: ________

Answer:
Estimate: 15,000
Product: 13,848

Explanation: Round off 4,616 to 5,000 then 5000×3= 15,000.
4,616
×    3
———
13,848

Question 6.
2,854
×    9
————-
Estimate: ________
Product: ________

Answer:
Estimate: 27,000
Product: 25,686

Explanation: Round off 2,854 to 3000 then 3000×9= 27,000.
2,854
×    9
———
25,686

Question 7.
7,500
×    2
————-
Estimate: ________
Product: ________

Answer:
Estimate: 16,000
Product: 15,000

Explanation: Round off 7,500 to 8000 then 8000×2= 16,000.
7,500
×    2
———
15,000

Question 8.
9 4 8
×   7
————-
Estimate: ________
Product: ________

Answer:
Estimate: 6,300
Product: 6,636

Explanation: Explanation: Round off 948 to 900 then 900×7= 6,300.
9 4 8
×   7
——-
6,636

Question 9.
1,752
×    6
————-
Estimate: ________
Product: ________

Answer:
Estimate: 12,000.
Product: 10,512.

Explanation: Explanation: Round off 1,752 to 2000 then 2000×6= 12,000.
1,752
×    6
———–
10,512

Question 10.
5 5 0
×   9
————-
Estimate: ________
Product: ________

Answer:
Estimate: 5,400
Product: 4,950

Explanation: Round off 550 to 600 then 600×9= 5,400.
5 5 0
×   9
——–
4,950

Question 11.
6,839
×    4
————-
Estimate: ________
Product: ________

Answer:
Estimate: 28,000
Product: 27,356

Explanation: Round off 6,839 to 7000 then 7000×4= 28,000.
6,839
×    4
———-
27,356

Question 12.
$9,614
×      6
————-
Estimate: $ ________
Product: $ ________

Answer:
Estimate: 60,000.
Product: 57,684.

Explanation: Round off 9,614 to 10,000 then 10,000×6= 60,000.
$9,614
×      6
———-
57,684

Problem Solving

Question 13.
Lafayette County has a population of 7,022 people. Columbia County’s population is 8 times as great as Lafayette County’s population. What is the population of Columbia County?

Answer: 56,176 people

Explanation: Lafayette County has a population of 7,022 people and Columbia County’s population is 8 times Lafayette County which means 7,022×8= 56,176.

Question 14.
A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all?

Answer: 54,750 pounds.

Explanation: As the seafood company sold 9,125 pounds of fishes last month and 6 seafood companies also sold the same amount which means 9,125×6= 54,750 pounds.

Common Core – Multiply 3-Digit and 4-Digit Numbers with Regrouping – Lesson Check – Page No. 130

Question 1.
By recycling 1 ton of paper, 6,953 gallons of water are saved. How many gallons of water are saved by recycling 4 tons of paper?
Options:
a. 24,602 gallons
b. 27,612 gallons
c. 27,812 gallons
d. 28,000 gallons

Answer: c

Explanation: As 1 ton of paper saves 6,953 gallons of water, So 4 tons of paper can save 6,953×4= 27,812.

Question 2.
Esteban counted the number of steps it took him to walk to school. He counted 1,138 steps. How many steps does he take walking to and from school each day?
Options:
a. 2,000
b. 2,266
c. 2,276
d. 22,616

Answer: c

Explanation: As Esteban counted 1,138 steps to school and from school, it will be 1,138+1,138=2,276 steps

Spiral Review

Question 3.
A website has 13,406 people registered. What is the word form of this number?
Options:
a. thirty thousand, four hundred six
b. thirteen thousand, four hundred sixty
c. thirteen thousand, four hundred six
d. thirteen thousand, six hundred six

Answer: c

Explanation: 13,406 in words are thirteen thousand four hundred six.

Question 4.
In one year, the McAlister family drove their car 15,680 miles. To the nearest thousand, how many miles did they drive their car that year?
Options:
a. 15,000 miles
b. 15,700 miles
c. 16,000 miles
d. 20,000 miles

Answer: c

Explanation: 15,680 nearest thousand is 16,000

Question 5.
Connor scored 14,370 points in a game. Amy scored 1,089 fewer points than Connor. How many points did Amy score?
Options:
a. 12,281
b. 13,281
c. 15,359
d. 15,459

Answer: b

Explanation: Connor scored 14,370 points and Amy scored 1,089 fewer points, So Amy score is 14,370-1089= 13,281.

Question 6.
Lea buys 6 model cars that each cost $15. She also buys 4 bottles of paint that each cost $11. How much does Lea spend in all on model cars and paint?
Options:
a. $134
b. $90
c. $44
d. $36

Answer: a

Explanation: Lea buys 6 model cars that each cost $15, So the total cost for cars is $15×6= $90.
And 4 bottles of paint that each cost $11, So the total cost of paints is $11×4= $44. Then
$90+$44= $134.

Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 133

Question 1.
Use the order of operations to find the value of n.
5 × 17 + 5 × 20 – 32 = n
n = ______

Answer: 153

Explanation: (5×17)+5×20 –32=
= 85+100-32
=185-32
=153

Find the value of n.

Question 2.
3 × 22 + 7 × 41 – 24 = n
n = ______

Answer: 329.

Explanation: 3×22+7×41–24
=66+287-24
=329.

Question 3.
4 × 34 + 6 × 40 – 66 = n
n = ______

Answer: 310.

Explanation: 4×34+6×40–66=
=136+240-66
=310.

Question 4.
2 × 62 + 8 × 22 – 53 = n
n = ______

Answer: 247

Explanation: 2×62+8×22–53=
= 124+176-53
=300-53
=247.

Question 5.
6 × 13 + 9 × 34 – 22 = n
n = ______

Answer: 362.

Explanation: 6×13+9×34–22=
=78+306-22
=384-22
=362.

Find the value of n.

Question 6.
8 × 42 + 3 × 59 – 62 = n
n = ______

Answer: 451.

Explanation: 8×42+3×59–62=
=336+177-62
=513-62
=451.

Question 7.
6 × 27 + 2 × 47 – 83 = n
n = ______

Answer: 173

Explanation: 6×27+2×47–83=
=162+94-83
=256-83
=173

Question 8.
Maggie has 3 binders with 25 stamps in each binder. She has 5 binders with 24 baseball cards in each binder. If she gives 35 stamps to a friend, how many stamps and cards does she have left?

Answer: 160

Explanation: Maggie has 3 binders with 25 stamps each binder, so total stamps are 3×25= 75. And 5 binders with 24 baseball cards in each binder. So total baseball cards are 24×5=120.
As she gave 35 stamps to a friend, so 75-35= 40. Total stamps and cards she has
120+40= 160

Question 9.
Evaluate Maddox has 4 boxes with 32 marbles in each box. He has 7 boxes with 18 shells in each box. If he gets 20 marbles from a friend, how many marbles and shells does he have?

Answer: 274.

Explanation: Maddox has 4 boxes and 32 marbles in each box, so 4×32= 128. And 7 boxes with 18 shells in each box which means 7×18= 126. And he got 20 marbles from a friend, so
128+20= 148 marbles. So total marbles and shells he has 148+126= 274.

Question 10.
The soccer team sells 54 bagels with cream cheese for $2 each and 36 muffins for $1 each during a bake sale. The coach uses the money to buy socks for the 14 players. The socks cost $6 per pair. How much money does the coach have left? Explain how you found your answer.

Answer: $60.

Explanation: Soccer team sells 54 bagels with cream cheese for $2 each, so 54×2= $108 total amount raised by selling bagels with cream cheese. And 36 muffins for $1 each which means 36×$1= $36 raised by selling muffins. So the total amount raised is $108+$36= $144. And he uses the money to buy socks for 14 players and each pair is $6, So 14×$6= $84 needed to buy socks for the players. So $144-$84= $60 left with the coach after buying socks for the players.

Multiply 3-Digit and 4-Digit Numbers with Regrouping – Page No. 134

Question 11.
What’s the Error? Dominic has 5 books with 12 postcards in each book. He has 4 boxes with 20 coins in each box. If he gives 15 post cards to a friend, how many postcards and coins does he have?
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 47
Dominic drew this model.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 48
Dominic used these steps to solve.
5 × 12 + 4 × 20 – 15 = n
60 + 4 × 20 – 15 = n
64 × 20 – 15 = n
1,280 – 15 = n
1,265 = n
Look at the steps Dominic used to solve this problem. Find and describe his error.

Answer: Dominic didn’t follow the order of operations

Question 11.
Use the correct steps to solve the problem.

Answer:
5 × 12 + 4 × 20 – 15 = n
60+4×20-15=n
60+80-15=n
140-15=n
125=n

Common Core – Solve Multistep Problems Using Equations – Page No. 135

Find the value of n.

Question 1.
4 × 27 + 5 × 34 – 94 = n
108 + 5 × 34 – 94 = n
108 + 170 – 94 = n
278 – 94 = n
184 = n

Question 2.
7 × 38 + 3 × 45 – 56 = n
_____ = n

Answer: 345.

Explanation: 7×38+3×45-56=
=266+135-56
=401-56
=345

Question 3.
6 × 21 + 7 × 29 – 83 = n
_____ = n

Answer: 246

Explanation: 6×21+7×29-83=
=126+203-83
=329-83
=246

Question 4.
9 × 19 + 2 × 57 – 75 = n
_____ = n

Answer: 210.

Explanation: 9×19+2×57-75=
=171+114-75
=285-75
=210.

Question 5.
5 × 62 + 6 × 33 – 68 = n
_____ = n

Answer: 440.

Explanation: 5 × 62 + 6 × 33 – 68=
=310+198-68
=508-68
=440

Question 6.
8 × 19 + 4 × 49 – 39 = n
_____ = n

Answer: 309

Explanation: 8×19+4×49-39=
=152+196-39
=348-39
=309

Problem Solving

Question 7.
A bakery has 4 trays with 16 muffins on each tray. The bakery has 3 trays of cupcakes with 24 cupcakes on each tray. If 15 cupcakes are sold, how many muffins and cupcakes are left?

Answer: 121 muffins and cupcakes.

Explanation: 4×16+3×24-15=n
64+3×24-15=n
64+72-15=n
136-15=n
121=n

Question 8.
Katy bought 5 packages of stickers with 25 stickers in each package. She also bought 3 boxes of markers with 12 markers in each box. If she receives 8 stickers from a friend, how many stickers and markers does Katy have now?

Answer: 169 stickers and markers.

Explanation: 5×25+3×12+8=n
125+3×12+8=n
125+36+8=n
169=n

Common Core – Solve Multistep Problems Using Equations – Lesson Check – Page No. 136

Question 1.
What is the value of n?
9 × 23 + 3 × 39 – 28 = n
Options:
a. 240
b. 296
c. 2,310
d. 8,162

Answer: 296

Explanation: 9×23+3×39–28=
=207+117-28
=324-28
=296

Question 2.
Which expression has a value of 199?
Options:
a. 4 × 28 + 6 × 17 – 15
b. 4 × 17 + 6 × 28 – 38
c. 4 × 38 + 6 × 15 – 28
d. 4 × 15 + 6 × 38 – 88

Answer: a

Explanation: 4×28+6×17-15=
=112+102-15
=214-15
=199.

Spiral Review

Question 3.
Which expression shows how you can multiply 9 × 475 using expanded form and the Distributive Property?
Options:
a. (9 × 4) + (9 × 7) + (9 × 5)
b. (9 × 4) + (9 × 70) + (9 × 700)
c. (9 × 400) + (9 × 70) + (9 × 5)
d. (9 × 400) + (9 × 700) + (9 × 500)

Answer: c

Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.
9 × 475= (9×400)+(9×70)+(9×5)

Question 4.
Which equation best represents the comparison sentence?
32 is 8 times as many as 4
Options:
a. 32 = 8 × 4
b. 32 × 8 = 4
c. 32 = 8 + 4
d. 8 + 4 = 32

Answer: a

Explanation: 32=8×4

Question 5.
Between which pair of numbers is the exact product of 379 and 8?
Options:
a. between 2,400 and 2,500
b. between 2,400 and 2,800
c. between 2,400 and 3,000
d. between 2,400 and 3,200

Answer: d

Explanation: 379×8= 3,032

Question 6.
Which of the following statements shows the halving and doubling strategy to find 28 × 50?
Options:
a. 28 × 50 = 14 × 100
b. 28 × 50 = (14 × 25) × (14 × 25)
c. 28 × 50 = (20 × 50) × (8 × 50)
d. 28 × 50 = 2 × (14 × 25)

Answer: a

Explanation: 28×50 = 14×100

Review/Test – Page No. 137

For 1–3, use the table.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 49

Question 1.
What is the cost of 3 Bur Oak trees? Show your work.

Answer: $96.

Explanation: Each Bur oak tree costs $32 for 3 and above, so $32×3=$96.

Question 2.
Mr. Tan buys 4 White Pine trees and 5 Birch trees. What is the cost of the trees? Show your work and explain how you found the answer.

Answer: $188.

Explanation: As 4 white pine trees cost is $37 each, so $37×4= $148 and 5 birch trees cost $8 each, so 5×$8= $40. Total cost of trees are $148+$40= $188.

Question 3.
Rudy will buy 3 Ivory Silk Lilac trees or 2 Bur Oak trees. He wants to buy the trees that cost less. What trees will he buy? How much will he save? Show your work.

Answer: Rudy will take 3 Ivory Silk Lilac trees which costs $66.

Explanation: If Rudy buys 3 Ivory Silk Lilac trees which costs $22 each, so $22×3=$66. And if 2 Bur Oak trees price is $35 each which means $35×2= $70. As Rudy wants to buy the trees that cost less, so he will take 3 Ivory Silk Lilac trees which cost $66.

Review/Test – Page No. 138

Question 4.
For numbers 4a–4d, select True or False for each equation.
a. 7 × 194 = 1,338
i. True
ii. False

Answer: False

Explanation: 7×194= 1,338.

Question 4.
b. 5 × 5,126 = 25,630
i. True
ii. False

Answer: True

Explanation: 5×5,126= 25,630.

Question 4.
c. 8 × 367 = 2,926
i. True
ii. False

Answer: False

Explanation: 8×367= 2,936

Question 4.
d. 4 × 3,952 = 15,808
i. True
ii. False

Answer: True

Explanation: 4×3952= 15,808

Question 5.
Part A
Draw a line to match each section in the model to the partial product it represents.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 50

 

Question 5.
Part B
Then find 3 × 146. Show your work and explain.

Answer: 438.

Explanation: By distributive property
3×146= 3×(100+40+6)
=(3×100)+(3×40)+( 3×6)
=300+120+18
=438.

Review/Test – Page No. 139

Question 6.
For numbers 6a–6c, write an equation or a comparison sentence using the numbers on the tiles.
a.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 51
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 52
______ times as many as ______ is ______ .

Answer: 8 times as many as 4 is 32.

Explanation: 8×4= 32.

Question 6.
b.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 53
______ × ______ = ______

Answer: 6 times as many as 8 is 48.

Explanation: 6×8= 48.

Question 6.
c.
9 × 3 = 27
______ times as many as ______ is ______ .

Answer: 9 times as many as 3 is 27

Question 7.
Multiply 7 × 43. For 7a–7d, select True or False for each statement.
a. A reasonable estimate of the product is 280.
i. True
ii. False

Answer: True

Explanation: 7×43= 301. Take 43 and round off to 40 then 40×7= 280.

Question 7.
b. Using partial products, the products are 21 and 28.
i. True
ii. False

Answer: False

Explanation: 7×43= 7×(40+3)
=(7×40)+(7×3)
=280+21. So partial products are 280 and 21.

Question 7.
c. Using regrouping, 21 ones are regrouped as 1 ten and 2 ones.
i. True
ii. False

Answer: False.

Explanation: 1 ten and 2 ones is 12

Question 7.
d. The product is 301.
i. True
ii. False

Answer: True.

Explanation: 7×43= 7×(40+3)
=(7×40)+(7×3)
=280+21
=301.

Question 8.
It costs 9,328 points to build each apartment building in the computer game Big City Building. What is the cost to build 5 apartment buildings? Show your work.

Answer: 46,640 points.

Explanation: The cost of each building apartment is 9,328 points. To build 5 apartments its costs 9,3287×5= 46,640 points.

Review/Test – Page No. 140

Question 9.
Multiply 7 × 462 using place value and expanded form.
Choose the number from the box to complete the expression.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 54

Answer: 400, 60, 2

Explanation: 7×462= 7×(400+60+2).

Question 10.
For numbers 10a–10b, use place value to find the product.
a.
3 × 600 = 3 × ______ hundreds
= ______ hundreds
______

Answer: 6 hundreds, 18 hundreds , 1800

Explanation: 3 × 600 = 3 × 6 hundreds
= 18 hundreds
= 1800.

Question 10.
b.
5 × 400 = 5 × ______ hundreds
______ hundreds
______

Answer: 4hundreds, 20hundreds, 2,000.

Explanation: 5 × 400 = 5 × 4hundreds
= 20 hundreds
= 2,000.

Question 11.
Liam has 3 boxes of baseball cards with 50 cards in each box. He also has 5 boxes with 40 basketball cards in each box. If Liam goes to the store and buys 50 more baseball cards, how many baseball and basketball cards does Liam have? Show your work.

Answer: Liam has 400 baseball and baseball cards.

Explanation: Liam has 3 boxes of baseball cards and there are 50 cards in each box, so total cards are 50×3= 150 baseball cards. And he has 5 boxes with 40 baseball cards in each box which means 5×40= 200. So total baseball cards are 150+200= 350. And he went to the store to buy 50 more baseball cards, so total baseball cards are 350+50= 400.

Review/Test – Page No. 141

Question 12.
There is a book sale at the library. The price for each book is $4. Which expression can be used to show how much money the library will make if it sells 289 books? Use the numbers on the tiles to complete your answer.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 55
(4 × ______) + (4 × ______) + (4 × ______)

Answer: 200, 80, 9.

Explanation: As the price of each book is $4, so for 289 books it will be 4×289
= 4×(200+80+9)
=(4×200)+(4×80)+(4×9)
=800+320+36
=1,156.

Question 13.
Find 8 × 397. Show your work and explain why the strategy you chose works best with the factors.

Answer: 3,176.

Explanation: 8×397= 8×(300+90+7)
=(8×300)+(8×90)+(8×7)
=2400+720+56
=3,176.

Question 14.
A clown bought 6 bags of round balloons with 24 balloons in each bag. The clown also bought 3 bags of long balloons with 36 balloons in each bag.
Part A
How many more long balloons than round balloons did the clown buy? Show your work.
______ balloons

Answer: 36.

Explanation: As clown bought 6 bags of round balloons with 24 balloons in each bag, so
6×24= 144 and 3 bags of long balloons with 36 balloons in each bag, so 3×36= 108, So
144-108= 36.

Question 14.
Part B
The clown also bought 5 bags of heart-shaped balloons with 14 balloons in each bag. When the clown blew up all of the round, long, and heart-shaped balloons, 23 balloons burst. How many blown-up balloons were left? Explain your answer.
______ blown-up balloons

Answer: 299.

Explanation: The no. of heart-shaped balloons 5×14= 70. Then add that number to the number of round balloons and long balloons 70+144+108= 322 balloons in all. Then subtract the number of burst balloons, so 322-23= 299 balloons left.

Review/Test – Page No. 142

Question 15.
Hector planted 185 flowers in 2 days. There were 5 volunteers, including Hector, who each planted about the same number of flowers. About how many flowers did they plant?
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 56

Answer: 1000.

Explanation: Hector planted 185 flowers in 2 days, so 5 volunteers can plant 185×5= 925.

Question 16.
Jay and Blair went fishing. Together, they caught 27 fish. Jay caught 2 times as many fish as Blair. How many fish did Jay and Blair each catch? Write an equation and solve. Explain your work.
Jay: ______ fish;         Blair: ______ fish

Answer: Blair caught 9 fishes and Jay caught 18 fishes.

Explanation: Blair caught n fish and Jay caught 2×n fish. Together they caught 3×n fish, so
3×n= 27 and n= 9 fishes, and 2×n= 18 fishes. Blair caught 9 fishes and Jay caught 18 fishes

Question 17.
At the pet fair, Darlene’s dog weighed 5 times as much as Leah’s dog. Together, the dogs weighed 84 pounds. How much did each dog weigh? Complete the bar model. Write an equation and solve.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 57
Leah’s dog: ______ pounds; Darlene’s dog: ______ pounds;

Answer: Leah’s dog is 14 pound and Darlene’s dog weight is 70 pounds.

Explanation:
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers
Let Leah’s dog weight be X and Darlene’s is 5 times as many as Leah’s, so Darlene’s dog weight be 5X. As together weight is 84 pounds, then X+5X= 84 and X= 14. So Leah’s dog weight is 14 and Darlene’s dog weight is 5×14= 70.

Question 18.
Use the Distributive Property to model the product on the grid.
Record the product.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers Review/Test img 58
4 × 12 = ______

Answer: 4×12= 48.

Explanation: 4×12=4×(10+2)
=(4×10)+(4×2)
=40+8
=48

Page No. 147

Question 1.
Find 20 × 27. Tell which method you chose. Explain what happens in each step.

Answer: 540

Explanation: It is mental maths. Because 2×27= 54 and 20×27= 540.

Choose a method. Then find the product.

Question 2.
10 × 12 = ______

Answer: 120

Explanation: Mental math, as 1×12=12 and 10×12= 120

Question 3.
20 × 20 = ______

Answer: 400

Explanation: Mental math, as 2×2=4 and 20×20= 400

Question 4.
40 × 24 = ______

Answer: 960

Explanation: Mental math, as 4×24=96 and 40×24= 960

Question 5.
11 × 60 = ______

Answer: 660

Explanation: Mental math, as 11×6=66 and 11×60= 660

Choose a method. Then find the product.

Question 6.
70 × 55 = ______

Answer: 3850

Explanation: Mental math, as 7×55=385 and 70×55= 3850

Question 7.
17 × 30 = ______

Answer: 510

Explanation: Mental math, as 17×3=51 and 17×30= 510

Question 8.
30 × 60 = ______

Answer: 1800

Explanation: Mental math, as 30×60=1800 and 30×60= 1800

Question 9.
12 × 90 = ______

Answer: 1080

Explanation: Mental math, as 12×9=108 and 12×90= 1080.

Reason Quantitatively Algebra Find the unknown digit in the number.

Question 10.
64 × 40 = 2,56■
■ = ______

Answer: 2,560

Explanation: Mental math, as 64×4=256 and 64×40= 510

Question 11.
29× 50 = 1,★50
★ = ______

Answer: 4

Explanation: Mental math, as 29×5=145 and 29×50= 1450

Question 12.
3⧫× 47 = 1,410
⧫ = ______

Answer: 0

Explanation: Mental math, as 3×47=1410 and 30×47= 1410

Question 13.
Caroline packs 12 jars of jam in a box. She has 40 boxes. She has 542 jars of jam. How many jars of jam will she have left when all the boxes are full?

Answer: 62 jars.

Explanation: Caroline packs 12 jars in a box and she has 40 boxes, so total boxes are
12×40= 480 boxes. As she has 542 jars of jam, so total jars left are 542-480= 62 jars.

Question 14.
Alison is preparing for a math contest. Each day, she works on multiplication problems for 20 minutes and division problems for 10 minutes. How many minutes does Alison practice multiplication and division problems in 15 days?

Answer: 450 mins.

Explanation: As Alison works on multiplication problems for 20 mins and 10 mins on division problems, So total time taken by Alison is 20+10=30 mins. So for 15 days Alison takes
15×30= 450 mins.

Page No. 148

Use the table for 15–16.
Go Math Grade 4 Answer Key Chapter 2 Multiply by 1-Digit Numbers img 59

Question 15.
Use Graphs How many frames did it take to produce 50 seconds of Pinocchio?

Answer: 950 Frames.

Explanation: Total frames are 50×19= 950 frames.

Question 16.
Are there fewer frames in 10 seconds of The Flintstones or in 14 seconds of The Enchanted Drawing? What is the difference in the number of frames?

Answer: 40

Explanation: The Flintstone frames in 10 seconds are 10×24= 240 and The Enchanted Drawing frames are 14×20= 280. So the difference between them is 280-240= 40.

Question 17.
The product of my number and twice my number is 128. What is half my number? Explain how you solved the problem.

Answer: 4.

Explanation: First make a table to test numbers less than 10 since 10×20= 200, and 2×8= 16 then 8×16= 128 and 8÷2= 4.

Question 18.
Tanya says that the product of a multiple of ten and a multiple of ten will always have only one zero. Is she correct? Explain.

Answer: No.

Explanation: The product of two multiples of ten will always have at least 2 zeros.

Question 19.
For numbers 19a–19e, select Yes or No to tell whether the answer is correct.
a. 28 × 10 = 280
i. yes
ii. no

Answer: Yes

Question 19.
b. 15 × 20 = 300
i. yes
ii. no

Answer: Yes

Question 19.
c. 17 × 10 = 17
i. yes
ii. no

Answer: No

Question 19.
d. 80 × 10 = 800
i. yes
ii. no

Answer: Yes

Question 19.
e. 16 × 30 = 1,800
i. yes
ii. no

Answer: No

Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers

go-math-grade-4-chapter-8-multiply-fractions-by-whole-numbers-pages-155-167-answer-key

Students to master mathematical concepts must require the best resources to understand the logic and learn the concept easily. The only resource that helps all grade 4 students are Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers. With the help of Grade 4 Go Math Solutions Homework Practice FL Ch 8 Multiply Fractions by Whole Numbers, students can learn the fundamentals and become a master in maths. So, students are recommended to utilize the detailed solutions covered in Go Math Grade 4 Answer Key Chapter 8.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers

Refer to the concepts of Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers before you ace up your preparation. Click on the links provided here and get a free pdf of chapterwise Go Math 4th Grade Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers and practice the problems regularly on your own for experiencing the best learnings.

Lesson: 1 – Multiples of Unit Fractions

Lesson: 2 – Multiples of Fractions

Lesson: 3 – Multiply a Fraction by a Whole Number Using Models

Lesson: 4 – Multiply a Fraction or Mixed Number by a Whole Number.

Lesson: 5 – Problem Solving Comparison

Lesson: 6

Common Core – Multiply Fractions by Whole Numbers – Page No. 157

Multiples of Unit Fractions

Write the fraction as a product of a whole number and a unit fraction.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 1

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
5/6 = 5 x 1/6.

Question 2.
\(\frac{7}{8}\)
Type below:
_________

Answer:
7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
7/8 = 7 x 1/8.

Question 3.
\(\frac{5}{3}\)
Type below:
_________

Answer:
5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

Question 4.
\(\frac{9}{10}\)
Type below:
_________

Answer:
9 x 1/10

Explanation:
Given that 9/10 or 9 tenth-size parts.
Each tenth-size part of the given fraction can be shown by the unit fraction 1/10.
You can use unit fractions to show 9/10
9/10 = 9 x 1/10.

Question 5.
\(\frac{3}{4}\)
Type below:
_________

Answer:
3 x 1/4

Explanation:
Given that 3/4 or 3 fourth-size parts.
Each fourth-size part of the given fraction can be shown by the unit fraction 1/4.
You can use unit fractions to show 5/6
3/4 = 3 x 1/4.

Question 6.
\(\frac{11}{12}\)
Type below:
_________

Answer:
11 x 1/12

Explanation:
Given that 11/12 or 11 twelve-size parts.
Each twelve-size part of the given fraction can be shown by the unit fraction 1/12.
You can use unit fractions to show 5/6
11/12 = 11 x 1/12.

Question 7.
\(\frac{4}{6}\)
Type below:
_________

Answer:
4 x 1/6

Explanation:
Given that 4/6 or 4 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 4/6
4/6 = 4 x 1/6.

Question 8.
\(\frac{8}{20}\)
Type below:
_________

Answer:
8 x 1/20

Explanation:
Given that 8/20 or 8 twenty-size parts.
Each twenty-size part of the given fraction can be shown by the unit fraction 1/20.
You can use unit fractions to show 8/20
8/20 = 8 x 1/20.

Question 9.
\(\frac{13}{100}\)
Type below:
_________

Answer:
13 x 1/100

Explanation:
Given that 13/100 or 13 hundred-size parts.
Each hundred-size part of the given fraction can be shown by the unit fraction 1/100.
You can use unit fractions to show 13/100
13/100 = 13 x 1/100.

List the next four multiples of the unit fraction.

Question 10.
\(\frac{1}{5}\),
Type below:
_________

Answer:
2/5, 3/5, 4/5, 5/5

Explanation:
Grade 4 Chapter 8 Multiply Fractions Image 2
2/5, 3/5, 4/5, 5/5

Question 11.
\(\frac{1}{8}\),
Type below:
_________

Answer:
2/8, 3/8, 4/8, 5/8

Explanation:
Grade 4 Chapter 8 Multiply Fractions Image 3
2/8, 3/8, 4/8, 5/8

Problem Solving

Question 12.
So far, Monica has read \(\frac{5}{6}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) of the book

Answer: 1/6 of the book

Explanation:
Monica has read 5/6 of a book. She has read the same number of pages each day for 5 days.
For 1 day, she read one page. In total, she read 5 pages in 5 days. So, Monica read 1/6 of a book each day.

Question 13.
So far, Monica has read \(\frac{3}{8}\) of a book. She has read the same number of pages each day for 5 days. What fraction of the book does Monica read each day?
\(\frac{□}{□}\) pound of cheese

Answer: 1/8 pound of cheese

Explanation:
Nicholas buys 3/8 pound of cheese. He bought 3 sandwiches. Then, he applied 3/8 pound of cheese on 3 sandwiches. So, 3 x 1/8 cheese he put on 3 sandwiches. So, for one sandwich he put 1/8 pound of cheese.

Common Core – Multiply Fractions by Whole Numbers – Page No. 158

Lesson Check

Question 1.
Selena walks from home to school each morning and back home each afternoon. Altogether, she walks \(\frac{2}{3}\) mile each day. How far does Selena live from school?
Options:
a. \(\frac{1}{3}\) mile
b. \(\frac{2}{3}\) mile
c. 1 \(\frac{1}{3}\) miles
d. 2 miles

Answer: a. 1/3 mile

Explanation:
Selena walks from home to school each morning and back home each afternoon.
Altogether, she walks 2/3 miles each day.
The distance between home and school will remain the same.
So, 2/3 x 1/2 = 1/3 mile far Selena live from the school.
Thus the correct answer is option a.

Question 2.
Will uses \(\frac{3}{4}\) cup of olive oil to make 3 batches of salad dressing. How much oil does Will use for one batch of salad dressing?
Options:
a. \(\frac{1}{4}\) cup
b. \(\frac{1}{3}\) cup
c. 2 \(\frac{1}{3}\) cups
d. 3 cups

Answer: \(\frac{1}{4}\) cup

Explanation:
Will uses 3/4 cups of olive oil to make 3 batches of salad dressing.
To know the one batch of salad dressing, we need to take one part of salad dressing = 1/3.
So, 3/4 x 1/3 = 1/4 cup of olive oil will use for one batch of salad dressing.
Thus the correct answer is option a.

Spiral Review

Question 3.
Liza bought \(\frac{5}{8}\) pound of trail mix. She gives \(\frac{2}{8}\) pound of trail mix to Michael. How much trail mix does Liza have left?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. \(\frac{3}{8}\) pound
d. \(\frac{4}{8}\) pound

Answer: c. 3/8 pound

Explanation:
Liza bought 58 pound of trail mix. She gives 28 pounds of trail mix to Michael.
So, Liza has left 5/8 – 2/8 = 3/8 trail mix.
Thus the correct answer is option c.

Question 4.
Leigh has a piece of rope that is 6 \(\frac{2}{3}\) feet long. How do you write 6 \(\frac{2}{3}\) as a fraction greater than 1?
Options:
a. \(\frac{11}{3}\) pound
b. \(\frac{15}{3}\) pound
c. \(\frac{20}{3}\) pound
d. \(\frac{62}{3}\) pound

Answer: c. 20/3

Explanation:
Multiply the denominator with the whole number. i.e Multiply 3 with 6 in the given example, 6 (2/3).
3 x 6 =18.
Add 18 + 2 =20.
Keep the Denominator the same i.e. 3.
The obtained fraction is 20/3.
Thus the correct answer is option c.

Question 5.
Randy’s house number is a composite number. Which of the following could be Randy’s house number?
Options:
a. 29
b. 39
c. 59
d. 79

Answer: b. 39

Explanation:
The composite numbers can be defined as the whole numbers that have more than two factors. Whole numbers that are not prime are composite numbers because they are divisible by more than two numbers. 39 is the composite number. 39 is divide by 13 and 3.
Thus the correct answer is option b.

Question 6.
Mindy buys 12 cupcakes. Nine of the cupcakes have chocolate frosting and the rest have vanilla frosting. What fraction of the cupcakes have vanilla frosting?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}\)

Answer: a. 1/4

Explanation:
Mindy buys 12 cupcakes.
Nine of the cupcakes have chocolate frosting = 9/12.
The rest have vanilla frosting. So, there are 3 cups remained = 3/12 = 1/4.
1/4 cupcakes have vanilla frosting.
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 159

Multiples of Fractions

List the next four multiples of the fraction.

Question 1.
\(\frac{3}{5}\),
Type below:
_________

Answer:
6/5, 9/5, 12/5, 20/5

Explanation:
1 x 3/5 = 3/5.
2 x 3/5 = 6/5.
3 x 3/5 = 9/5.
4 x 3/5 = 12/5.
5 x 4/5 = 20/5.
The next four multiples of 3/5 are 6/5, 9/5, 12/5, 20/5.

Question 2.
\(\frac{2}{6}\),
Type below:
_________

Answer:
4/6, 6/6, 8/6, 10/6

Explanation:
1 x 2/6 = 2/6.
2 x 2/6 = 4/6.
3 x 2/6 = 6/6.
4 x 2/6 = 8/6.
5 x 2/6 = 10/6.
The next four multiples of 2/6 are 4/6, 6/6, 8/6, 10/6.

Question 3.
\(\frac{4}{8}\),
Type below:
_________

Answer:
8/8, 12/8, 16/8, 20/8

Explanation:
1 x 4/8 = 4/8.
2 x 4/8 = 8/8.
3 x 4/8 = 12/8.
4 x 4/8 = 16/8.
5 x 4/8 = 20/8.
The next four multiples of 4/8 are 8/8, 12/8, 16/8, 20/8.

Question 4.
\(\frac{5}{10}\),
Type below:
_________

Answer:
10/10, 15/10, 20/10, 25/10

Explanation:
1 x 5/10 = 5/10.
2 x 5/10 = 10/10.
3 x 5/10 = 15/10.
4 x 5/10 = 20/10.
5 x 5/10 = 25/10.
The next four multiples of 5/10 are 10/10, 15/10, 20/10, 25/10.

Write the product as the product of a whole number and a unit fraction.

Question 5.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 2
2 × \(\frac{4}{5}\) =
Type Below:
_________

Answer: 8/5 = 8 x 1/5

Explanation:
1 group of 4/5 = 4/5
2 groups of 4/5 = 8/5
2 x 4/5 = 8/5 = 8 x 1/5.

Question 6.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 3
5 × \(\frac{2}{3}\) =
Type below:
_________

Answer:
10/3 = 10 x 1/3

Explanation:
1 group of 2/3 = 2/3
2 group of 2/3 = 4/3
3 group of 2/3 = 6/3
4 group of 2/3 = 8/3
5 group of 2/3 = 10/3
5 x 2/3 = 10/3 = 10 x 1/3.

Problem Solving

Question 7.
Jessica is making 2 loaves of banana bread. She needs \(\frac{3}{4}\) cup of sugar for each loaf. Her measuring cup can only hold \(\frac{1}{4}\) cup of sugar. How many times will Jessica need to fill the measuring cup in order to get enough sugar for both loaves of bread?
_____ times

Answer: 6 times

Explanation:
Jessica is making 2 loaves of banana bread. She needs a 3/4 cup of sugar for each loaf.
For 2 loaves, she needs 2 x 3/4 = 6/4 cups of sugar.
Her measuring cup can only hold 1/4 cup of sugar. So, to get the 3/4 cup of sugar, she needs to fill the cup 3 times. 1/4 + 1/4 + 1/4 = 3/4.
So, to fill 2 loaves, she needs to fill cup 3 x 2 = 6 times.

Question 8.
A group of four students is performing an experiment with salt. Each student must add \(\frac{3}{8}\) teaspoon of salt to a solution. The group only has a \(\frac{1}{8}\) teaspoon measuring spoon. How many times will the group need to fill the measuring spoon in order to perform the experiment?
_____ times

Answer: 12 times

Explanation:
A group of four students is performing an experiment with salt. Each student must add a 3/8 teaspoon of salt to a solution. 4 x 3/8 = 12/8 teaspoon of salt required to finish the experiment.
If they have 1/8 teaspoon measuring spoon, 12 x 1/8.
So, the group needs to fill the measuring spoon 12 times in order to perform the experiment.

Common Core – Multiply Fractions by Whole Numbers – Page No. 160

Lesson Check

Question 1.
Eloise made a list of some multiples of \(\frac{5}{8}\). Which of the following lists could be Eloise’s list?
Options:
a. \(\frac{5}{8}, \frac{10}{16}, \frac{15}{24}, \frac{20}{32}, \frac{25}{40}\)
b. \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
c. \(\frac{5}{8}, \frac{6}{8}, \frac{7}{8}, \frac{8}{8}, \frac{9}{8}\)
d. \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}\)

Answer: b. 5/8, 10/8, 15/8, 20/8, 25/8
Explanation:
1 x 5/8 = 5/8.
2 x 5/8 = 10/8.
3 x 5/8 = 15/8.
4 x 5/8 = 20/8.
5 x 5/8 = 25/8.
The next four multiples of 5/8 are \(\frac{5}{8}, \frac{10}{8}, \frac{15}{8}, \frac{20}{8}, \frac{25}{8}\)
Thus the correct answer is option b.

Question 2.
David is filling five \(\frac{3}{4}\) quart bottles with a sports drink. His measuring cup only holds \(\frac{1}{4}\) quart. How many times will David need to fill the measuring cup in order to fill the 5 bottles?
Options:
a. 5
b. 10
c. 15
d. 20

Answer: c. 15

Explanation:
David is filling five 3/4 quart bottles with a sports drink = 5 x 3/4 = 15/4.
His measuring cup only holds 1/4 quart.
So, 15 x 1/4. David needs to fill the measuring cup 15 times in order to fill the 5 bottles.
Thus the correct answer is option c.

Spiral Review

Question 3.
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages. How many stamps are on each page?
Options:
a. 12
b. 14
c. 16
d. 18

Answer: c. 16

Explanation:
Ira has 128 stamps in his stamp album. He has the same number of stamps on each of the 8 pages.
128/8 = 16 stamps on each page.
So, there are 16 stamps on each page.
Thus the correct answer is option b.

Question 4.
Ryan is saving up for a bike that costs $198. So far, he has saved $15 per week for the last 12 weeks. How much more money does Ryan need in order to be able to buy the bike?
Options:
a. $ 8
b. $ 18
c. $ 48
d. $ 180

Answer: b. $ 18

Explanation:
Ryan is saving up for a bike that costs $198.
So far, he has saved $15 per week for the last 12 weeks = $15 x 12 = $180.
$198 – $180 = $18 need in order to buy the bike.
Thus the correct answer is option b.

Question 5.
Tina buys 3 \(\frac{7}{8}\) yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 \(\frac{3}{8}\) yards of the fabric leftover. How many yards of material did Tina use?
Options:
a. 1 \(\frac{4}{8}\)
b. 2 \(\frac{1}{8}\)
c. 2 \(\frac{4}{8}\)
d. 5 \(\frac{2}{8}\)

Answer: c. 2  4/8

Explanation:
Tina buys 3 7/8 yards of material at the fabric store. She uses it to make a skirt. Afterward, she has 1 3/8 yards of the fabric leftover.
3 -1 = 2; 7/8 – 3/8 = 4/8.
So, the answer is 2 \(\frac{4}{8}\).
Thus the correct answer is option c.

Question 6.
Which list shows the fractions in order from least to greatest?
Options:
a. \(\frac{2}{3}, \frac{3}{4}, \frac{7}{12}\)
b. \(\frac{7}{12}, \frac{3}{4}, \frac{2}{3}\)
c. \(\frac{3}{4}, \frac{2}{3}, \frac{7}{12}\)
d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Answer: d. \(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)

Explanation:
2/3 = 0.666
3/4 = 0.75
7/12 = 0.5833
\(\frac{7}{12}, \frac{2}{3}, \frac{3}{4}\)
Thus the correct answer is option d.

Common Core – Multiply Fractions by Whole Numbers – Page No. 161

Multiply a Fraction by a Whole Number Using Models

Multiply.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 4

Question 2.
3 × \(\frac{2}{5}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 1 473
3 x 2/5 = 6/5

Question 3.
7 × \(\frac{3}{10}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 2 473
7 x 3/10 = 21/10

Question 4.
3 × \(\frac{5}{12}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 3 473
3 x 5/12 = 15/12

Question 5.
6 × \(\frac{3}{4}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 4 473

6 x 3/4 = 18/4

Question 6.
4 × \(\frac{2}{8}\) = \(\frac{□}{□}\)

Answer:

Grade 4 Chapter 8 Image 5 473

4 x 2/8 = 8/8

Question 7.
5 × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 6 473

5 x 2/3 = 10/3

Question 8.
2 × \(\frac{7}{8}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 7 473
2 x 7/8 = 14/8

Question 9.
6 × \(\frac{4}{5}\) = \(\frac{□}{□}\)

Answer:
Grade 4 Chapter 8 Image 8 473

6 x 4/5 = 28/5

Problem Solving

Question 10.
Matthew walks \(\frac{5}{8}\) mile to the bus stop each morning. How far will he walk in 5 days?
\(\frac{□}{□}\)

Answer: 25/8 miles

Explanation:
Matthew walks 5/8 mile to the bus stop each morning.
In 5 days, 5 x 5/8 = 25/8 miles.

Question 11.
Emily uses \(\frac{2}{3}\) cup of milk to make one batch of muffins. How many cups of milk will Emily use if she makes 3 batches of muffins?
\(\frac{□}{□}\)

Answer: 6/3 cups of milk

Explanation:
Emily uses a 2/3 cup of milk to make one batch of muffins.
Emily use 3 x 2/3 = 6/3 cups of milk to make 3 batches of muffins

Common Core – Multiply Fractions by Whole Numbers – Page No. 162

Lesson Check

Question 1.
Aleta’s puppy gained \(\frac{3}{8}\) pound each week for 4 weeks. Altogether, how much weight did the puppy gain during the 4 weeks?
Options:
a. \(\frac{8}{12}\) pound
b. 1 \(\frac{2}{8}\) pounds
c. \(\frac{12}{8}\) pounds
d. 4 \(\frac{3}{8}\) pounds

Answer: \(\frac{12}{8}\) pounds

Explanation:
Aleta’s puppy gained 3/8 pound each week.
It gained 4 x 3/8 = 12/8 pounds in 4 weeks.
Thus the correct answer is option c.

Question 2.
Pedro mixes \(\frac{3}{4}\) teaspoon of plant food into each gallon of water. How many teaspoons of plant food should Pedro mix into 5 gallons of water?
Options:
a. \(\frac{3}{20}\) teaspoon
b. \(\frac{4}{15}\) teaspoon
c. \(\frac{8}{4}\) teaspoons
d. \(\frac{15}{4}\) teaspoons

Answer: d. \(\frac{15}{4}\) teaspoons

Explanation:
If Pedro mixes 3/4 teaspoon of plant food into each gallon of water, then 5 x 3/4 = 15/4 teaspoon of plant food mix into 5 gallons of water.
Thus the correct answer is option d.

Spiral Review

Question 3.
Ivana has \(\frac{3}{4}\)pound of hamburger meat. She makes 3 hamburger patties. Each patty weighs the same amount. How much does each hamburger patty weigh?
Options:
a. \(\frac{1}{4}\) pound
b. \(\frac{1}{3}\) pound
c. 2 \(\frac{1}{4}\) pounds
d. 3 pounds

Answer: a. \(\frac{1}{4}\) pound

Explanation:
Ivana has 3/4 pound of hamburger meat. She makes 3 hamburger patties.
Each patty weighs the same amount. So, each hamburger patty weighs 1/4 pound.
Thus the correct answer is option a.

Question 4.
Which of the following expressions is NOT equal to \(\frac{7}{10}\)?
Options:
a. \(\frac{5}{10}+\frac{1}{10}+\frac{1}{10}\)
b. \(\frac{2}{10}+\frac{2}{10}+\frac{3}{10}\)
c. \(\frac{3}{10}+\frac{3}{10}+\frac{2}{10}\)
d. \(\frac{4}{10}+\frac{2}{10}+\frac{1}{10}\)

Answer: c. 3/10+3/10+2/10

Explanation:
a. 5/10+1/10+1/10 = 7/10
b. 2/10+2/10+3/10 = 7/10
c. 3/10+3/10+2/10 = 8/10
d. 4/10+2/10+1/10 = 7/10
The expression not equal to \(\frac{7}{10}\) is \(\frac{8}{10}\)
Thus the correct answer is option c.

Question 5.
Lance wants to find the total length of 3 boards. He uses the expression \(3 \frac{1}{2}+\left(2+4 \frac{1}{2}\right)\). How can Lance rewrite the expression using both the Associative and Commutative Properties of Addition?
Options:
a. \(5+4 \frac{1}{2}\)
b. \(\left(3 \frac{1}{2}+2\right)+4 \frac{1}{2}\)
c. \(2+\left(3 \frac{1}{2}+4 \frac{1}{2}\right)\)
d. \(3 \frac{1}{2}+\left(4 \frac{1}{2}+2\right)\)

Answer: She can write as (3 1/2 + 2) + 4 1/2

Question 6.
Which of the following statements is true?
Options:
a. \(\frac{5}{8}>\frac{9}{10}\)
b. \(\frac{5}{12}>\frac{1}{3}\)
c. \(\frac{3}{6}>\frac{4}{5}\)
d. \(\frac{1}{2}>\frac{3}{4}\)

Answer: \(\frac{1}{2}>\frac{3}{4}\)

Explanation:
0.625 > 0.9
0.416 > 0.333
0.5 > 0.8
0.5 > 0.75
Thus the correct answer is option d.

Common Core – Multiply Fractions by Whole Numbers – Page No. 163

Multiply a Fraction or Mixed Number by a Whole Number.

Multiply. Write the product as a mixed number.

Question 1.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 5

Answer:
1  5/10

Explanation:
5 × 3/10 = 15/10 = 1 and remainder is 5. So, the mixed fraction is 1  5/10

Question 2.
3 × \(\frac{3}{5}\) =
_____ \(\frac{□}{□}\)

Answer:
1 × 4/5

Explanation:
3 × 3/5 = 9/5 = 1 and remainder is 4. So, the mixed fraction is 1  4/5

Question 3.
5 × \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer:
3  3/4
Explanation:
15/4 = 3 and the remainder is 3. So, the mixed fraction is 3  3/4

Question 4.
4 × 1 \(\frac{1}{5}\) =
_____ \(\frac{□}{□}\)

Answer:
4  4/5
Explanation:
1 ×15 = 6/5.
4 x 6/5 = 24/5 = 4 and the remainder is 4. So, the mixed fraction is 4× 4/5

Question 5.
2 × 2 \(\frac{1}{3}\) =
_____ \(\frac{□}{□}\)

Answer:
4  2/3
Explanation:
2 13 = 7/3.
2 x 7/3 = 14/3.
14/3 = 4 and the remainder is 2. So, the mixed fraction is 4 2/3

Question 6.
5 × 1 \(\frac{1}{6}\) =
_____ \(\frac{□}{□}\)

Answer: 5 5/6

Explanation:
1 1/6 = 7/6
5 x 7/6 = 35/6.
35/6 = 5 and the remainder is 5.
So, the mixed fraction is 5 5/6

Question 7.
2 × 2 \(\frac{7}{8}\) =
_____ \(\frac{□}{□}\)

Answer: 6 1/1

Explanation:
2 7/8 = 23/8
2 x 23/8 = 46/8 = 6 1/1

Question 8.
7 × 1 \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/4

Explanation:
1 3/4 = 7/4
7 x 7/4 = 39/4
39/4 = 9 and the remainder is 3.
So, the mixed fraction is 9 3/4

Question 9.
8 × 1 \(\frac{3}{5}\) =
_____ \(\frac{□}{□}\)

Answer: 12 4/5

Explanation:
1 3/5 = 8/5
8 x 8/5 = 64/5
64/5 = 12 and the remainder is 4.
So, the mixed fraction is 12 4/5

Problem Solving

Question 10.
Brielle exercises for \(\frac{3}{4}\) hour each day for 6 days in a row. Altogether, how many hours does she exercise during the 6 days?
_____ \(\frac{□}{□}\)

Answer: 4 2/4

Explanation:
6 x 3/4 = 18/4 = 4 and the remainder is 2.
So, the mixed fraction is 4 2/4.

Question 11.
A recipe for quinoa calls for 2 \(\frac{2}{3}\) cups of milk. Conner wants to make 4 batches of quinoa. How much milk does he need?
_____ \(\frac{□}{□}\)

Answer: 10 2/3

Explanation:
quinoa calls for 8/3 cups of milk. Conner wants to make 4 batches of quinoa.
So, 4 x 8/3 = 32/3 = 10 and the remainder is 2.
So, the mixed fraction is 10 2/3

Common Core – Multiply Fractions by Whole Numbers – Page No. 164

Lesson Check

Question 1.
A mother is 1 \(\frac{3}{4}\) times as tall as her son. Her son is 3 feet tall. How tall is the mother?
Options:
a. 4 \(\frac{3}{4}\) feet
b. 5 \(\frac{1}{4}\) feet
c. 5 \(\frac{1}{2}\) feet
d. 5 \(\frac{3}{4}\) feet

Answer: b. 5 1/4 feet

Explanation:
A mother is 1 3/4 times as tall as her son. Her son is 3 feet tall.
So, 3 x 7/4 = 21/4 = 5 and the remainder is 1.
The mixed fraction is 5 1/4 feet.
Thus the correct answer is option b.

Question 2.
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 \(\frac{1}{3}\) times the width of the banner. How long is the banner?
Options:
a. 8 \(\frac{1}{3}\) feet
b. 8 \(\frac{3}{8}\) feet
c. 10 \(\frac{1}{3}\) feet
d. 10 \(\frac{2}{3}\) feet

Answer: d. 10 2/3 feet

Explanation:
The cheerleaders are making a banner that is 8 feet wide. The length of the banner is 1 1/3 times the width of the banner.
So, 8 x 4/3 = 32/3 =10 and the remainder is 2.
The mixed fraction is 10 2/3 feet.
Thus the correct answer is option d.

Spiral Review

Question 3.
Karleigh walks \(\frac{5}{8}\) mile to school every day. How far does she walk to school in 5 days?
Options:
a. \(\frac{5}{40}\) mile
b. \(\frac{25}{40}\) mile
c. \(\frac{10}{8}\) miles
d. \(\frac{25}{8}\) miles

Answer: d. 25/8 miles

Explanation:
5 x 5/8 = 25/8.
Thus the correct answer is option d.

Question 4.
Which number is a multiple of \(\frac{4}{5}\)?
Options:
a. \(\frac{8}{10}\)
b. \(\frac{12}{15}\)
c. \(\frac{16}{20}\)
d. \(\frac{12}{5}\)

Answer: d. 12/5

Explanation:
The multiple of 45 has the denominator 5.
So, 12/5 is the correct answer.
Thus the correct answer is option d.

Question 5.
Jo cut a key lime pie into 8 equal-size slices. The next day, \(\frac{7}{8}\) of the pie is left. Jo puts each slice on its own plate. How many plates does she need?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: c. 7

Explanation:
Jo cut a key lime pie into 8 equal-size slices.
The next day, 78 of the pie is left. Jo puts each slice on its own plate.
She needs 7 plates.
Thus the correct answer is option c.

Question 6.
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project. Altogether, how much time did Ed spend doing homework over the weekend?
Options:
a. 3 hours
b. 2 \(\frac{3}{4}\) hours
c. 2 \(\frac{1}{2}\) hours
d. 2 hours

Answer: a. 3 hours

Explanation:
Given,
Over the weekend, Ed spent 1 \(\frac{1}{4}\) hours doing his math homework and 1 \(\frac{3}{4}\) hours doing his science project.
5/4 + 7/4 = 12/4 = 3 hours
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 165

Problem Solving Comparison

Problems with Fractions

Read each problem and solve.

Question 1.
A shrub is 1 \(\frac{2}{3}\) feet tall. A small tree is 3 times as tall as the shrub. How tall is the tree?
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 6

Answer: 5 feet

Explanation:
Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers Common Core - New img 19

Question 2.
You run 1 \(\frac{3}{4}\) miles each day. Your friend runs 4 times as far as you do. How far does your friend run each day?
_________ miles

Answer: 7 miles

Explanation:
Given,
You run 1 \(\frac{3}{4}\) miles each day.
Your friend runs 4 times as far as you do.
4 x 7/4 = 7 miles each day

Question 3.
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey. Tasha buys 2 times as much ground turkey as Ayla. How much ground turkey does Tasha buy?
_____ \(\frac{□}{□}\) pounds

Answer: 2 2/3 pounds

Explanation:
Given,
At the grocery store, Ayla buys 1 \(\frac{1}{3}\) pounds of ground turkey.
Tasha buys 2 times as much ground turkey as Ayla.
2 x 4/3 = 8/3 = 2 and the remainder is 2.
The mixed fraction is 2 2/3 pounds.

Question 4.
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour. When Nathan walks to school, it takes him 4 times as long to get to school. How long does it take Nathan to walk to school?
\(\frac{□}{□}\) hours

Answer: 4/5 hours

Explanation:
Given,
When Nathan’s mother drives him to school, it takes \(\frac{1}{5}\) hour.
When Nathan walks to school, it takes him 4 times as long to get to school.
4 x 1/5 = 4/5 hour
It takes 4/5 hour Nathan to walk to school.

Common Core – Multiply Fractions by Whole Numbers – Page No. 166

Lesson Check

Question 1.
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet. A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel. About how wide is the wingspan of the California Condor?
Options:
a. \(\frac{4}{21}\) foot
b. 2 \(\frac{1}{3}\) feet
c. 7 \(\frac{1}{3}\) feet
d. 9 \(\frac{1}{3}\) feet

Answer: d. 9 1/3 feet

Explanation:
Given,
A Wilson’s Storm Petrel is a small bird with a wingspan of 1 \(\frac{1}{3}\) feet.
A California Condor is a larger bird with a wingspan almost 7 times as wide as the wingspan of the petrel.
Convert from mixed fraction to the improper fraction.
1 1/3 = 4/3.
7 x 4/3 = 28/3 feet = 9 and the remainder is 1.
The mixed fraction is 9 1/3
Thus the correct answer is option d.

Question 2.
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile. The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far. About how far is Sue’s hotel from the Empire State Building?
Options:
a. \(\frac{9}{80}\) mile
b. \(\frac{72}{80}\) mile
c. 1 \(\frac{7}{10}\) miles
d. 7 \(\frac{2}{10}\) miles

Answer: d. 7 2/10 miles

Explanation:
Given,
The walking distance from the Empire State Building in New York City to Times Square is about \(\frac{9}{10}\) mile.
The walking distance from the Empire State Building to Sue’s hotel is about 8 times as far.
8 x 9/10 mile = 72/10 mile = 7 and the remainder is 2.
The mixed fraction is 7 2/10 miles.
Thus the correct answer is option d.

Spiral Review

Question 3.
Which of the following expressions is NOT equal to 3 × 2 \(\frac{1}{4}\)?
Options:
a. \(3 \times \frac{9}{4}\)
b. (3 × 2) + (3 × \(\frac{1}{4}\))
c. 6 \(\frac{3}{4}\)
d. 3 × 2 + \(\frac{1}{4}\)

Answer: d. 3 × 2 + 14

Explanation:
3 × 2 14 = 3 x 9/4 = 27/4
a. 3 × 94 = 27/4
b. (3 × 2) + (3 × 14) = 6 + 3/4 = 27/4
c. 6 3/4 = 27/4
d. 3 × 2 + 14 = 6 + 1/4 = 25/4
Thus the correct answer is option d.

Question 4.
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie. Altogether, how much pie does he sell at the bake sale?
Options:
a. \(\frac{2}{8}\)
b. \(\frac{12}{16}\)
c. \(\frac{12}{8}\)
d. \(\frac{35}{8}\)

Answer: c. 12/8

Explanation:
Given,
At a bake sale, Ron sells \(\frac{7}{8}\) of an apple pie and \(\frac{5}{8}\) of a cherry pie.
7/8 + 5/8 = 12/8
The bake sale 12/8 pie.
Thus the correct answer is option c.

Question 5.
On a ruler, which measurement is between \(\frac{3}{16}\) inch and \(\frac{7}{8}\) inch?
Options:
a. \(\frac{1}{16}\) inch
b. \(\frac{1}{8}\) inch
c. \(\frac{11}{16}\) inch
d. \(\frac{15}{16}\) inch

Answer: c. 11/16 inch

Explanation:
Subtract \(\frac{3}{16}\) inch and \(\frac{7}{8}\)
Make denominators as common.
\(\frac{7}{8}\) × \(\frac{2}{2}\) = \(\frac{14}{16}\)
\(\frac{14}{16}\) – \(\frac{3}{16}\) = \(\frac{11}{16}\) inch.
Thus the correct answer is option c.

Question 6.
Which of the following numbers is composite?
Options:
a. 4
b. 3
c. 2
d. 1

Answer:
a. 4

Explanation:
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself.
The factors of 4 are 1, 2, 4.
4 has more than 2 factors.
Thus the correct answer is option a.

Common Core – Multiply Fractions by Whole Numbers – Page No. 167

Lesson 8.1

Write the fraction as a product of a whole number and a unit fraction.

Question 1.
\(\frac{5}{6}\) =
Type below:
________

Answer: 5 x 1/6

Explanation:
Given that 5/6 or 5 sixth-size parts.
Each sixth-size part of the given fraction can be shown by the unit fraction 1/6.
You can use unit fractions to show 5/6
\(\frac{5}{6}\) = 5 x 1/6.

Question 2.
\(\frac{7}{8}\) =
Type below:
________

Answer: 7 x 1/8

Explanation:
Given that 7/8 or 7 eighth-size parts.
Each eighth-size part of the given fraction can be shown by the unit fraction 1/8.
You can use unit fractions to show 7/8
\(\frac{7}{8}\) = 7 x 1/8.

Question 3.
\(\frac{3}{5}\) =
Type below:
________

Answer: 5 x 1/3

Explanation:
Given that 5/3 or 5 third-size parts.
Each third-size part of the given fraction can be shown by the unit fraction 1/3.
You can use unit fractions to show 5/6
5/3 = 5 x 1/3.

List the next four multiples of the unit fraction

Question 4.
\(\frac{1}{2}\),
Type below:
________

Answer: 2/2, 3/2, 4/2, 5/2

Explanation:
1 x 1/2 = 1/2.
2 x 1/2 = 2/2.
3 x 1/2 = 3/2.
4 x 1/2 = 4/2.
5 x 1/2 = 5/2.
The next four multiples of 1/2 are 2/2, 3/2, 4/2, 5/2.

Question 5.
\(\frac{1}{6}\),
Type below:
________

Answer: 2/6, 3/6, 4/6, 5/6,6/6.

Explanation:
1 x 1/6 = 1/6.
2 x 1/6 = 2/6.
3 x 1/6 = 3/6.
4 x 1/6 = 4/6.
5 x 1/6 = 5/6.
6 x 1/6 = 6/6.
The next four multiples of 1/6 are 2/6, 3/6, 4/6, 5/6,6/6.

Lesson 8.2

List the next four multiples of the fraction.

Question 6.
\(\frac{3}{10}\),
Type below:
________

Answer: 6/10, 9/10, 12/10, 15/10

Explanation:
1 × 3/10 = 3/10
2 × 3/10 = 6/10
3 × 3/10 = 9/10
4 × 3/10 = 12/10
5 × 3/10 = 15/10

Question 7.
\(\frac{7}{12}\),
Type below:
________

Answer: 7/12, 14/12, 21/12, 28/12, 35/12

Explanation:
1 × 7/12 = 7/12
2 × 7/12 = 14/12
3 × 7/12 = 21/12
4 × 7/12 = 28/12
5 × 7/12 = 35/12

Write the product as the product of a whole number and a unit fraction.

Question 8.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 7
2 × \(\frac{3}{6}\) =
Type below:
________

Answer:
1 group of \(\frac{3}{6}\) is \(\frac{3}{6}\)
2 groups of \(\frac{3}{6}\) is \(\frac{6}{6}\)
2 × \(\frac{3}{6}\) = \(\frac{6}{6}\)

Question 9.
Go Math Grade 4 Answer Key Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers Common Core - Multiply Fractions by Whole Numbers img 8
3 × \(\frac{2}{8}\) =
Type below:
________

Explanation:
1 group of \(\frac{2}{8}\) is \(\frac{2}{8}\)
2 group of \(\frac{2}{8}\) is \(\frac{4}{8}\)
3 group of \(\frac{2}{8}\) is \(\frac{6}{8}\)
3 × \(\frac{2}{8}\) = \(\frac{6}{8}\)

Common Core – Multiply Fractions by Whole Numbers – Page No. 168

Lesson 8.3

Multiply.

Question 1.
3 × \(\frac{7}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{21}{10}\)

Explanation:
Multiply 7 and 3
3 × 7 = 21
3 × \(\frac{7}{10}\) = \(\frac{21}{10}\)

Question 2.
5 × \(\frac{4}{8}\) =
\(\frac{□}{□}\)

Answer: 20/8

Explanation:
Multiply 5 and 4
5 × 4 = 20
5 × \(\frac{4}{8}\) = \(\frac{20}{8}\)

Question 3.
4 × \(\frac{6}{12}\) =
\(\frac{□}{□}\)

Answer: 24/12

Explanation:
Multiply 4 and 6
4 × 6 = 24
4 × \(\frac{6}{12}\) = \(\frac{24}{12}\)

Question 4.
2 × \(\frac{3}{4}\) =
\(\frac{□}{□}\)

Answer: 6/4

Explanation:
Multiply 2 and 3
2 × 3 = 6
2 × \(\frac{3}{4}\) = \(\frac{6}{4}\)

Question 5.
6 × \(\frac{3}{5}\) =
\(\frac{□}{□}\)

Answer: 18/5

Explanation:
Multiply 6 and 3
6 × 3 =18
6 × \(\frac{3}{5}\) = \(\frac{18}{5}\)

Question 6.
7 × \(\frac{2}{10}\) =
\(\frac{□}{□}\)

Answer: 14/10

Explanation:
Multiply 7 and 2.
7 × 2 =14
7 × \(\frac{2}{10}\) = \(\frac{14}{10}\)

Lesson 8.4

Multiply. Write the product as a mixed number.

Question 7.
4 × \(\frac{8}{10}\) =
_____ \(\frac{□}{□}\)

Answer: 3 2/10

Explanation:
Given,
4 × \(\frac{8}{10}\)
First multiply 4 and 8
4 × 8 = 32
4 × \(\frac{8}{10}\) = 32/10
Now convert from improper fraction to the mixed fraction.
32/10 = 3 \(\frac{2}{10}\)

Question 8.
3 × \(\frac{5}{6}\) =
_____ \(\frac{□}{□}\)

Answer: 2 3/6

Explanation:
Given,
3 × \(\frac{5}{6}\)
First multiply 3 and 5.
3 × 5 =15
3 × \(\frac{5}{6}\) = 15/6
Now convert from improper fraction to the mixed fraction.
15/6 = 2 3/6

Question 9.
2 × 3 \(\frac{1}{3}\) =
_____ \(\frac{□}{□}\)

Answer: 6 2/3

Explanation:
Given,
2 × 3 \(\frac{1}{3}\)
3 \(\frac{1}{3}\) = 10/3
2 × 10/3 = 20/3
Now convert from improper fraction to the mixed fraction.
20/3 = 6 2/3

Question 10.
4 × 2 \(\frac{2}{5}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/5

Explanation:
Given,
4 × 2 \(\frac{2}{5}\)
2 \(\frac{2}{5}\) = 4/5
4 × 12/5 = 48/5
Now convert from improper fraction to the mixed fraction.
48/5 = 9 3/5

Question 11.
5 × 1 \(\frac{7}{8}\) =
_____ \(\frac{□}{□}\)

Answer: 9 3/8

Explanation:
Given,
5 × 1 \(\frac{7}{8}\)
5 × 15/5 = 75/5
Now convert from improper fraction to the mixed fraction.
75/5 = 9 3/8

Question 12.
3 × 3 \(\frac{3}{4}\) =
_____ \(\frac{□}{□}\)

Answer: 11 1/4

Explanation:
Given,
3 × 3 \(\frac{3}{4}\)
3 × 15/4 = 45/4
Now convert from improper fraction to the mixed fraction.
45/4 = 11 1/4

Lesson 8.5

Question 13.
A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall. A small tree in her back yard is 7 times as tall as the shrub. About how tall is the tree?
_____ \(\frac{□}{□}\) feet

Answer: 9 5/2 feet.
Explanation:
Given,
A shrub in Pam’s back yard is about 1 \(\frac{3}{8}\) feet tall.
A small tree in her back yard is 7 times as tall as the shrub.
9.625 ft because 1 3/8 × 7 is equal to 9 5/2 feet
Therefore the tree is 9 5/2 feet.

Question 14.
A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much. How much does the mother weigh?
_____ \(\frac{□}{□}\) pounds

Answer: 7 \(\frac{2}{10}\) pounds

Explanation:
Given,
A puppy weighs \(\frac{9}{10}\) pound. Its mother weighs 8 times as much.
\(\frac{9}{10}\) × 8 = 72/10
Convert from improper fraction to the mixed fraction.
72/10 = 7 \(\frac{2}{10}\) pounds
Thus the mother weigh 7 \(\frac{2}{10}\) pounds.

Conclusion:

Here the provided HMH Go Math Solution Key for Grade 4 Homework Practice FL Chapter 8 Multiply Fractions by Whole Numbers will increase your subject knowledge & get good scores in the exams. By understanding the difficulty of fractions, it can be easy to grasp the logic and tricks to solve the covered number of questions from Go Math Grade 4 Answer Key Chapter 8 Multiply Fractions by Whole Numbers.

Go Math Grade 6 Answer Key of All Chapters | Middle School Grade 6 Solutions Key

go-math-grade-6-answer-key

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Grade 6 HMH Go Math – Answer Keys

Grade 6 McGraw Hill Glencoe – Answer Keys

  • Chapter 1: Ratios and Rates
  • Chapter 2: Fractions, Decimals, and Percents
  • Chapter 3: Compute with Multi-Digit Numbers
  • Chapter 4: Multiply and Divide Fractions
  • Chapter 5: Integers and Coordinate Plane
  • Chapter 6: Expressions
  • Chapter 7: Equations
  • Chapter 8: Functions and Inequalities
  • Chapter 9: Area
  • Chapter 10: Volume and Surface Area
  • Chapter 11: Statistical Measures
  • Chapter 12: Statistical Display

Go Math Middle School Grade 6 Answer Key of all Chapters

Avail Grade 6 Solutions provided over here and understand the concepts in a better way.  Identify the Knowledge Gap and allot time to the areas you feel difficult. Detailed description provided in the Go Math Grade 6th Solutions Key reflects more of the topics in your Middle School Textbooks. You can use them during your Homework or while preparing for Tests. Tap on the respective chapter you wish to practice and clarify all your concerns at one go.

Why to read Go Math 6th Std. Solutions Key?

There are plenty of benefits that come with solving the Go Math 6th Standard Answer Key. Refer to them and know the need of practicing through Grade 6 HMH Go Math Answer Key. They are as follows

  • Go Math Answer Key for Grade 6 ensures success for every learner.
  • Middle School Go Math Solutions Key makes learning easier for both Students and Teachers.
  • Elaborate Explanation provided to all the Math Practice Problems helps you enhance your subject knowledge.
  • Go Math Grade 6 Answer Key lays a stronger foundation of Fundamentals of your Mathematical Concepts.

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You can find the Go Math 6th Std Solutions Key of all Chapters on our page. Simply prepare the Chapter you want to access through the direct links and learn accordingly.

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Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test

Make use of the Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test to understand the areas you are lagging.  3rd Grade Go Math Answer Key Ch 7 Division Facts and Strategies Assessment Test includes all the topics via quick links. Prepare whichever topic you want and solve all the questions in it and know the Solutions from Go Math Grade 3 Answer Key Ch 7 Division Facts and Strategies Assessment Test.

Teachers can use this Go Math Grade 3 Answer Key for Chapter 7 Assessment Test as a sample test to check their student’s knowledge. We tried mentioning the Step by Step Solutions for all the Problems from Practice Tests, Chapter Tests, Cumulative Practice. Use the 3rd Grade Go Math Chapter 7 Answer Key Assessment Test as a quick reference to check your knowledge after preparing the concepts within it.

Chapter 7: Division Facts and Strategies Assessment Test

Test – Page 1 – Page No. 71

Question 1.
Shang shared 28 postcards among 7 different people. Each person received the same number of postcards. How many postcards did Shang give to each person?
28 ÷ 7 = n
7 × n = 28
Options:
a. 4
b. 5
c. 6
d. 21

Answer: a

Explanation:
As Shang shared 28 postcards to 7 different people so 28 ÷ 7 = 4 , 7 × 4 = 28. Shang gave 4 postcards to each person.

Question 2.
Lionel has 14 mittens.
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 1 img 1
Select one number from each column to show the division equation represented by the picture.
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 1 img 2
14 ÷ ______ = ______

Answer: 14 ÷ 2 = 7.

Explanation: 14 ÷ 2 = 7 which is 7 pairs of mitten given the model.

Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test

Test – Page 2 – Page No. 72

Question 3.
Fifteen people are going rafting. They brought 5 rafts. An equal number of people ride in each raft. How many people will be in each raft?
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 2 img 3
______ people

Answer: 3 people.

Explanation:
No of people going for rafting = 15
Total no of rafts available = 5
No of people will be in each raft = 15 ÷ 5 = 3 people.

Question 4.
Circle a number for the unknown factor and quotient that makes the equation true.
4 × Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 2 img 4 = 24
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 2 img 5 = 24 ÷ 4
4 × ______ = 24 ;               ______ = 24 ÷ 4

Answer:
4×6= 24
6= 24 ÷ 4

Explanation:

= 24

Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test= 24 ÷ 4

Question 5.
There are 20 students in science class. There are 10 students sitting at each table. How many tables are there?
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 2 img 6
Write a division equation to represent the repeated subtraction.
______ ÷ ______ = ______

Answer: 20 ÷ 10 = 2.

Explanation:
Total no of students in class = 20
No of students sitting at each table = 10
Therefore no of tables = 20 ÷ 10 = 2

Question 6.
Complete the chart to show the quotients.
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 2 img 7

Answer:
63÷9= 7.
72÷9= 8.
81÷9= 9.
90÷9= 10.

Explanation:

Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test

Test – Page 3 – Page No. 73

Question 7.
For numbers 7a–7e, select True or False for each equation.
a. 0 ÷ 6 = 6
i. True
ii. False

Answer: False

Explanation: 0 ÷ 6 = 0, so the answer is false. 

Question 7.
b. 6 ÷ 6 = 1
i. True
ii. False

Answer: True

Explanation: As 6 ÷ 6 = 1, so the answer is true.

Question 7.
c. 18 ÷ 6 = 2
i. True
ii. False

Answer: False.

Explanation: As 18 ÷ 6 = 3, so the answer is false.

Question 7.
d. 54 ÷ 6 = 9
i. True
ii. False

Answer: True.

Explanation: As 54 ÷ 6 = 9, so the answer is true.

Question 7.
e. 60 ÷ 10 = 6
i. True
ii. False

Answer: True.

Explanation: As 60 ÷ 10 = 6, so the answer is true.

Question 8.
Kaitlyn says that 8 ÷ 2 × 4 is the same as 4 × 2 ÷ 8.
Is Kaitlyn correct or incorrect? Explain.

Answer: No. 8 ÷ 2 × 4 and 4 × 2 ÷ 8 are not the same.

Expplanation:Lets calculate 8 ÷ 2 × 4 = 4 × 4 = 16 by using BODMAS, first we did division later multiplication
4 × 2 ÷ 8 = 4 × ¼ = 1. Thus both results are not same.

Question 9.
Brian is dividing 64 baseball cards equally among 8 friends. How many baseball cards will each friend get?
_______ baseball cards

Answer: 8 baseball cards.

Explanation:
Total cards available = 64
No of friends = 8
No of baseball cards each gets = 64 ÷ 8 = 8

Question 10.
Tara made $18 selling cookies. She wants to know how many cookies she sold. Tara used this number line.
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 3 img 8
Write the division equation that the number line represents.
______ ÷ ______ = ______

Answer: 18 ÷ 3 = 6.

Explanation:
Possible answers could be if she sells each cookie at $ 3 then 18 ÷ 3 = 6 were sold

Test – Page 4 – Page No. 74

Question 11.
Each team at a science competition has 6 players. How many teams are there if 42 players are at the competition? Explain the strategy you used to solve the problem.
_____ teams

Answer: 7 teams.

Explanation:
Given that there is a total of 42 players
Each team has 6 players, therefore the total number of teams = 42 ÷ 6 = 7 teams.

Question 12.
Carly bought 3 packs of baseball cards. Each pack had the same number of cards. She gave 5 cards to her sister. Now she has 19 cards. How many baseball cards were in each pack? Explain how you solved the problem.
_____ baseball cards

Answer: 24 ÷ 3 = 8 baseball cards.

Explanation:
Total packs bought were = 3
No of cards she has = 19
No of cards given to her sister = 5
Total number cards = 19+5 = 24
No of cards in each pack = 24 ÷ 3 = 8 cards.

Question 13.
Andrea used 35 craft sticks to make 7 door hangers. She used the same number of craft sticks for each door hanger. How many craft sticks did Andrea use for each door hanger?
_____ craft stick

Answer: 5 craft sticks.

Explanation:
Total no of craft sticks used by Andrea = 35
No of door hangers made = 7
Therefore no of craft sticks used for each door hanger = (Total no of craft sticks ÷  no of door hangers)
= 35 ÷ 7
= 5 craft sticks.

Question 14.
For numbers 14a–14e, use the order of operations. Select True or False for each equation.
a. 45 ÷ 5 − 3 = 6
i. True
ii. False

Answer: True.

Explanation:
By BODMAS rule
45 ÷ 5 − 3
= 9 – 3
= 6

Question 14.
b. 12 + 4 ÷ 4 = 13
i. True
ii. False

Answer: True.

Explanation:
By BODMAS rule
12 + 4 ÷ 4
= 12 + 1
= 13

Question 14.
c. 3 + 7 × 8 = 80
i. True
ii. False

Answer: false.

Explanation:
By BODMAS rule
3 + 7 × 8
= 3 + 56
= 59

Question 14.
d. 32 ÷ 8 × 2 = 2
i. True
ii. False

Answer: false.

Explanation:
By BODMAS rule
32 ÷ 8 × 2
= 4 × 2
= 8.

Question 14.
e. 40 − 10 × 3 = 10
i. True
ii. False

Answer: True.

Explanation:
By BODMAS rule
40 − 10 × 3
= 40 – 30
= 10.

Test – Page 5 – Page No. 75

Question 15.
Patrick sells homemade pretzels in bags with 9 pretzels in each bag. He sells 54 pretzels in all. How many bags of pretzels does he sell?
______ bags

Answer: 6 bags.

Explanation:
No of bags sold = (Total no of pretzels / no of pretzels in each bag)
= 54/9
= 6 bags.

Question 16.
Enrique started a table showing a division pattern.
Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test Test - Page 5 img 9
Part A
Complete the table.
Compare the quotients when dividing by 10 and when dividing by 5. Describe a pattern you see in the quotients.

Answer:
10÷10= 1
10÷5= 2
20÷10= 2
20÷5= 4
30÷10= 3
30÷5= 6
40÷10= 4
40÷5= 8.

Explanation:

Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Assessment Test

Question 16.
Part B
Find the quotient, a.
80 ÷ 10 = a
a = ______

Answer: 8.

Explanation:
80 ÷ 10 = 8.
The quotient is 8.

How could you use a to find the value of n?
Find the value of n.
80 ÷ 5 = n
n = ______
a = ______
n = ______

Answer:
a= 8.
n= 16.

Explanation: By doubling the value of ‘a’ we can get the value of ‘n’. As the value of ‘a’ is 8, so the value of ‘n’= 8+8= 16

Question 17.
Eve needs 2 limes to make a glass of limeade. If limes come in bags of 12, how many glasses of limeade can she make using one bag?
______ glasses

Answer: 6 glasses.

Explanation: The limes in the bags are 12 and Eve needs 2 glasses of limeade, so the number of glasses she can make is 12÷2= 6 glasses.

Test – Page 6 – Page No. 76

Question 18.
For numbers 18a–18e, select True or False for each equation.
a. 18 ÷ 9 = 2
i. True
ii. False

Answer: True

Explanation: As 18 ÷ 9 = 2, so the answer is true.

Question 18.
b. 27 ÷ 9 = 4
i. True
ii. False

Answer: False.

Explanation: As 27 ÷ 9 = 3, so the answer is false.

Question 18.
c. 45 ÷ 9 = 5
i. True
ii. False

Answer: True.

Explanation: As 45 ÷ 9 = 5, so the answer is true.

Question 18.
d. 72 ÷ 9 = 7
i. True
ii. False

Answer: False

Explanation: As 72 ÷ 9 = 8, so the answer is false.

Question 18.
e. 81 ÷ 9 = 8
i. True
ii. False

Answer: False.

Explanation: As 81 ÷ 9 = 9, so the answer is true.

Question 19.
Holly is making 4 vegetable trays for a party. She wants to divide 36 carrot sticks equally among the trays. How many carrot sticks will she put on each tray?
______ carrot sticks

Answer: 9 carrot sticks.

Explanation: No of carrot sticks on each tray = (Total carrot sticks ÷ no of vegetable trays)
= 36 ÷ 4
= 9 carrot sticks in each tray

Question 20.
Hector is buying books at a book store.
Part A
He buys 2 used books and 1 new book for $26. The new book costs $18. Each used book costs the same amount. What is the price of each used book? Explain the steps you used to solve the problem.
$ ______

Answer: Each used book costs $ 4.

Explanation:
Given that cost of one new book = $ 18
Cost of 2 used books + 1 new book = $ 26
Cost of 2 used books = 26 – 18 = 8
Cost of 1 used book = 8/2 = $4

Question 20.
Part B
Hector also buys a reading light for $12 and 2 journals for $8 each to give as gifts. Write one equation to describe the total amount Hector spends on gifts. Explain how to use the order of operations to solve the equation.
Total amount: $ ______

Answer: $ 28.

Explanation:
Hector bought a reading light for $12
2 journals for $8 each
Total money spent on gifts = 12 + (2 x 8)
= 12 + 16
= $ 28.

Final Words

We wish the knowledge shared regarding the Go Math Grade 3 Chapter 7 Division Facts and Strategies Assessment Test has helped you in your way. To know more about the topics check out our Go Math Grade 3 Answer Key Chapter 7 Division Facts and Strategies Extra Practice.

Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test

Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test covers all the topics of Chapter 2. Through this assessment test, you can test your preparation level and get a good grip on the concepts easily. 3rd Grade Go Math Chapter 2 Represent and Interpret Data Assessment Test you can cover the entire syllabus easily.

Enhance your math skills, by referring to the Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test and score better grades in your exam. We even Provided Step by Step Solutions for all the Grade 3 Go Math Answer Key Ch 2 making it easy for you to get grip on the subject.

Chapter 2: Represent and Interpret Data Assessment Test

Test – Page 1 – Page No. 21

Question 1.
John made a tally table to record the animals he saw on a trip to Alaska.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 1 img 1
For numbers 1a–1c, select True or False for each statement.
a. John saw twice as many bears as foxes.
i. True
ii. False

Answer: False

Explanation: John saw foxes 4 times wherein bears 7 times, which is not double to 4.

Question 1.
b. John saw 5 more caribou than bears.
i. True
ii. False

Answer: False

Explanation: He saw 4 more caribou than bears.

Question 1.
c. John saw 4 fewer moose than foxes.
i. True
ii. False

Answer: False

Explanation: He saw 2 fewer moose than foxes, not 4.

Question 2.
Kayla asked 26 students in her class how they traveled to school. The frequency table shows the results.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 1 img 2
Part A
Complete the table and explain how you found the answer.
______ girls

Answer: 6 girls.

Explanation:
Total no of students in class = 26
Let’s consider no of girls travel by bus = X
Total no of girls traveled to school = 3+X+5 = 8+X
Total no of boys traveled to school = 12
Therefore no of girls travel by bus X=(Total no of students in the class– (No of girls travel by walk and car + boys traveled by all three))
= 26 – (8+12)
= 6.

Question 2.
Part B
How many more students are there who travel by car or bus to school than students who walk to school? Show your work.
______ more students

Answer: 10 more students.

Explanation:
No of students travel by car or bus = 4 + 6 + 3 + 5 = 18
No of students travel by walk = 5 + 3 = 8
Difference between both = 10
Therefore 10 more students travel by car or bus to school than students who walk to school.

Test – Page 2 – Page No. 22

Use the picture graph for 3– 6.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 2 img 3
Three friends are collecting canned food for the food bank. The picture graph shows the number of cans collected so far.

Question 3.
How many cans were collected? Explain how you found the total.
______ cans

Answer: 85 cans.

Explanation: Soo collected 7 symbols, Jen collected 4 symbols and Sam collected 6 symbols
Total symbols collected by all three = 7+4+6 = 17
Given that each symbol = 5 cans, Total no of cans collected = 17 × 5 = 85 cans.

Question 4.
Choose the name from each box that makes the sentence true.
Ten fewer cans were collected by Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 2 img 4 than Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 2 img 5.

Answer: Jen collected Ten fewer cans than Sam

Explanation:

Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test
Jen collected 4×5 = 20 cans, Sam collected 6×5 = 30 cans and
Soo collected 7×5 = 35cans
Difference between Jen and Sam = 30 -20 = 10
Difference between Jen and Soo = 35 – 20 = 15
Therefore the given statement can be written as Jen collected Ten fewer cans than Sam.

Question 5.
How many more cans did Soo collect than Jen?
______ cans

Answer: 15 more cans.

Explanation:
Jen collected 4×5 = 20 cans, Soo collected 7×5 = 35cans
Difference between Jen and Soo = 35 – 20 = 15cans.

Question 6.
Jen collects 20 more cans. Draw a picture to show how the graph will change.

Answer: In the below picture added 4 more symbols to Jen, which means added 20 more cans.

Explanation:

Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test

Test – Page 3 – Page No. 23

Use the frequency table for 7–8.

Question 7.
Ms. Green’s class is recycling bottles to help the environment. The frequency table shows the number of bottles the class recycled each week.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 3 img 6
Part A
Use the data in the table to complete the picture graph.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 3 img 7

Answer: Since we circle symbol represents 10 bottles. We drew 7 for week 1, 4 half for week 2, and 6 for week 3.

Explanation:

Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test

 

Question 7.
Part B
How many pictures did you draw for Week 2? Explain.

Answer: 4 ½

Explanation: Because each circle represents 10 bottles, we drew 4 circles to represent 40 bottles and 1 half circle to represent 5 bottles.

Question 8.
The class has a goal of recycling 250 bottles during the month. How many more bottles do they need to recycle in Week 4 to meet that goal?
Options:
a. 100 bottles
b. 175 bottles
c. 75 bottles
d. 55 bottles

Answer: 75 bottles.

Explanation: Given 70 bottles are recycled in week 1, 45 in week 2, 60 in week 3, so in week 4 the number of bottles recycled is
250-175= 75 bottles.

Test – Page 4 – Page No. 24

Use the bar graph for 9–12.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 4 img 8

Question 9.
Two more students play basketball than which other sport?
_________

Answer: Two more students play basketball than baseball.

Explanation: From the graph, we understood that 8 students play baseball and 10 students play Basketball. Therefore 2 more students play basketball than baseball.

Question 10.
How many students play either baseball or soccer?
______ students

Answer: 19 students.

Explanation: 8 students play baseball wherein 11 students play soccer. Therefore a total of 19 students play either baseball or soccer.

Question 11.
For numbers 11a–11d, select True or False for each statement.
a. Ten more students play basketball than play football.
i. True
ii. False

Answer: False.

Explanation: Only two more students play basketball than play football.

Question 11.
b. Eleven students play soccer.
i. True
ii. False

Answer: True.

Explanation: We can see in the graph as 11 students played soccer.

Question 11.
c. 34 students play a sport.
i. True
ii. False

Answer: False

Explanation: We can see in the graph as a total of 35 students plays a sport.

Question 11.
d. Five fewer students play football than play soccer.
i. True
ii. False

Answer: True.

Explanation: No of students play football = 8, No of students play soccer = 11.
The difference between both is 3, so about 5 fewer students play football than soccer.

Question 12.
There are more students who play volleyball than play football, but fewer students play volleyball than play basketball. Explain how you could change the bar graph to show the number of students who play volleyball.

Answer: Since it was given that more students play volleyball than football, the bar for volleyball will be somewhere between 6 and 10. We could add the data at the top of the graph, above the bar for baseball.

Test – Page 5 – Page No. 25

Use the frequency table for 13–14.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 5 img 9

Question 13.
For the class picnic people have a choice of four kinds of sandwiches. The frequency tableshows the number of sandwiches chosen.
Part A
Use the data in the table to complete the bar graph.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 5 img 10

Answer:

Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test

Question 13.
Part B
How do you know how long to make the bars on your graph? How did you show 14 chicken sandwiches? Explain.

Answer: I drew the bars to end at the number of choices shown in the table. Since 14 is halfway between 12 and 16 the bar stops in the middle of the space between 12 and 16.

Question 14.
How many more are there of the two sandwiches that were chosen the most than of the two sandwiches that were chosen the least? Explain how you solved the problem.
______ sandwiches

Answer: 12 Sandwiches.

Explanation: People chose 10 + 14 = 24 of the two most popular sandwiches. People chose 8 + 4 12 of the least popular sandwiches. The difference is 24 − 12 = 12 sandwiches.

Test – Page 6 – Page No. 26

Use the line plot for 15–16.

Yuji made a line plot to show the number of hours each student in his music class practiced every week.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 6 img 11

Question 15.
For numbers 15a–15d, select True or False for each statement.
a. Three students practiced exactly 5 hours each week.
i. True
ii. False

Answer: True

Explanation: We can see on the graph as 3 students practiced exactly 5 hours each week.

Question 15.
b. Seven students practiced 4 hours or less each week.
i. True
ii. False

Answer: True.

Explanation: We can see on the graph as Seven students practiced 4 hours or less each week.

Question 15.
c. Six students practiced exactly 1 hour each week.
i. True
ii. False

Answer: False

Explanation: In the graph, one hour is not represented.

Question 15.
d. Two students practiced more than 6 hours each week.
i. True
ii. False

Answer: True

Explanation: We can see on the graph as two students practiced more than 6 hours each week.

Question 16.
What if two more students joined the class and each practiced 9 hours a week? Describe what the line plot would look like.

Answer: If two more students join, each practicing 9 hrs a week. Then the line plot would be extended to 9. There would be two Xs above the 9. The 8 in the line plot would have no Xs marked.

Use the line plot for 17–18.

Paige grew squash in her garden. She measured the length of each squash to the nearest inch and recorded the data in the line plot.
Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test Test - Page 6 img 12

Question 17.
How many squash were 10 inches or longer?
_____ squash

Answer: 6 squashes.

Explanation: 6 squashes were 10 inches and more than 10 inches longer

Question 18.
How many more squash were 9 inches long than 7 inches long?
_____ squash

Answer: 2 squashes

Explanation: 2 more squash was 9 inches longer than 7 inches long.

Conclusion

Test your knowledge using the Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data Assessment Test and identify the knowledge gap. To get more help lookup to Go Math Grade 3 Answer Key Chapter 2 Represent and Interpret Data and clear your queries.

Go Math Grade K Answer Key Chapter 12 Classify and Sort Data

Students of Grade K can get a strong foundation on mathematics concepts by referring to the Go Math Grade K Chapter 12 Answer Key Classify and Sort Data. It was developed by highly professional mathematics educators and the solutions prepared by them are in a concise manner for easy grasping.

Go Math Grade K Chapter 12 Answer Key 12 Classify and Sort Data

To achieve high score s in Grade K, students need to solve all questions and exercises included in Go Math Grade K. So, teachers and students can find this Go Math Answer Key for Grade K more helpful in raising students’ scores and supporting teachers to educate the students. With the help of Go Math Primary School Grade K Answer Key, you can think deeply regarding what you are learning, and you will really learn math easily just like that.

Classify and Sort Data Show What You Know

DIRECTIONS 1. Circle the fruits that are red. 2. Circle the triangles. 3. Count and write how many in each set. Circle the set with more objects. 4. Count and write how many in each set. Circle the set with fewer objects.

Color and Shape
Question 1.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.1

Answer:
The number of fruits that are in red color = 4.

Explanation:
In the above-given figure,
given that,
the fruits are apple, watermelon, pineapple, orange, cherries, banana, strawberry.
out of all, there are 4 fruits in red color.
The number of fruits that are in red color = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-1

Question 2.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.2

Answer:
The number of Triangles = 2.

Explanation:
In the above-given figure,
given that,
Circle the triangles.
the number of triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-2

Compare Sets
Question 3.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.3

Answer:
The number of butterflies = 6.

Explanation:
In the above-given figure,
given that,
There are 6 butterflies.
the number of butterflies = 6.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-3

Question 4.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.4

Answer:
The number of butterflies = 6.

Explanation:
In the above-given figure,
given that,
There are 6 butterflies.
the number of butterflies = 6.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-4

Answer:
The number of shells = 7.

Explanation:
In the above-given figure,
given that,
There are 7 shells.
the number of shells = 7.

Question 5.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.5

Answer:
The number of bees = 8.

Explanation:
In the above-given figure,
given that,
There are 8 bees.
the number of bees = 8.

Answer:
The number of flowers = 9.

Explanation:
In the above-given figure,
given that,
There are 9 flowers.
the number of flowers = 9.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-5

Classify and Sort Data Vocabulary Builder

DIRECTIONS Tell what you know about the ladybugs. Some of the ladybugs are different. Circle those ladybugs and tell why they are different. Tell what you know about the butterflies.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.6

Answer:
The number of butterflies = 5.
The butterflies are in a different colors.

Explanation:
In the above-given figure,
given that,
There are 5 butterflies.
the number of butterflies = 5.

Answer:
The number of ladybugs = 8.
Some ladybugs are dancing and some of them are blowing mike.

Explanation:
In the above-given figure,
given that,
There are 8 ladybugs.
the number of ladybugs = 8.

Classify and Sort Data Game At the Farm

DIRECTIONS Use the picture to play I Spy with a partner. Decide who will go first. Player 1 looks at the picture, selects an object, and tells Player 2 the color of the object. Player 2 must guess what Player 1 sees. Once Player 2 guesses correctly, it is his or her turn to choose an object and have Player 1 guess.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.7

Answer:
The number of ducks = 4.

Explanation:
In the above-given figure,
given that,
There are 4 ducks.
the number of ducks = 4.

Answer:
The number of baskets = 3.

Explanation:
In the above-given figure,
given that,
There are 3 baskets.
the number of baskets = 3.

Classify and Sort Data Vocabulary Game

Guess the Word
DIRECTIONS Players take turns. A player chooses a secret word from the Word Box and then sets the timer. The player gives hints about the secret word. If the other player guesses the secret word before time runs out, he or she puts a connecting cube in the chart. The first player who has connecting cubes in all his or her boxes is the winner.

MATERIALS timer, connecting cubes for each player
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 1.8

The Write Way
DIRECTIONS Choose one idea.

  • Draw to show how to classify objects by size.
  • Draw to show a graph. Reflect Be ready to tell about your drawing.

Lesson 12.1 Algebra • Classify and Count by Color

Essential Question How can you classify and count objects by color?

Listen and Draw

DIRECTIONS Choose a color. Use that color crayon to color the clouds. Sort and classify a handful of shapes into a set of that color and a set of not that color. Draw and color the shapes.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 1

Answer:
The color of the cloud is the blue color.
The color of the heart symbol is red color.

Explanation:
In the above-given question,
given that,
the color of the cloud is blue color.
The color of the heart symbol is red color.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-1

Share and Show

Question 1.
DIRECTIONS 1. Place shapes as shown. Sort and classify the shapes by the category of color. Draw and color the shapes in each category.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 2

Answer:
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.

Explanation:
In the above-given question,
given that,
the shapes are red, blue, yellow, and green.
the shapes are circle, triangle, square, and rectangle.
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-2

DIRECTIONS Look at the categories of color in Exercise 1. Count how many in each category. 2. Circle the categories of color that have one shape. Write the number. 3. Circle the category that has two shapes. Write the number. 4. Circle the category that has three shapes. Write the number.
Question 2.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 3

Answer:
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.

Explanation:
In the above-given question,
given that,
the shapes are red, blue, yellow, and green.
the shapes are circle, triangle, square, and rectangle.
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-3

Question 3.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 4

Answer:
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.

Explanation:
In the above-given question,
given that,
the shapes are red, blue, yellow, and green.
the shapes are circle, triangle, square, and rectangle.
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-4

Question 4.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 5

Answer:
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.

Explanation:
In the above-given question,
given that,
the shapes are red, blue, yellow, and green.
the shapes are circle, triangle, square, and rectangle.
The number of shapes that are in red color = 3.
The number of shapes that are in blue color = 2.
The number of shapes that are in yellow color = 1.
The number of shapes that are in green color = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-5

Problem Solving • Applications

DIRECTIONS 5. Ava placed her shapes as shown. How did she sort and classify her shapes? Draw one more shape in each category. 6. Draw to show what you know about sorting and classifying by color.
Question 5.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 6

Answer:
The number of shapes in the 1st category = 6.
The number of shapes in the 2nd category = 6.

Explanation:
In the above-given question,
given that,
the shapes are
rectangle, triangle, square, circle.
The number of shapes in the 1st category = 6.
The number of shapes in the 2nd category = 6.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-6

Question 6.
Answer:
Sorting = Arrange systematically in groups and separating according to type.

Explanation:
In the above-given question,
given that,
draw the shapes and sort it.
Sorting = Arrange systematically in groups and separating according to type.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-7

HOME ACTIVITY • Provide your child with different colors of the same objects, such as straws, socks, or toys. Ask him or her to sort and classify the objects into two sets, a set of all one color and a set of all the other colors.

Algebra • Classify and Count by Color Homework & Practice 12.1

DIRECTIONS 1. Place a yellow square, red triangle, red rectangle, yellow square, and red triangle at the top of the page as shown. Sort and classify the shapes by the category of color. Draw and color the shapes in each category. 2. Look at the categories in Exercise 1. Count how many in each category. Circle the category that has 3 shapes. Write the number.
Question 1.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 7

Answer:
The number of squares = 2.
The number of rectangle = 1.
the number of triangles = 2.

Explanation:
In the above-given question,
given that,
the yellow square, red rectangle, red triangle, yellow square, and red triangle.
Sort and classify the shapes by category.
The number of squares = 2.
The number of rectangle = 1.
the number of triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-8

Question 2.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 8

Answer:
The shape that has red color = 3.

Explanation:
In the above-given question,
given that,
the number of shapes that are in red color = 3.
The shape that has red color = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-9

DIRECTIONS 1. Look at the set of shapes. Which shape belongs in the same category? Draw that shape in the box and color it. How many shapes are in the category now? Write the number. 2. Which shape does not stack? Mark an X on the shape. 3. Count and tell how many pieces of fruit. Write the number.
Lesson Check
Question 1.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 9

Answer:
The number of triangles = 4.

Explanation:
In the above-given figure,
given that,
There are 4 triangles.
the number of triangles = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-10

Spiral Review
Question 2.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 10

Answer:
The shape does not stack = sphere.

Explanation:
In the above-given question,
given that,
the shapes are prism, cylinder, sphere, and cylinder.
The shape does not stack = sphere.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-11

Question 3.
Grade K Go Math Answer Key Chapter 12 Classify and Sort Data 12.1 11

Answer:
The number of fruits = 20.

Explanation:
In the above-given question,
given that,
There are 20 fruits.
The number of fruits = 20.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-12

Lesson 12.2 Algebra • Classify and Count by Shape

Essential Question How can you classify and count objects by shape?

Listen and Draw

DIRECTIONS Choose a shape. Draw the shape at the top of each side. Sort and classify a handful of shapes into a set of the shape you chose and a set that is not that shape. Draw and color the shapes.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 1

Answer:
0.93.

Explanation:
In the above-given question,
given that,
the numbers are (3/10), (41/100), and (22/100).
(3/10) = 0.3.
(41/100) = 0.41.
(22/100) = 0.22.
0.3 + 0.41 + 0.22 = 0.93.

Share and Show

DIRECTIONS 1. Place shapes as shown. Sort and classify the shapes by the category of shape. Draw and color the shapes in each category.
Question 1.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 2

Answer:
The number of circles = 1.

Explanation:
In the above-given figure,
given that,
There is 1 circle.
the number of circles = 1.

Answer:
The number of squares = 1.

Explanation:
In the above-given figure,
given that,
There is 1 square.
the number of squares = 1.

Answer:
The number of triangles = 2.

Explanation:
In the above-given figure,
given that,
There are 2 triangles.
the number of triangles = 2.

Answer:
The number of rectangles = 3.

Explanation:
In the above-given figure,
given that,
There are 3 rectangles.
the number of rectangles = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-1

DIRECTIONS Look at the categories of shapes in Exercise 1. Count how many in each category. 2. Circle the categories of shapes that have one shape. Write the number. 3. Circle the category that has two shapes. Write the number. 4. Circle the category that has three shapes. Write the number.
Question 2.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 3

Answer:
The number of circles = 1.

Explanation:
In the above-given figure,
given that,
There is 1 circle.
the number of circles = 1.

Answer:
The number of squares = 1.

Explanation:
In the above-given figure,
given that,
There is 1 square.
the number of squares = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-2

Question 3.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 4

Answer:
The number of triangles = 2.

Explanation:
In the above-given figure,
given that,
There are 2 triangles.
the number of triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-3

Question 4.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 5

Answer:
The number of rectangles = 3.

Explanation:
In the above-given figure,
given that,
There are 3 rectangles.
the number of rectangles = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-4

Problem Solving • Applications

DIRECTIONS 5. Brandon used his shapes. How did he sort and classify his shapes? Draw one more shape in each category. 6. Using the same shapes, draw to show what you know about sorting and classifying by shape in a different way.
Question 5.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 6

Answer:
The number of squares = 3.

Explanation:
In the above-given figure,
given that,
There are 3 squares.
the number of squares = 3.

Answer:
The number of rhombus = 2.

Explanation:
In the above-given figure,
given that,
There are 2 rhombus.
the number of rhombus = 2.

Answer:
The number of circles = 1.

Explanation:
In the above-given figure,
given that,
There is 1 circle.
the number of circles = 1.

Answer:
The number of triangles = 2.

Explanation:
In the above-given figure,
given that,
There are 2 triangles.
the number of triangles = 2.

Answer:
The number of rectangles = 3.

Explanation:
In the above-given figure,
given that,
There are 3 rectangles.
the number of rectangles = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-5

Question 6.

Answer:
Sorting = Distinguish between necessary and unnecessary items and eliminate the unnecessary items.

Explanation:
In the above-given question,
given that,
the meaning of sorting is
Distinguish between necessary and unnecessary items and eliminate the unnecessary items.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.1-7

HOME ACTIVITY • Have your child sort objects in a house into categories of shape.

Algebra • Classify and Count by Shape Homework & Practice 12.2

DIRECTIONS 1. Place a green triangle, blue circle, red triangle, and blue circle at the top of the page as shown. Sort and classify the shapes by the category of shape. Draw and color the shapes in each category. 2. Look at the categories in Exercise 1. Count how many in each category. Circle the categories that have two shapes. Write the number.
Question 1.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 7

Answer:
The number of circles = 2.
the number of triangles = 2.

Explanation:
In the above-given question,
given that,
green triangle, blue circle, red triangle, and blue circle.
Sort and classify the shapes by category.
The number of squares = 2.
The number of rectangle = 1.
the number of triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-6

Question 2.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 8

Answer:
The number of triangles = 2.
The number of circles = 2.

Explanation:
In the above-given question,
given that,
the shapes of triangles and circles.
the number of triangles = 2.
the number of circles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-7

DIRECTIONS 1. Look at the set of shapes. Which shape belongs in the same category? Draw that shape in the oval. How many shapes are in the category now? Write the number. 2. Find two crayons. Place one end of each crayon on the line. Compare the lengths. Draw the crayons. Say longer than, shorter than, or about the same length to describe the lengths. Circle the longer crayon. 3. Complete the addition sentence to show the numbers that match the cube train.
Lesson Check
Question 1.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 9

Answer:
The number of triangles = 4.

Explanation:
In the above-given figure,
given that,
There are 4 triangles.
the number of triangles = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-8

Spiral Review
Question 2.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 10

Answer:
The length of the 1st crayon = 4 cm.
The length of the 2nd crayon = 2 cm.

Explanation:
In the above-given question,
given that,
there are 2 crayons.
the 1st crayon is longer than the 2nd crayon.
The length of the 1st crayon = 4 cm.
The length of the 2nd crayon = 2 cm.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-9

Question 3.
Go Math Grade K Answer Key Chapter 12 Classify and Sort Data 12.2 11

Answer:
The number is 5.

Explanation:
In the above-given question,
given that,
the number is 5.
5 = 1 + 4.
so the number is 5.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.2-10

Lesson 12.3 Algebra • Classify and Count by Size

Essential Question How can you classify and count objects by size?

Listen and Draw

DIRECTIONS Sort and classify a handful of shapes by size. Draw and color the shapes.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 1

Answer:
The objects which are in short length = small objects.
The objects which are in long length = large objects.

Explanation:
In the above-given question,
given that,
the number of objects is short and large.
The objects which are in short length = small objects.
The objects which are in long length = large objects.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-1

Share and Show

DIRECTIONS 1. Place shapes as shown. Sort and classify the shapes by the category of size. Draw and color the shapes in each category.
Question 1.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 2

Answer:
The number of triangles = 2.
The number of rectangles = 3.
The number of squares = 1.
The number of circles = 1.

Explanation:
In the above-given question,
given that,
the shapes are triangle, rectangle, squares, and circle.
The number of triangles = 2.
The number of rectangles = 3.
The number of squares = 1.
The number of circles = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-2

DIRECTIONS Look at the categories of size in Exercise 1. Count how many in each category. 2. Circle the category that has three per category. Write the number. 3. Circle the category that has four per category. Write the number.
Question 2.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 3

Answer:
The number of rectangles = 3.

Explanation:
In the above-given figure,
given that,
There is 1 small and 2 big rectangles.
the number of rectangles = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-4

Question 3.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 4

Answer:
The number of rectangles = 3.

Explanation:
In the above-given figure,
given that,
There is 1 small and 2 big rectangles.
the number of rectangles = 3.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-5
Algebra • Classify and Count by Size Homework & Practice 12.3

DIRECTIONS 1. Place a yellow square, blue circle, red rectangle, and blue rectangle at the top of the page as shown. Sort and classify the shapes by the category of size. Draw and color the shapes in each category. 2. Look at the categories in Exercise 1. Count how many in each category. Circle the category that has one per category. Write the number.
Question 1.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 5

Answer:
The number of circles = 1.
the number of rectangles = 2.
the number of squares = 1.

Explanation:
In the above-given question,
given that,
yellow square, blue circle, red rectangle, and blue rectangle.
Sort and classify the shapes by category.
The number of squares = 1.
The number of rectangle = 2.
the number of circles = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-6

Question 2.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 6

Answer:
The number of rectangle = 1.

Explanation:
In the above-given question,
given that,
The number of small rectangles = 1.
The number of rectangle = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-7

DIRECTIONS 1. Sort and classify the shapes by the category of size. Draw the shapes in each category. 2. How many flat surfaces does the cylinder have? Write the number. 3. Sarah makes a five-cube train. She takes the cube train apart to show how many cubes are gray. Trace and write to show the subtraction sentence for Sarah’s cube train.
Lesson Check
Question 1.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 7

Answer:
The number of small objects = 3.
The number of big objects = 1.

Explanation:
In the above-given question,
given that,
the shapes are circle, square, rectangle, and triangle.
The number of small objects = 3.
The number of big objects = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-8

Spiral Review
Question 2.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 8

Answer:
The number of flat surfaces = 2.

Explanation:
In the above-given question,
given that,
The number of flat surfaces = 2
there are 2 flat surfaces for the cylinder.
the number of flat surfaces = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-9

Question 3.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 9

Answer:
The number is 3.

Explanation:
In the above-given question,
given that,
the number is 5.
5 – 2 = 3.
The number is 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-10

Classify and Sort Data Mid-Chapter Checkpoint

Concepts and Skills

DIRECTIONS 1. Look at the set at the beginning of the row. Circle the shape that belongs in that set. (K.MD.B.3) 2. Look at the shape at the beginning of the row. Mark an X on the set in which the shape belongs. (K.MD.B.3) 3. Draw lines to match the shapes to the category.
Question 1.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 10

Answer:
The shape of the circle = yellow.

Explanation:
In the above-given question,
given that,
The shapes are blue, green, and yellow.
the yellow color matches the 1st category.
The shapes of the circle = yellow.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-11

Question 2.
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 11

Answer:
The Triangle belongs to the 2nd category.

Explanation:
In the above-given question,
given that,
The shape is a triangle,
the triangle belongs to the 2nd category.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-12

Question 3.
THINK SMARTER
Go Math Answer Key Grade K Chapter 12 Classify and Sort Data 12.3 12

Answer:
The circle, square, and triangle in green color.
The triangles are big.
The circle, square, and triangle are small.

Explanation:
In the above-given question,
given that,
the shapes are triangles.
The circle, square, and triangle in green color.
The triangles are big.
The circle, square, and triangle are small.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.3-13

Lesson 12.4 Make a Concrete Graph

Essential Question How can you make a graph to count objects that have been classified into categories?

Listen and Draw

DIRECTIONS Place a handful of orange and green cubes on the workspace. Sort and classify the cubes by the category of color. Move the cubes to the graph by category. Draw and color the cubes. Tell a friend how many in each category.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 1

Answer:
The number of orange cubes = 4.
The number of green cubes = 3.

Explanation:
In the above-given question,
given that,
There are 4 orange and 3 green cubes.
The number of orange cubes = 4.
The number of green cubes = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-1

Share and Show

DIRECTIONS 1. Place a handful of red and blue cubes on the workspace. Sort and classify the cubes by category. 2. Move the cubes to the graph. Draw and color the cubes. 3. Write how many of each cube.
Question 1.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 2

Answer:
The number of cubes = 5.
the number of green cubes = 3.
the number of orange cubes = 2.

Explanation:
In the above-given question,
given that,
the number of cubes = 5.
the number of green cubes = 3.
the number of orange cubes = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-2

Question 2.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 3

Answer:
The number of red cubes = 4.
The number of blue cubes = 3.

Explanation:
In the above-given question,
given that,
The number of red cubes = 4.
The number of blue cubes = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-3

Question 3.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 4

Answer:
The number of red cubes = 4.
The number of blue cubes = 3.

Explanation:
In the above-given question,
given that,
The number of red cubes = 4.
The number of blue cubes = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-4

DIRECTIONS 4. Place a handful of green circles and triangles on the workspace. Sort and classify the shapes by category. 5. Move the shapes to the graph. Draw and color the shapes. 6. Write how many of each shape.
Question 4.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 5

Answer:
the number of green circles = 3.
the number of green triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of green circles = 3.
the number of green triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-5

Question 5.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 6

Answer:
the number of green circles = 3.
the number of green triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of green circles = 3.
the number of green triangles = 2.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-6

Question 6.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 7

Answer:
the number of green circles = 3.
the number of green triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of green circles = 3.
the number of green triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-7

Problem Solving • Applications

DIRECTIONS 7. Use five cubes of two colors. Color the cubes to show the categories. Draw and color to show what you know about making a graph with those cubes. How many are in each category? Write the numbers.
Question 7.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 8

Answer:
The number of green cubes = 3.
the number of orange cubes = 2.

Explanation:
In the above-given question,
given that,
the number of cubes = 5.
the number of green cubes = 3.
the number of orange cubes = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-8

HOME ACTIVITY • Have your child tell about the graph that he or she made on this page.

Make a Concrete Graph Homework & Practice 12.4

DIRECTIONS 1. Place a handful of green circles and triangles on the workspace. Sort and classify the shapes by category. 2. Move the shapes to the graph. Draw and color the shapes. 3. Write how many of each shape.
Question 1.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 9

Answer:
the number of green circles = 3.
the number of green triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of green circles = 3.
the number of green triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-5

Question 2.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 10

Answer:
the number of green circles = 3.
the number of green triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of green circles = 3.
the number of green triangles = 2.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-6

Question 3.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 11

Answer:
the number of green circles = 3.
the number of green triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of green circles = 3.
the number of green triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-9

DIRECTIONS 1. Look at the shapes. Draw and color the shapes in the graph. Write how many of each shape. 2. Make a cube train that is about the same height as the cube train shown. Draw and color the cube train. 3. How many tiles are there? Write the number.
Lesson Check
Question 1.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 12

Answer:
The number of triangles = 5.
The number of squares = 2.

Explanation:
In the above-given question,
given that,
The shapes are triangles, and squares.
The number of triangles = 5.
The number of squares = 2.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-10

Spiral Review
Question 2.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 13

Answer:
The number of cubes = 3.

Explanation:
In the above-given question,
given that,
the number of cubes = 3.
cube train = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-11

Question 3.
Go Math Grade K Answer Key Chapter Classify and Sort Data 12.4 14

Answer:
The number of tiles = 14.

Explanation:
In the above-given question,
given that,
there are 14 tiles.
the number of tiles = 14.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.4-12

Lesson 12.5 Problem Solving • Read a Graph

Essential Question How can you read a graph to count objects that have been classified into categories?

Try Another Problem

DIRECTIONS 1. Billy made a graph showing his counters. Color the counters to show his categories. How many counters are in each category? Write the numbers. 2. Circle the category that has more counters on the graph.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 1
Question 1.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 2

Answer:
The number of yellow counter = 5.
The number of red counters = 4.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 5.
The number of red counters = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-1

Question 2.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 3

Answer:
The number of yellow counter = 5.
The number of red counters = 4.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 5.
The number of red counters = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-2

Share and Show

DIRECTIONS 3. Rong made a graph of her counters. Color the counters to show her categories. How many counters are in each category? Write the numbers. 4. Circle the category that has fewer counters on the graph.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 4
Question 3.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 5

Answer:
The number of yellow counter = 4.
The number of red counters = 3.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 4.
The number of red counters = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-3

Question 4.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 6

Answer:
The number of yellow counter = 4.
The number of red counters = 3.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 4.
The number of red counters = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-4

On Your Own

DIRECTIONS 5. Brian has more blue cubes than red cubes. Draw and color to show his cubes on the graph. Count how many in each category. Write the numbers.
Question 5.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 7.1

Answer:
The number of red cubes = 3.
The number of blue cubes = 4.

Explanation:
In the above-given question,
given that,
The number of red cubes = 3.
The number of blue cubes = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-5

HOME ACTIVITY • Have your child tell about the graph he or she made on this page. Ask him or her which category has more cubes and which category has fewer cubes.

Problem Solving • Read a Graph Homework & Practice 12.5

DIRECTIONS 1. Color the counters to show the categories. R is for red, and Y is for yellow. How many counters are in each category? Write the numbers. 2. Circle the category that has more counters on the graph.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 7.2
Question 1.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 7

Answer:
The number of yellow counter = 3.
The number of red counters = 4.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 3.
The number of red counters = 4.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-6
Question 2.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 8

Answer:
The number of yellow counter = 3.
The number of red counters = 4.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 3.
The number of red counters = 4.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-7

DIRECTIONS 1. How many counters are in each category? Write the numbers. Circle the category that has more counters. 2. Complete the addition sentence to show the numbers that match the cube train. 3. Make a cube train that is about the same length as the cube train shown. Draw and color the cube train.
Lesson Check
Question 1.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 9

Answer:
The number of yellow counter = 5.
The number of red counters = 3.

Explanation:
In the above-given question,
given that,
there are yellow and red counters.
The number of yellow counter = 5.
The number of red counters = 3.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-8

Spiral Review
Question 2.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 10

Answer:
The number of cubes = 8.

Explanation:
In the above-given question,
given that,
the number of cubes = 8.
3 + 5 = 8.
cube train = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-9

Question 3.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data 12.5 11

Answer:
The number of cubes = 8.

Explanation:
In the above-given question,
given that,
the number of cubes = 8.
3 + 5 = 8.
cube train = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-10

Classify and Sort Data Review/Test

DIRECTIONS 1. Lin sorted some shapes into categories by color. Look at the shape at the beginning of the row. Mark an X on the category that shows where the shape belongs. 2. Draw and color a shape that belongs in this category. 3. Look at the shape at the beginning of the row. Mark under all of the categories the shape can belong.
Question 1.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 1

Answer:
The number of circles = 1.

Explanation:
In the above-given question,
given that,
The number of circles = 1.
The number of circles = 1.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-11
Question 2.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 2

Answer:
The number of circles = 2.
The number of triangles = 2.
The number of square = 1.
The number of rhombus = 1.

Explanation:
In the above-given question,
given that,
the shapes are circle, triangle, square, and rhombus.
The number of circles = 2.
The number of triangles = 2.
The number of square = 1.
The number of rhombus = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-12

Question 3.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 3

Answer:
The number of circles = 2.
The number of triangles = 2.
The number of square = 1.
The number of rhombus = 1.

Explanation:
In the above-given question,
given that,
the shapes are circle, triangle, square, and rhombus.
The number of circles = 2.
The number of triangles = 2.
The number of square = 1.
The number of rhombus = 1.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-13

DIRECTIONS 4. Draw and color a shape that belongs in this category. 5. Mark an X on each big shape. Write how many big objects. Draw a circle around each of the small objects. Write how many small objects. 6. Draw lines to match the shapes to the way they were sorted.
Question 4.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 4

Answer:
The number of rectangles.

Explanation:
In the above-given question,
given that,
There are squares and rectangles.
The number of rectangles.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-14

Question 5.
THINK SMARTER+
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 5

Answer:
The number of big objects = 2.
The number of small objects = 4.

Explanation:
In the above-given question,
given that,
the big objects and small objects.
The number of big objects = 2.
The number of small objects = 4.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-15

Question 6.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 6

Answer:
The big objects are square, triangle, and circe.
the small objects are square, circle, and triangle.

Explanation:
In the above-given question,
given that,
the shapes are square, triangle, and circle.
The big objects are square, triangle, and circe.
the small objects are square, circle, and triangle.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-16

DIRECTIONS 7. Sort and classify the shapes by category. Draw each shape on the graph. Write how many of each shape. 8. Jake sorted some shapes. Then he made a graph. Count how many shapes there are in each category. Mark an X on the category that has more shapes.
Question 7.
THINK SMARTER+
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 7

Answer:
the number of circles = 3.
the number of triangles = 2.

Explanation:
In the above-given question,
given that,
the number of circles and triangles.
the number of circles = 3.
the number of triangles = 2.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-17

Question 8.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 8

Answer:
The number of squares = 2.
The number of circles = 3.

Explanation:
In the above-given question,
given that,
the shapes are square and circles.
The number of squares = 2.
The number of circles = 3.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-18

DIRECTIONS 9. Is this chart sorted by color, size, and shape? Choose Yes or No. 10. Choose all of the sets with the same number of objects.
Question 9.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 9

Answer:
The square is red in color.
The circle is blue in color.

Explanation:
In the above-given question,
given that,
the shapes are circle and square.
The square is red in color.
The circle is blue in color.
Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-19

Question 10.
Go Math Grade K Chapter 12 Answer Key Pdf Classify and Sort Data rt 10

Answer:
The number of objects in all sets = 3.

Explanation:
In the above-given question,
given that,
there are 4 sets.
each set contains different objects.
so we have to choose 3 sets equal.
The number of objects in all sets = 3.

Go-Math-Grade-K-Chapter-12-Answer-Key-12 Classify and Sort Data-12.5-20

Go Math Grade 3 Answer Key Chapter 6 Understand Division

go-math-grade-3-chapter-6-understand-division-answer-key

Are you looking everywhere to learn about Go Math Grade 3 Answer Key Chapter 6 Understand Division? This Answer Key includes topics like related multiplication and division facts, repeated subtraction, number of equal groups, and so on. Those who are preparing for the Grade 3 Ch 6 will find the HMH Go Math Grade 3 Answer Key Chapter 6 Understand Division extremely helpful. You can identify your knowledge gap by solving the Questions from 3rd Grade Go Math Answer Key Chapter 6 Understand Division.

Go Math Grade 3 Answer Key Chapter 6 Understand Division

Before you begin your preparation learn the topics included in Grade 3 Go Math Answer Key Chapter Understand Division. You can always look up to Go Math Grade 3 Chapter 6 Key as a reference to clear all your queries. Practice the problems in 3rd Grade Go Math Answer Key Ch 6 Understand Division and understand the concepts easily.

Lesson 1: Problem Solving • Model Division

Lesson 2: Size of Equal Groups

Lesson 3: Number of Equal Groups

Lesson 4: Model with Bar Models

Lesson 5: Algebra • Relate Subtraction and Division

Mid-Chapter Checkpoint

Lesson 6: Investigate • Model with Arrays

Lesson 7: Algebra • Relate Multiplication and Division

Lesson 8: Algebra • Write Related Facts

Lesson 9: Algebra • Division Rules for 1 and 0

Chapter 6 Review/Test

Model Division Page No 305

Question 1.
Six customers at a toy store bought 18 jump ropes. Each customer bought the same number of jump ropes. How many jump ropes did each customer buy?
__________

Answer: 3 jump ropes

Explanation:

Given that there are Six customers at a toy store bought 18 jump ropes
Each customer bought the same number of jump ropes
To know the number of jump roses that each customer bought
You must place each jump ropes until all the jump ropes are used.
That means 18 jump ropes to all 6 customers
= 18 ÷ 6 = 3
Therefore each customer bought 3 jump ropes

Question 2.
Hiro has 36 pictures of his summer trip. He wants to put them in an album. Each page of the album holds 4 pictures. How many pages will Hiro need for his pictures?
__________

Answer: 9 pages

Explanation:

Hiro has 36 pictures of his summer trip. He wants to put them in an album
Each page of the album holds 4 pictures
Make it into the equal groups and put 4 pictures in each page
= 36 ÷ 4 = 9
Thus Hiro need 9 pages for his pictures

Question 3.
Katia has 42 crayons in a box. She buys a storage bin that has 6 sections. She puts the same number of crayons in each section. How many crayons does Katia put in each section of the storage bin?
__________

Answer: 7 crayons

Explanation:

Katia has 42 crayons in a box
She buys a storage bin that has 6 sections
Make 42 crayons as a group and place 1 crayon in each section. Then you get 7 crayons in each section
42 ÷ 6 = 42/6 = 7
Therefore 7 crayons do Katia put in each section of the storage bin

Question 4.
Ms. Taylor’s students give cards to each of the 3 class parent helpers. There are 24 cards. How many cards will each helper get if the students give an equal number of cards to each helper?
__________

Answer: 8 cards

Explanation:

Ms. Taylor’s students give cards to each of the 3 class parent helpers
Total number of cards = 24
Make 3 equal groups and place each card for 3 class parent helpers
You get 8 cards for each helper
24 ÷ 3 = 8

Question 5.
Jamie divides 20 baseball stickers equally among 5 of his friends. How many stickers does each friend get?
__________

Answer: 4 stickers

Explanation:

Jamie divides 20 baseball stickers equally among 5 of his friends
Give each baseball sticker to each friend and repeat the process until you finish all the stickers
So, each friend gets 4 baseball stickers.
20 ÷ 5 = 4 stickers

Model Division Page No 306

Question 1.
Maria buys 15 apples at the store and places them into bags. She puts 5 apples into each bag. How many bags does Maria use for all the apples?
Options:
a. 2
b. 3
c. 4
d. 10

Answer: 3

Explanation:

Maria buys 15 apples at the store and places them into bags
She puts 5 apples into each bag
That means each bag contains 5 apples
Now, Divide the apples into equal groups and place them in each bag
15 ÷ 5 = 3
Therefore Maria uses 3 bags to put 15 apples.

Question 2.
Tom’s neighbor is fixing a section of his walkway. He has 32 bricks that he is placing in 8 equal rows. How many bricks will Tom’s neighbor place in each row?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given: Tom’s neighbor is fixing a section of his walkway
He has 32 bricks that he is placing in 8 equal rows
Now place each brick in all 8 rows  equally and repeat until the bricks are over
32 ÷ 8 = 4
So, you get 4 bricks in each row
Thus the correct answer is option B

Question 3.
Find the unknown factor.
7 × _ = 56
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

Let the unknown factor be x
7 × x = 56
Go Math Grade 3 Chapter 6 Answer Key Division Method img_1

So, the correct answer is option C

Question 4.
How many students practiced the piano more than 3 hours a week?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model Division img 1
Options:
a. 2
b. 6
c. 8
d. 10

Answer: 6

Explanation:

3 students practiced the piano for 4 hours
2 students practiced the piano for 5 hours and
1 student practiced the piano for 6 hours
= 3 + 2 + 1 = 6
The above line plot shows that there are 6 students who practiced the piano for more than 3 hours

Question 5.
Count equal groups to find how many there are.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model Division img 2
Options:
a. 3
b. 4
c. 12
d. 16

Answer: 12

Explanation:

The above figure shows that there are 4 circles and each circle is divided into 3 equal groups
So, multiply number of circles with equal groups
= 4 × 3 = 12
Thus the correct answer is option C

Question 6.
Which is another way to group the factors?
(3 × 2) × 5
Options:
a. (3 + 2) + 5
b. (3 × 2) + 5
c. 3 × (2 + 5)
d. 3 × (2 × 5)

Answer: 3 × (2 × 5)

Explanation:

The another way to group (3 × 2) × 5 is 3 × (2 × 5)
Because there is no change in the symbol and number
So, the correct answer is option D

Size of Equal Groups Page No 311

Use counters or draw a quick picture. Make equal groups. Complete the table.

Question 1.

CountersNumber of Equal GroupsNumber in Each Group
1.153__________
2.217__________
3.287__________
4.324__________
5.93__________
6.183__________
7.205__________
8.168__________
9.355__________
10.243__________

Answer:

CountersNumber of Equal GroupsNumber in Each Group
1.1535
2.2173
3.2874
4.3248
5.933
6.1836
7.2054
8.1682
9.3557
10.2438

Explanation:

1. No. of counters = 15
Number of equal groups = 3
Place 1 counter to each group, you get 5 in each group

2. No. of counters = 21
Number of equal groups = 7
Place 1 counter to each group, you get 3 in each group

3. No. of counters = 28
Number of equal groups = 7
Place 1 counter to each group, you get 4 in each group

4. No. of counters = 32
Number of equal groups = 4
Place 1 counter to each group, you get 8 in each group

5. No. of counters = 9
Number of equal groups = 3
Place 1 counter to each group, you get 3 in each group

6. No. of counters = 18
Number of equal groups = 3
Place 1 counter to each group, you get 6 in each group

7. No. of counters = 20
Number of equal groups = 5
Place 1 counter to each group, you get 4 in each group

8. No. of counters = 16
Number of equal groups = 8
Place 1 counter to each group, you get 2 in each group

9. No. of counters = 35
Number of equal groups = 5
Place 1 counter to each group, you get 7 in each group

10. No. of counters = 24
Number of equal groups = 3
Place 1 counter to each group, you get 8 in each group

Question 11.
Alicia has 12 eggs that she will use to make 4 different cookie recipes. If each recipe calls for the same number of eggs, how many eggs will she use in each recipe?
__________

Answer: 3 eggs

Explanation:

Total number of eggs Alicia has = 12
she will use to make 4 different cookie recipes
Make 4 groups and place 12 eggs in each group
You get 3 eggs in each group
12/4 = 3 eggs

Question 12.
Brett picked 27 flowers from the garden. He plans to give an equal number of flowers to each of 3 people. How many flowers will each person get?
__________

Answer: 9 flowers

Explanation:

Given,
Brett picked 27 flowers from the garden
He plans to give an equal number of flowers to each of 3 people
Give each flower to 3 people until 27 flowers complete
So, Each person get 9 flowers
27 ÷ 3 = 9 flowers

Size of Equal Groups Page No 312

Question 1.
Ryan has 21 pencils. He wants to put the same number of pencils in each of 3 pencil holders. How many pencils will he put in each pencil holder?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 7

Explanation:

Ryan has 21 pencils
He wants to put the same number of pencils in each of 3 pencil holders
Split it into 3 groups and share each pencil to each group
You get 7 pencils for each of 3 groups
21/3 = 7
Thus the correct answer is option B

Question 2.
Corrine is setting out 24 plates on 6 tables for a dinner. She sets the same number of plates on each table. How many plates does Corrine set on each table?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given,
Corrine is setting out 24 plates on 6 tables for a dinner
She sets the same number of plates on each table
Make a group of 6 tables and place 1 plate for each group
You get 4 plates for each table
24/6 = 4 plates
So, the correct answer is Option B

Question 3.
Each table has 4 legs. How many legs do 4 tables have?
Options:
a. 1
b. 8
c. 16
d. 20

Answer: 16

Explanation:

Given that Each table has 4 legs
4 tables have x number of legs
x = 4 × 4 = 16
Therefore 4 tables have 16 legs

Question 4.
Tina has 3 stacks of 5 CDs on each of 3 shelves. How many CDs does she have in all?
Options:
a. 14
b. 30
c. 35
d. 45

Answer: 45

Given,
Tina has 3 stacks of 5 CDs on each of 3 shelves
How many CDs does she have in all = x
To know the number of CDs in all we have to multiply no. of stacks, no. of CDs on each of 3 shelves
x = 3 × 5 × 3 = 15 × 3 = 45
So, the answer is option D

Question 5.
What is the unknown factor?
7 × _= 35
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

Let the unknown factor be x
7 × x = 35
x = 35/7 = 5
Therefore the correct answer is option B

Question 6.
Which of the following describes a pattern in the table?

Number of packs12345
Number of yo-yos36912?

Options:
a. Add 2.
b. Multiply by 2.
c. Multiply by 3.
d. Add 12.

Answer: Multiply by 3.

Explanation:

Add 3 yo-yos for each pack and multiply no. of pans by 3

Number of Equal Groups Page No 317

Draw counters on your MathBoard. Then circle equal groups. Complete the table.

Question 1.

CountersNumber of Equal GroupsNumber in Each Group
1.2438
2.35__________7
3.30__________5
4.16__________4
5.12__________6
6.36__________9
7.18__________3
8.15__________5
9.28__________4
10.27__________3

Answer:

CountersNumber of Equal GroupsNumber in Each Group
1.2438
2.3557
3.3065
4.1644
5.1226
6.3649
7.1863
8.1535
9.2874
10.2793

Explanation:

1. No. of counters = 24
Number in each group = 8
24/8 = 3
So, the number of equal groups = 3

2. No. of counters = 35
Number in each group = 7
35/7 = 5
So, the number of equal groups = 5

3. No. of counters = 30
Number in each group = 5
30/5 = 6
So, the number of equal groups = 6

4. No. of counters = 16
Number in each group = 4
16/4 = 4
So, the number of equal groups = 4

5. No. of counters = 12
Number in each group = 6
12/6 = 2
So, the number of equal groups = 2

6. No. of counters = 36
Number in each group = 9
36/9 = 4
So, the number of equal groups = 4

7. No. of counters = 18
Number in each group = 3
18/3 = 6
So, the number of equal groups = 6

8. No. of counters = 15
Number in each group = 5
15/5 = 3
So, the number of equal groups = 3

9. No. of counters = 28
Number in each group = 4
28/4 = 7
So, the number of equal groups = 7

10. No. of counters = 27
Number in each group = 3
27/3 = 9
So, the number of equal groups = 9

Question 11.
In his bookstore, Toby places 21 books on shelves, with 7 books on each shelf. How many shelves does Toby need?
__________

Answer: 3 shelves

Explanation:

Toby places 21 books on shelves, with 7 books on each shelf
No. of shelves does Toby need = x
x = 21/7 = 3
Thus Toby need 3 shelves

Question 12.
Mr. Holden has 32 quarters in stacks of 4 on his desk. How many stacks of quarters are on his desk?
__________

Answer: 8 stacks

Explanation:

Mr. Holden has 32 quarters in stacks of 4 on his desk
No. of stacks of quarters on his desk = y
y × 4 = 32
y = 32/4 = 8 stacks
No. of stacks of quarters on his desk = 8 stacks

Number of Equal Groups Page No 318

Question 1.
Ramon works at a clothing store. He puts 24 pairs of jeans into stacks of 8. How many stacks does Ramon make?
Options:
a. 5
b. 4
c. 3
d. 2

Answer: 3

Explanation:

Ramon puts 24 pairs of jeans into stacks of 8
Split the pair of jeans to 8 groups of the stack
You get 3 pair of jeans for each stack
24/8 = 3
Therefore the correct answer is option C

Question 2.
There are 36 people waiting in line for a hayride. Only 6 people can ride on each wagon. If each wagon is full, how many wagons are needed for all 36 people?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: 6

Explanation:

There are 36 people waiting in line for a hayride.
Only 6 people can ride on each wagon
Split 36 people into 6 groups
That means 36/6 = 6 Wagons
So, the correct answer is option B

Question 3.
Which multiplication sentence does the array show?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Number of Equal Groups img 3
Options:
a. 4 × 5 = 20
b. 4 × 6 = 24
c. 4 × 7 = 28
d. 4 × 8 = 32

Answer: 4 × 7 = 28

Explanation:

There are 4 rows and 7 columns
rows × columns = 4 × 7 = 28
Thus the answer is option C

Question 4.
Austin buys 4 boxes of nails for his project. There are 30 nails in each box. How many nails does Austin buy in all?
Options:
a. 12
b. 34
c. 70
d. 120

Answer: 120

Explanation:

Given,
Austin buys 4 boxes of nails for his project
There are 30 nails in each box
No. of nails does Austin buy in all = 30 + 30 + 30 + 30
4 × 30 = 120
So, the correct answer is option D

Question 5.
Which describes the number sentence?
8 + 0 + 8
Options:
a. odd + odd = odd
b. Identity Property of Addition
c. even + even = even
d. Commutative Property of Addition

Answer: Identity Property of Addition

Explanation:

In math, identity is a number, n, that when added to other numbers, gives the same number, n. The additive identity is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 6.
Each month for 6 months, Kelsey completes 5 paintings. How many more paintings does she need to complete before she has completed 38 paintings?
Options:
a. 2
b. 6
c. 8
d. 9

Answer: 8

Explanation:

Each month for 6 months
Kelsey completes 5 paintings
x no. of paintings she need to complete before she has completed 38 paintings
6 × 5 = 30 paintings
x + 30 = 38
x = 38 – 30
x = 8
So, the correct answer is option C

Model with Bar Models Page No 323

Write a division equation for the picture.

Question 1.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 4

Answer: 27 ÷ 3 = 9 or 27 ÷ 9 = 3

Explanation:

There are 27 counters and each circle has 9 groups. There are 3 groups of 9 counters.
27 ÷ 3 = 27/3 = 9
27 ÷ 9 = 27/9 = 3

Question 2.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 5
Type below:
___________

Answer: 16 ÷ 8 = 2 or 16 ÷ 2 = 8

Explanation:

The total number of counters is 16 and circle a group of 2 counters. Continue circling groups of 2 until all 16 counters are in the group.
So, Divide Total number of counters by number of equal groups
16 ÷ 8 = 16/8 = 2
Next, Divide total number of counters by no. of counters in each group.
16 ÷ 2 = 16/2 = 8

Question 3.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 6
Type below:
___________

Answer: 16 ÷ 4 = 4

Explanation:

The total number of counters is 16 and circle a group of 4 counters. Continue circling groups of 4 until all 16 counters are in the group
Divide No. of counters by no. of equal groups = 16 ÷ 4 = 4
And then divide no. of counters by no. of counters in each group = 16 ÷ 4 = 4

Question 4.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 7
Type below:
___________

Answer: 18 ÷ 3 = 6 or 18 ÷ 6 = 3

Explanation:

Number of counters = 18
Number of Equal groups = 3
Number of counters in each group = 6
Divide No. of counters by no. of equal groups
18 ÷ 3 = 18/3 = 6
Divide No. of counters by no. of counters in each group
18 ÷ 6 = 18/6 = 3

Complete the bar model to solve. Then write a division equation for the bar model.

Question 5.
There are 15 postcards in 3 equal stacks. How many postcards are in each stack?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 8
________ postcards

Answer: 5 postcards, 15 ÷ 3 = 5

Explanation:

Total number of postcards = 15
Number of equal stacks = 3
Number of postcards in each stack = x
x = No. of postcards/ No. of equal stacks
x = 15/3
x = 5
Thus each stack contains 5 postcards

Question 6.
There are 21 key rings. How many groups of 3 key rings can you make?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 9
________ groups

Answer: 7 groups, 21 ÷ 3 = 7

Explanation:

Divide the 21 key rings into 7 to make 7 groups with 3 key rings each group
21 ÷ 3 = 21/3 = 7 groups

There are 7 groups of 3 key rings.

Problem Solving

Question 7.
Jalyn collected 24 stones. She put them in 4 equal piles. How many stones are in each pile?
________ stones

Answer: 6 stones

Explanation:

Given,

Jalyn collected 24 stones
She put them in 4 equal piles
No. of stones in each pile = x
Divide total no. of stones by 4 equal piles
24 ÷ 4 = 24/4 = 6
There are 6 stones in each pile

Question 8.
Tanner has 30 stickers. He puts 6 stickers on each page. On how many pages does he put stickers?
________ pages

Answer: 5 pages

Explanation:

Tanner has 30 stickers
Tanner puts 6 stickers on each page
Now, Divide Number of stickers by number of stickers on each page
= 30 ÷ 6 = 30/6 = 5 pages

Model with Bar Models Page No 324

Question 1.
Jack and his little sister are stacking 24 blocks. They put the blocks in 3 equal stacks. How many blocks are in each stack?
Options:
a. 4
b. 6
c. 7
d. 8

Answer: 8

Explanation:

Total number of blocks = 24
They put the blocks in 3 equal stacks
To know the blocks in each stack, we have to divide no. of blocks by number of equal stacks
24 ÷ 3 = 24/3 = 8 blocks
There are 8 blocks in each stack
So, the correct answer is option D

Question 2.
Melissa made 45 greeting cards. She put them in 5 equal piles. How many cards did she put in each pile?
Options:
a. 9
b. 8
c. 7
d. 6

Answer: 9

Explanation:

Given,
Melissa made 45 greeting cards
She put them in 5 equal piles
To know the number of cards she put in each pile
We have to divide number of cards by no. of equal piles
= 45 ÷ 5 = 45/5 = 9 cards
Thus there are 9 cards in each pile
So, the correct answer is option A

Spiral Review

Question 3.
Angie puts 1 stamp on each envelope. She puts stamps on 7 envelopes. How many stamps does Angie use?
Options:
a. 0
b. 1
c. 7
d. 8

Answer: 7

Explanation:

Angie puts 1 stamp on each envelope
She puts stamps on 7 envelopes
To find Number of stamps Angie use, we have to divide no. of stamps on envelopes by no. of stamps on each envelope
= 7 ÷ 1 = 7

Question 4.
A carnival ride has 8 cars. Each car holds 4 people. How many people are on the ride if all the cars are full?
Options:
a. 34
b. 32
c. 28
d. 24

Answer: 32

Explanation:

Given,
A carnival ride has 8 cars
Each car holds 4 people
1 car = 4 people
8 cars = x
x × 1 = 4 × 8
x = 32
32 people are on the ride if all the cars are full

Use the line plot for 5–6.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Bar Models img 10

Question 5.
How many families have 1 computer at home?
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 6

Explanation:

The line plot shows that there are 6 families who have 1 computer at home

Question 6.
How many families have more than 1 computer at home?
Options:
a. 4
b. 5
c. 7
d. 8

Answer: 8

Explanation:

Number of Families have 2 computers at home = 3
Number of Families have 3 computers at home = 4
Number of Families have 4 computers at home = 1
Number of Families have more than 1 computer at home = 3 + 4 + 1 = 8

Relate Subtraction and Division Page No 329

Write a division equation.

Question 1.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Subtraction and Division img 11

Answer: 16 ÷ 4 = 4

Explanation:

Step 1:

Start with 16

Step 2:

Subtract with 4 until you get 0

Step 3:

Count the number of times you subtract 4

Since you subtract 4 times
There are 4 groups 4 in 16
So 16 ÷ 4 = 4
Sixteen divided by four equals four

Question 2.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Subtraction and Division img 12
______ ÷ ______ = ______

Answer: 12 ÷ 3 = 4

Explanation:

Step 1:

Start at 12

Step 2:

Count back by 3s as many times as you can.

Step 3:

Count the number of times you jumped back 3.

You jumped back 3 four times
There are 4 groups of 3 in 12
12 ÷ 3 = 4

Question 3.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Subtraction and Division img 13
______ ÷ ______ = ______

Answer: 10 ÷ 2 = 5

Explanation:

Step 1:

Start at 10

Step 2:

Count back by 2s as many times as you can.

Step 3:

Count the number of times you jumped back 2.

You jumped back 2 five times
There are 5 groups of 2 in 10
10 ÷ 2 = 5

Question 4.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Subtraction and Division img 14
______ ÷ ______ = ______

Answer: 20 ÷ 5 = 4

Explanation:

Step 1:

Start at 20

Step 2:

Subtract with 5 until you get 0

Step 3:

Count the number of times you subtract with 5

Since you subtract 4 times
There are 4 groups of 5 in 20
So 20 ÷ 5 = 4
Twenty divided by five equals four

Use repeated subtraction or a number line to solve.

Question 5.
28 ÷ 7 = ______

Answer: 4

Explanation:

Step 1:

Start at 28

Step 2:

Subtract with 7 until you get 0

Step 3:

Count the number of times you subtract with 7

Since you subtract 4 times
There are 4 groups of 7 in 28
So 28 ÷ 7 = 4
Twenty eight divided by seven equals four

Question 6.
18 ÷ 6 = ______

Answer: 3

Step 1:

Start at 18

Step 2:

Subtract with 6 until you get 0

Step 3:

Count the number of times you subtract with 6

Since you subtract 3 times
There are 3 groups of 6 in 18
So 18 ÷ 6 = 3
Eighteen divided by six equals three

Question 7.
8)\( \bar{ 4 0 }\)
________

Answer: 5

HMH Go Math solution Key Grade 3 Chapter Division image_2

Explanation:

Since you subtract 5 times
There are 5 groups of 8 in 40
40 divided by 8 equals 5

Question 8.
9)\( \bar{ 3 6 }\)
________

Answer: 4

Go Math Chapter 6 Answer Key Grade 3 Division image_1

Explanation:

You subtract 36 and 9 by 4 times
There are 4 groups of 9 in 36
So, 36 divided by 9 equals 4

Question 9.
Mrs. Costa has 18 pencils. She gives 9 pencils to each of her children for school. How many children does Mrs. Costa have?
________ children

Answer: 2 children

Explanation:

Given,
Mrs. Costa has 18 pencils
She gives 9 pencils to each of her children for school
Divide total number of pencils by no. pencils to each of her children for school
18 ÷ 9 = 2 pencils

Question 10.
Boël decides to plant rose bushes in her garden. She has 24 bushes. She places 6 bushes in each row. How many rows of rose bushes does she plant in her garden?
________ rows

Answer: 4 rows

Explanation:

Boel has 24 bushes
she places 6 bushes in each row
To know the number of rows of rose bushes does she plant in her garden
We have to divide the total number of bushes by bushes in each row
= 24 ÷ 6 = 24/6 = 4

Relate Subtraction and Division Page No 330

Question 1.
Which division equation is shown?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Subtraction and Division img 15
Options:
a. 3 × 4 = 12
b. 12 ÷ 6 = 2
c. 12 ÷ 3 = 4
d. 12 ÷ 4 = 3

Answer: 12 ÷ 6 = 2

Explanation:

Step 1:

Count starts at 12

Step 2:

Count back by 6s as many times as you can until you get 0

Step 3:

Count the number of times you jumped back
You jumped back 2 times
There are 2 jumps from 12 to 0
So the correct answer is option B

Question 2.
Isabella has 35 cups of dog food. She feeds her dogs 5 cups of food each day. For how many days will the dog food last?
Options:
a. 6 days
b. 7 days
c. 8 days
d. 9 days

Answer: 7 days

Explanation:

Given that,

Isabella has 35 cups of dog food
She feeds her dogs 5 cups of food each day
To find the number of days will the dog food last
We have to divide number of cups by the number of cups of food each day
= 35 ÷ 5 = 35/5 = 7
So, the correct answer is option B

Spiral Review

Question 3.
Ellen buys 4 bags of oranges. There are 6 oranges in each bag. How many oranges does Ellen buy?
Options:
a. 10
b. 12
c. 24
d. 30

Answer: 24

Explanation:

Given:
Ellen buys 4 bags of oranges
There are 6 oranges in each bag
Total number of oranges = no. of bags × no. of oranges in each bag
= 4 × 6 = 24
Therefore the correct answer is option B

Question 4.
Each month for 7 months, Samuel mows 3 lawns. How many more lawns does he need to mow before he has mowed 29 lawns?
Options:
a. 1
b. 3
c. 7
d. 8

Answer: 8

Explanation:

Each month for 7 months, Samuel mows 3 lawns
For one month Samuel mows 3 lawns
For 7 months Samuel mows = x
x = 7 × 3 = 21
Now, we need to know how many more lawns does he need to mow before he has mowed 29 lawns
Subtract 21 from 29
= 29 – 21 = 8
So the answer is option D

Use the graph for 5–6.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Subtraction and Division img 16

Question 5.
How many hours did Eli volunteer?
Options:
a. 4 hours
b. 8 hours
c. 9 hours
d. 10 hours

Answer: 9 hours

Explanation:

The bar graph shows that Eli volunteered 9 hours
So, the correct answer is option C

Question 6.
Madi volunteered 2 hours less than Jill. At what number should the bar for Madi end?
Options:
a. 3
b. 6
c. 8
d. 12

Answer: 8

Explanation:

The figure shows that Jill has volunteered 10 hours
If Madi has volunteered 2 hours less than Jill
= 10 – 2 = 8 hours
Thus the correct answer is option C

Mid-Chapter Checkpoint Page No 331

Vocabulary

Choose the best term from the box to complete the sentence.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 17
Question 1.
You _________ when you separate into equal groups.
_________

Answer: Divide

When you divide, you separate into equal groups.

Concepts and Skills

Use counters or draw a quick picture on your MathBoard.
Make or circle equal groups. Complete the table.

Question 2.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 18
Type below:
___________

Answer:

2. Number of counters = 6
Number of equal groups = 2
Number in each group =  __
= 6/2 = 3

3. Number of counters = 30
Number of equal groups = __
Number in each group = 5
= 30/5 = 6

4. Number of counters = 28
Number of equal groups = 7
Number in each group = __
= 28/7 = 4

Write a division equation for the picture.

Question 5.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 19
Type below:
___________

Answer: 8 ÷ 4 = 2 or 8 ÷ 2 = 4

Explanation:

The number of counters is 8 and a circle group of 4 counters.
Continue circling group of 4 until all the 8 counters are in the group
Divide Number of counters by Number of equal groups
= 8 ÷ 2 = 4
Divide Number of counters by number in each group
8 ÷ 4 = 2

Question 6.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 20
Type below:
___________

Answer: 15 ÷ 3 = 5 or 15 ÷ 5 = 3

Explanation:

Number of counters = 15
Number of groups = 3
Number in each group = 5
Divide Number of counters by number of groups
= 15 ÷ 3 = 5
Divide number of counters by number in each group
= 15 ÷ 5 = 3

Write a division equation.

Question 7.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 21
______ ÷ ______ = ______

Answer: 36 ÷ 9 = 4

Explanation:

Step 1:

Starts at 36

Step 2:

Subtract with 9 until you get 0

Step 3:

Count the number of times you subtract with 9

You subtract 4 times
There are 4 groups of 9 with 36
So, 36 ÷ 9 = 4

Question 8.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 22
______ ÷ ______ = ______

Answer: 21 ÷ 3 = 7

Explanation:

Step 1:

Starts at 21

Step 2:

Count back by 3s as many times as you can

Step 3:

Count the number of times you jumped back 3.
You jumped back by 21 seven times
There are 7 jumps of 3 in 21

Mid-Chapter Checkpoint Page No 332

Question 9.
Victor plants 14 seeds in some flowerpots. If he puts 2 seeds in each pot, how many flowerpots does he use?
_________ flowerpots

Answer: 7 flowerpots

Explanation:

Victor plants 14 seeds in some flowerpots
If he puts 2 seeds in each pot
Number of flowerpots he uses = x
x = 14/2
x = 7
So, Victor used 7 flowerpots

Question 10.
Desiree had 35 stickers. She gave each of 3 friends the same number of stickers. She now has 20 stickers left. She then gives the same number of stickers to each of another 5 friends. How many stickers did she give each of her 3 friends? Each of her 5 friends?
Type below:
___________

Answer: 5 stickers for 3 friends; 4 stickers for 5 friends

Explanation:

Given,
Desiree had 35 stickers
She gave each of 3 friends the same number of stickers
She now has 20 stickers left
To know how many stickers she gave to her friends
We have to subtract the number of stickers left from total number of stickers
35 – 20 = 15
That means she gave 15 stickers to her 3 friends equally
15 ÷ 3 = 5 stickers
So, each friend gets 5 stickers
Next, she gave remaining 20 stickers to 5 friends equally
20 ÷ 5 = 4
So, each friend gets 4 stickers

Question 11.
Jayden modeled a division equation with some counters. What division equation could Jayden have modeled?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 23
Type below:
___________

Answer: 14 ÷ 2 = 7 or 14 ÷ 7 = 2

Explanation:

Number of counter = 14
Number in each group = 7
Number of equal groups = 2
So, the division equation is the number of counters by number of equal groups = 14 ÷ 2 = 7
Or, Number of counters by number in each group = 14 ÷ 7 = 2

Question 12.
Lillian bought 24 cans of cat food. There were 4 cans in each pack. How many packs of cat food did Lillian buy?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Mid -Chapter Checkpoint img 24
_________ packs

Answer: 6 packs

Explanation:

Lillian bought 24 cans of cat food
There were 4 cans in each pack
Number of packs of cat food did Lillian buy
24 ÷ 4 = 6 packs

Model with Arrays Page No 337

Use square tiles to make an array. Solve

Question 1.
How many rows of 4 are in 12?
______ rows

Answer: 3 rows

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Explanation:

Step 1:

Total number of tiles are 12

Step 2:
Make a row of 4 tiles

Step 3:

Continue to make as many rows of 4 tiles as you can
We get 4 tiles in each row
3 rows of 4 are in 12

Question 2.
How many rows of 3 are in 21?
______ rows

Answer: 7 rows

■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■

Explanation:

Step 1:

Total number of tiles are 21

Step 2:

Make a row of 3 tiles

Step 3:

Continue to make as many rows of 3 tiles as you can
We get 3 tiles in each row
So, 7 rows of 3 are in 21

Question 3.
How many rows of 6 are in 30?
______ rows

Answer: 5 rows

■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■

Explanation:

Step 1:

First of all the count number of tiles = 30

Step 2:

Make a row of 6 tiles

Step 3:

Continue to make as many rows of 6 tiles as you can
We get 6 tiles in each row
So, there are 5 rows of 6 in 30

Question 4.
How many rows of 9 are in 18?
______ rows

Answer: 2 rows

Make an array. Then write a division equation.

Question 5.
20 tiles in 5 rows
______ ÷ ______ = ______

Answer: 20 ÷ 5 = 4

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Explanation:

Total number of tiles = 20
Make a row of 4 tiles
Continue to make as many rows of 4 tiles as you can
We get 4 tiles in each row
So, the division equation is 20 ÷ 5 = 4

Question 6.
28 tiles in 7 rows
______ ÷ ______ = ______

Answer: 28 ÷ 7 = 4

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Explanation:

Total number of tiles = 28
Make a row of 4 tiles
Continue to make as many rows of 4 tiles as you can
We get 4 tiles in each row
For 28 tiles we get 7 rows
So, the division equation is 28 ÷ 7 = 4

Question 7.
18 tiles in 9 rows
______ ÷ ______ = ______

Answer: 18 ÷ 9 = 2

■ ■
■ ■
■ ■
■ ■
■ ■
■ ■
■ ■
■ ■
■ ■

Explanation:

Number of tiles = 18
Number of rows = 9
Now we have to make a row of 2 tiles until we complete 18 tiles
So, you get 2 tiles in 9 rows
18 ÷ 9 = 2 tiles

Question 8.
36 tiles in 6 rows
______ ÷ ______ = ______

Answer: 36 ÷ 6 = 6

■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■

Explanation:

Total number of tiles = 36
Number of rows = 6
Now you have to make a row of 36 tiles in 6 rows
You get 6 tiles in each row
That means there are 6 tiles each in a row
So, the division equation is 36 ÷ 6 = 6

Problem Solving

Question 9.
A dressmaker has 24 buttons. He needs 3 buttons to make one dress. How many dresses can he make with 24 buttons?
______ dresses

Answer: 8 dresses

Explanation:

Given: A dressmaker has 24 buttons
He needs 3 buttons to make one dress
Number of dresses he can make with 24 buttons = y
y × 3 = 24
y = 24/3
y = 8

Question 10.
Liana buys 36 party favors for her 9 guests. She gives an equal number of favors to each guest. How many party favors does each guest get?
______ party favors

Answer: 4 party favors

Explanation:

Liana buys 36 party favors for her 9 guests.
She gives an equal number of favors to each guest.
To know how many party favors does a guest get
We must Divide number of 36 party favors by 9 guests
= 36 ÷ 9 = 4

Model with Arrays Page No 338

Question 1.
Mr. Canton places 24 desks in 6 equal rows. How many desks are in each row?
Options:
a. 2
b. 3
c. 4
d. 5

Answer: 4

Explanation:

Mr. Canton places 24 desks in 6 equal rows
Each row has x number of desks
Divide the number of desks by number of equal rows
24 ÷ 6 = 4
So, the correct answer is option C

Question 2.
Which division equation is shown by the array?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Arrays img 25
Options:
a. 12 ÷ 6 = 2
b. 12 ÷ 3 = 4
c. 12 ÷ 2 = 6
d. 12 ÷ 1 = 12

Answer: 12 ÷ 3 = 4

Explanation:

Number of counters is 12 and the number of rows are 3
To know number counters in each row
We have to divide number of counters by number of rows
= 12 ÷ 3 = 4
Thus the answer is option B

Spiral Review

Question 3.
Amy has 2 rows of 4 sports trophies on each of her 3 shelves. How many sports trophies does Amy have in all?
Options:
a. 8
b. 9
c. 12
d. 24

Answer: 24

Explanation:

Amy has 2 rows of 4 sports trophies on each of her 3 shelves
To know the total sports trophies does Amy have in all 3 shelves
We have to multiple number 2 × 4 × 3 = 24
So, the correct answer is option D

Question 4.
What is the unknown factor?
9 × p = 45
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

The unknown factor is p
9 × p = 45
p = 45/9 = 5
Therefore p = 5
Thus the answer is option B

Question 5.
Sam has 7 stacks with 4 quarters each. How many quarters does Sam have?
Options:
a. 11
b. 12
c. 24
d. 28

Answer: 28

Explanation:

Sam has 7 stacks with 4 quarters each
Each stack has 4 quarters
So, 7 stacks has 7 × 4 = 28
Thus 7 stacks have 28 quarters

Question 6.
How can you skip count to find how many counters in all?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Model with Arrays img 26
Options:
a. 3 groups of 2
b. 3 groups of 3
c. 9 groups of 2
d. 18 groups of 2

Answer: 9 groups of 2

Explanation:

Total number of Counters = 18
Number of equal groups = 9
Number in each group = 2
So, there are 9 groups of 2s
Thus the correct answer is option C

Relate Multiplication and Division Page No 343

Complete the equations.

Question 1.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 27

Answer:

5 rows of 4 = 20
5 × 4  = 20
20 ÷ 5 = 4

Explanation:

The above figure shows that, there are 5 rows of 4 circles
Total number of circles = 20
The related facts of 20, 5 and 4 are
5 × 4 = 20; 5 rows of 4 = 20; 20 ÷ 5 = 4

Question 2.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 28
4 rows of ______ = 24
4 × ______ = 24
24 ÷ 4 = ______

Answer:

4 rows of 6 = 24
4 × 6 = 24
24 ÷ 4 = 6

Explanation:

Number of counters = 24
Number of equal rows = 4
24 ÷ 4 = 6
The related facts of 24, 6 and 4 are 24 ÷ 4 = 6; 4 × 6 = 24

Question 3.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 29
3 rows of ______ = 24
3 × ______ = 24
24 ÷ 3 = ______

Answer:

3 rows of 8 = 24
3 × 8 = 24
24 ÷ 3 = 8

Explanation:

Total number of counters = 24
Number of equal rows = 3
Divide number of counters by number of equal rows
24 ÷ 3 = 8
Thus the related multiplication and division facts of 24, 3 , 8 are 3 × 8 = 24; 24 ÷ 3 = 8

Complete the equations.

Question 4.
4 × ______ = 28   28 ÷ 4 = ______

Answer: 7, 7

Explanation:
The related facts of 28 and 4 are 28 ÷ 4 = 7 and 4 × 7 = 28

Question 5.
6 × ______ = 36    36 ÷ 6 = ______

Answer: 6, 6

Explanation:

Let the unknown Number be x
6 × x = 36
x = 36/6 = 6
The related multiplication and division facts of 36 and 6 are 36 ÷ 6 = 6; 6 × 6 = 36

Question 6.
5 × ______ = 35    35 ÷ 7 = ______

Answer: 7, 5

Explanation:

X represents the unknown factor
5 × x = 35
x = 35/5 = 7
Therefore the related multiplication and division facts 35, 5 and 7 are 5 × 7 = 35; 35 ÷ 7 = 5

Question 7.
7 × ______ = 21  21 ÷ 7 = ______

Answer: 3, 3

Explanation:

7 × x = 21
x = 21/7 = 3
So, the related multiplication and division facts of 7, 21 are 7 × 3 = 21; 21÷ 7 = 3

Question 8.
9 × ______ = 27  27 ÷ 9 = ______

Answer: 3, 3

Explanation:

27 ÷ 9 = 3
The related multiplication and division facts of 27 and 9 are 9 × 3 = 27 and 27 ÷ 9 = 3

Question 9.
2 × ______ = 16  16 ÷ 2 = ______

Answer: 8, 8

Explanation:

16 ÷ 2 = 8
The related multiplication and division facts of 16 and 2 are 2 × 8 = 16; 16 ÷ 2 = 8

Question 10.
4 × ______ = 36 36 ÷ 4 = ______

Answer: 9, 9

Explanation:

36 ÷ 4 = 9
So, the related multiplication and division facts of 36 and 4 are 4 × 9 = 36; 36 ÷ 4 = 9

Question 11.
8 × ______ = 40 40 ÷ 8 = ______

Answer: 5, 5

Explanation:

Let x be the unknown factor
8 × x = 40
x = 40/8 = 5
The related facts of 40 and 8 are 8 × 5 = 40; 40 ÷ 8 = 5

Problem Solving

Question 12.
Mr. Martin buys 36 muffins for a class breakfast. He places them on plates for his students. If he places 9 muffins on each plate, how many plates does Mr. Martin use?
___________ plates

Answer: 4 plates

Explanation:

Number of muffins = 36
He places 9 muffins on each plate
Divide number of muffins by number of muffins on each plate
36 ÷ 9 = 4 plates

Question 13.
Ralph read 18 books during his summer vacation. He read the same number of books each month for 3 months. How many books did he read each month?
___________ books

Answer: 6 books

Explanation:

Given that Ralph read 18 books during his Summer vacation
He read same number of books each month for 3 months
To find the number of books he read each month we have to divide total number of books by number of books for 3 months
18 ÷ 3 = 6 books

Relate Multiplication and Division Page No 344

Question 1.
Which number will complete the equations?
6 × □ = 24
24 ÷ 6 = □
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

24 ÷ 6 = 4
The related multiplication and division facts of 6 and 24 is 6 × 4 = 24; 24 ÷ 6 = 4
So, the correct answer is option B

Question 2.
Alice has 14 seashells. She divides them equally between her 2 sisters. How many seashells does each sister get?
Options:
a. 7
b. 8
c. 12
d. 16

Answer: 7

Explanation:

Alice has 14 seashells
She divides them equally between her 2 sisters
To know the number of seashells each sister get
We have to divide number of seashells by the number of sisters
= 14 ÷ 2 = 7
Thus the answer is option A

Spiral Review

Question 3.
Sam and Jesse can each wash 5 cars in an hour. They both work for 7 hours over 2 days. How many cars did Sam and Jesse wash?
Options:
a. 70
b. 35
c. 24
d. 14

Answer: 70

Explanation:

Sam and Jesse can each wash 5 cars in an hour
They both work for 7 hours over 2 days
To find the total number of cars they washed
we need to multiply 5 × 7 × 2 = 35 × 2 = 70
So, the answer is option A

Question 4.
Keisha skip counted to find how many counters in all. How many equal groups are there?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 30
Options:
a. 3
b. 4
c. 5
d. 20

Answer: 4

Explanation:

By seeing the above figure we can say that there are 4 groups.
So, the answer is option B

Question 5.
The key for a picture graph showing the number of books students read is: Each Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 31 = 2 books. How many books did Nancy read if she has Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 32 by her name?
Options:
a. 2
b. 4
c. 5
d. 6

Answer: 5

Explanation:

Each Go Math Grade 3 Answer Key Chapter 6 Understand Division Relate Multiplication and Division img 31 = 2 books
There are 2 and half books = 2 + 2 + 1 = 5
Thus the answer is 5 i.e., option C

Question 6.
Jan surveyed her friends to find their favorite season. She recorded IIII III for summer. How many people chose summer as their favorite season?
Options:
a. 5
b. 8
c. 9
d. 13

Answer: 8

Explanation:

IIII = 5
III = 3
IIII III = 5 + 3 = 8
So, the people who chose summer as their favorite season are 8
Option B is the correct answer

Write Related Facts Page No 349

Write the related facts for the array.

Question 1.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Write Related Facts img 33

Answer:

2 × 6 = 12
6 × 2 = 12
12 ÷ 2 = 6
12 ÷ 6 = 2

Explanation:

Total number of counters = 12
Number of rows = 2
Number of counters in each row = 6
So, the related facts of 6, 2 and 12 are 2 × 6 = 12, 6 × 2 = 12, 12 ÷ 2 = 6 and 12 ÷ 6 = 2

Question 2.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Write Related Facts img 34
Type below:
_________

Answer:

5× 3 = 15
3×5 = 15
15 ÷ 3 = 5
15÷ 5 = 3

Explanation:

Total number of counters = 15
Number of rows = 5
Number of counters in each row = 3
The related facts of 5, 3 and 15 are 5× 3 = 15, 3×5 = 15, 15 ÷ 3 = 5 and 15÷ 5 = 3

Question 3.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Write Related Facts img 35
Type below:
_________

Answer:

2 × 4 = 8
4× 2 = 8
8 ÷ 2 = 4
8 ÷ 4 = 2

Explanation:

Total number of counters = 8
Number of rows = 2
Number of counters in each row = 4
The related facts of 8, 2, 4 are 2 × 4 = 8, 4× 2 = 8, 8 ÷ 2 = 4 and 8 ÷ 4 = 2

Write the related facts for the set of numbers.

Question 4.
3, 7, 21
Type below:
_________

Answer:

3 × 7 = 21
7 × 3 = 21
21 ÷ 3 = 7
21 ÷ 7 = 3

Explanation:

Total number of counters = 21
The related facts of 3, 7, 21 are 3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7 and 21 ÷ 7 = 3

Question 5.
2, 9, 18
Type below:
_________

Answer:

2 × 9 = 18
9 × 2 = 18
18 ÷ 2 = 9
18 ÷ 9 = 2

Explanation:

Total number of counters = 18
The related facts of 2, 9, 18 are 2 × 9 = 18, 9 × 2 = 18, 18 ÷ 2 = 9 and 18 ÷ 9 = 2

Question 6.
4, 8, 32
Type below:
_________

Answer:

4 × 8 = 32
8 × 4 = 32
32 ÷ 8 = 4
32 ÷ 4 = 8

Explanation:

Total number of counters = 32
The related facts of 4, 8, 32 are 4 × 8 = 32, 8 × 4 = 32, 32 ÷ 8 = 4 and 32 ÷ 4 = 8

Complete the related facts.

Question 7.
4 × 9 = _______
9 × _______ = 36
36 ÷ _______ = 4
_______ ÷ 4 = 9

Answer: The related facts of 4, 9 and 36 are given below

4 × 9 = 36
9 × 4 = 36
36 ÷ 9 = 4
36 ÷ 4 = 9

Question 8.
_______ × 7 = 35
_______ × 5 = 35
_______ ÷ 7 = 5
35 ÷ 5 _______

Answer:

5 × 7 = 35
7 × 5 = 35
35 ÷ 7 = 5
35 ÷ 5= 7

Explanation:

Let the unknown factor be x
x × 7 = 35
x = 35/7 = 5
5 × 7 = 35

x × 5 = 35
x = 35/5 = 7
7 × 5 = 35

x ÷ 7 = 5
x = 5 × 7 = 35
35 ÷ 7 = 5

35 ÷ 5 = x
x = 35/5 = 7
35 ÷ 5= 7

Question 9.
6 × _______ = 18
3 × 6 _______
18 ÷ _______ = 3
_______ ÷ 3 = 6

Answer:

6 × 3 = 18
3 × 6 = 18
18 ÷ 6 = 3
18 ÷ 3 = 6

Explanation:

Let the unknown factor be x
6 × x = 18
x = 18/6 = 3
6 × 3 = 18

3 × 6 = x
x = 18
3 × 6 = 18

18 ÷ x = 3
x = 18/3 = 6
18 ÷ 6 = 3

x ÷ 3 = 6
x = 6 × 3 = 18
18 ÷ 3 = 6

Problem Solving 

Question 10.
CDs are on sale for $5 each. Jennifer has $45 and wants to buy as many as she can. How many CDs can Jennifer buy?
_______

Answer: 9 CDs

Explanation:

CDs are on sale for $5 each
Jennifer has $45 and wants to buy as many as she can
= 45 ÷ 5 = 9
so, the number of CDs can Jennifer buy = 9

Question 11.
Mr. Moore has 21 feet of wallpaper. He cuts it into sections that are each 3 feet long. How many sections does Mr. Moore have?
_______ sections

Answer: 7 sections

Explanation:

Mr. Moore has 21 feet of wallpaper
He cuts it into sections that are each 3 feet long
Number of sections does Mr. Moore have = x
= 21/3 = 7
Mr. Moore have 7 sections

Write Related Facts Page No 350

Question 1.
Which number completes the set of related facts?
5 × □ = 40  40 ÷ □ = 5
□ × 5 = 40  40 ÷ 5 = □
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

i. 5 × □ = 40
□ = 40/5 = 8
ii. 40 ÷ □ = 5
□ = 40/5 = 8
iii. □ × 5 = 40
□ = 40/5 = 8
iv. 40 ÷ 5 = □
40/5 = □
□ = 8
So, the answer is 8

Question 2.
Which equation is not in the same set of related facts as 4 × 7 = 28?
Options:
a. 7 × 4 = 28
b. 4 + 7 = 11
c. 28 ÷ 4 = 7
d. 28 ÷ 7 = 4

Answer: 4 + 7 = 11

Explanation:

The related facts of 4, 7 and 28 are 4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7, 28 ÷ 7 = 4
But 4 + 7 = 11 is not set of related multiplication and division equations.

Spiral Review

Question 3.
Beth runs 20 miles each week for 8 weeks. How many miles does Beth run in 8 weeks?
Options:
a. 16 miles
b. 28 miles
c. 100 miles
d. 160 miles

Answer: 160 miles

Explanation:

Beth runs 20 miles each week for 8 weeks
Each week Beth runs 20 miles
For 8 weeks = x miles
x = 8 × 20
x = 160 miles
So, the answer is 160 miles

Question 4.
Find the product.
5 × 0
Options:
a. 0
b. 1
c. 5
d. 10

Answer: 0

Explanation:

Any number multiplied with 0 is always 0.
So, the answer is option A.

Question 5.
Uri’s bookcase has 5 shelves. There are 9 books on each shelf. How many books in all are in Uri’s bookcase?
Options:
a. 14
b. 36
c. 45
d. 54

Answer: 45

Explanation:

Uri’s bookcase has 5 shelves
There are 9 books on each shelf
Number of books in 5 shelves = y
y = 9 × 5 = 45
Thus the answer is option C

Question 6.
There are 6 batteries in one package. How many batteries will 6 packages have?
Options:
a. 12
b. 18
c. 24
d. 36

Answer: 36

Explanation:

There are 6 batteries in one package
Number of batteries in 6 packages = x
x = 6 × 6 = 36
Thus the Number of batteries in 6 packages = 36

Division Rules for 1 and 0 Page No 355

Find the quotient.

Question 1.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Division Rules for 1 and 0 img 36

Answer: 3

Explanation:

Any number divided by 1 equals that number. The quotient is that number
So, 3/1 = 3 is the quotient

Question 2.
8 ÷ 8 = ________

Answer: 1

Explanation:

Any number divided by the same number other than 0 equals 1. The quotient is always 1
8/8 = 1
So, the quotient is 1

Question 3.
________ = 0 ÷ 6

Answer: 0

Explanation:

Zero divided by any number is always 0. The quotient is 0.
0/6 = 0
Thus the quotient is 0

Question 4.
2 ÷ 2 = ________

Answer: 1

Explanation:

Any number divided by the same number equals 1. The quotient is always 1
2/2 = 1
Thus the quotient is 1

Question 5.
________ = 9 ÷ 1

Answer: 9

Explanation:

Any number divided by 1 equals that number. The quotient is that number
9/1 = 9
So, the quotient is 9

Question 6.
0 ÷ 2 = ________

Answer: 0

0 divided by any number is always 0.
0/2 = 0
So, the quotient is 0

Question 7.
0 ÷ 3 = ________

Answer: 0

Explanation:

0 divided by any number is always 0.
0/3 = 0
So, the quotient is 0

Question 8.
________ = 0 ÷ 4

Answer: 0

Explanation:

0 divided by any number is 0
0/4 = 0
Thus the quotient is 0

Question 9.
7)\( \bar{ 7  }\)
________

Answer: 1

Explanation:

Any number divided by the same number is always 1.
7/7 = 1
So, the quotient is 1

Question 10.
1)\( \bar{ 6  }\)
________

Answer: 6

Explanation:

Any number divided by 1 is the same number.
6/1 = 6
So, the quotient is 6

Question 11.
9)\( \bar{  0 }\)
________

Answer: 0

Explanation:

0 divided by any number remains 0.
0/9 = 0
Thus the quotient is 0

Question 12.
1)\( \bar{ 5  }\)
________

Answer: 5

Explanation:

Any number divided by 1 gives the same number as a quotient
5/1 = 5
Therefore the quotient is 5

Question 13.
1)\( \bar{  0 }\)
________

Answer: 0

Explanation:

0 divided by any thing is 0
0/1 = 0
So, the quotient is 0

Question 14.
4)\( \bar{ 4  }\)
________

Answer: 1

Explanation:

Any number divided by the same number gives the quotient as 1.
4/4 = 1
So, the quotient is 1

Question 15.
1)\( \bar{ 10 }\)
________

Answer: 10

The number which is divided by 1 gives the same number as a quotient.
10/1 = 10
Thus the quotient is 10

Question 16.
2)\( \bar{ 2  }\)
________

Answer: 1

Explanation:

Any number divided by the same number is 1.
2/2 = 1
Thus the quotient is 1

Problem Solving

Question 17.
There are no horses in the stables. There are 3 stables in all. How many horses are in each stable?
________

Answer: 0 horses

Explanation:

If there are no horses then there will be nothing in the stables.
Zero divided by any number is 0
0/3 = 0

Question 18.
Jon has 6 kites. He and his friends will each fly 1 kite. How many people in all will fly a kite?
________

Answer: 6 people

Explanation:

John has 6 kites
He and his friends will each fly 1 kite
= 6/1 = 6
So, 6 people will fly the kites

Division Rules for 1 and 0 Page No 356

Question 1.
Candace has 6 pairs of jeans. She places each pair on its own hanger. How many hangers does Candace use?
Options:
a. 0
b. 1
c. 6
d. 12

Answer: 6

Explanation:

Given,
Candace has 6 pairs of jeans
She places each pair on its own hanger
That means one pair of jeans for one hanger
To find the number of hangers we need to divide the total number of hangers by each pair
6 ÷ 1 = 6
So, option C is the correct answer

Question 2.
There are 0 birds and 4 bird cages. Which division equation describes how many birds are in each cage?
Options:
a. 0 ÷ 4 = 0
b. 4 ÷ 4 = 1
c. 4 ÷ 1 = 4
d. 0 × 4 = 0

Answer: 0 ÷ 4 = 0

Explanation:

There are no birds so nothing to divide. Zero divided by anything is 0.
So, the answer is 0 ÷ 4 = 0

Spiral Review

Question 3.
There are 7 plates on the table. There are 0 sandwiches on each plate. How many sandwiches are on the plates in all?
7 × 0
Options:
a. 0
b. 1
c. 7
d. 70

Answer: 0

Explanation:

There are 7 plates on the table
There are 0 sandwiches on each plate
Any number multiplied with 0 is always 0.
So, the answer is option A.

Question 4.
Which shows a way to break apart the array to find the product?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Division Rules for 1 and 0 img 37
Options:
a. (3 × 5) + (3 × 2)
b. (2 × 8) + (1 × 8)
c. (4 × 7) + (1 × 7)
d. (3 × 6) + (3 × 3)

Answer: (3 × 5) + (3 × 2)

Explanation:

There are 3 rows and 7 columns
The columns are divided into 2 parts 5 and 2.
By using the distributive property we can write it as (3 × 5) + (3 × 2)
Thus the answer is option A

Question 5.
Which of the following describes a pattern in the table?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Division Rules for 1 and 0 img 38
Options:
a. Add 5.
b. Multiply by 2.
c. Subtract 1.
d. Multiply by 6.

Answer:

Multiply by 6.

Explanation:

Multiple 6 with a number of vans.
By seeing the above table we can say that it is the multiple of 6.
So, the answer is option D

Question 6.
Use the graph.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Division Rules for 1 and 0 img 39
How many more cans did Sam bring in than Lee?
Options:
a. 4
b. 5
c. 7
d. 9

Answer: 9

Explanation:

Number of cans sam brings = 18
Number of cans Lee bring = 9
To know number of cans Sam bring in than Lee we have to subtract
Number of cans of Lee from Number of cans of Sam = 18 – 9 = 9
By using the above graph we can say that number of cans Sam bring in than Lee is 9.
Thus the correct answer is option D

Review/Test Page No 361

Question 1.
For numbers 1a–1d, select True or False for each equation.
a. 3 ÷ 1 = 1
i. True
ii. False

Answer: False

Explanation:

Any number divided by 1 is always the same number. The quotient is 1.
So, the above equation is false.

Question 1.
b. 0 ÷ 4 = 0
i. True
ii. False

Answer: True

Explanation:

0 divided by any number is always 0. So, the above statement is true.

Question 1.
c. 7 ÷ 7 = 1
i. True
ii. False

Answer: True

Explanation:

Any number divided by the same number remains 1. So, the given statement is true.

Question 1.
d. 6 ÷ 1 = 6
i. True
ii. False

Answer: True

Explanation:

Any number divided by 1 will be the same number. Thus the statement given above is true.

Question 2.
Elizabeth has 12 horses on her farm. She puts an equal number of horses in each of 3 pens. How many horses are in each pen?
Circle a number that makes the sentence true.
There are Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 40 horses in each pen.
_________

Answer: 12 ÷ 3 = 4

There are HMH Go Math Chapter 6 Grade 3 Answer Key Review solution img_6 horses in each pan

Question 3.
Chris plants 25 pumpkins seeds in 5 equal rows. How many seeds does Chris plant in each row?
Make an array to represent the problem. Then solve the problem.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 41
_______ seeds
Explain:
_________

Answer: 5 seeds

Go Math Grade 3 Key Chapter 6 Review solution image_1

Explanation:

Total number of seeds = 25
Number of equal rows = 5
25 ÷ 5 = 5 seeds

Page No. 358

Question 4.
Becca spent 24 minutes walking around a track. It took her 3 minutes to walk each time around the track. How many times did Becca walk around the track?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 42
Make equal groups to model the problem. Then explain how you solved the problem.
_______ times

Answer: 24 ÷ 3 = 8 times

Go Math Grade 3 Chapter 6 key review solution image_7

Question 5.
There are 7 cars in an amusement park ride. There are 42 people divided equally among the 7 cars. An equal number of people ride in each car. How many people ride in one car?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 43
_______people

Answer: 6 people

Explanation:

Number of cars = 7
There are 42 people divided equally among the 7 cars
Divide the total number of people by the number of cars
You get, 42 ÷ 7 = 6 people

Question 6.
Select the equations that represent the array. Mark all that apply.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 44
Options:
a. 3 × 5 = ■
b. 2 × ■ = 12
c. ■ ÷ 3 = 5
d. 5 × ■ = 15
e. 12 ÷ 3 = ■
f. 15 ÷ 5 = ■

Answer: 3 × 5 = ■; ■ ÷ 3 = 5; 5 × ■ = 15; 15 ÷ 5 = ■

Explanation:

Related facts are a set of related multiplication and division equations.

Number of rows = 3
Number of blocks in each row = 5
Total Number of blocks = 15
So, the relation between these 3 numbers are 3 × 5 = ■; ■ ÷ 3 = 5; 5 × ■ = 15; 15 ÷ 5 = ■

Review/Test Page No 359

Question 7.
Eduardo visited his cousin for 28 days over the summer. There are 7 days in each week. How long, in weeks, was Eduardo’s visit?
Part A
Draw jumps on the number line to model the problem.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 45
Type below:
___________

Answer:

HMH Go math grade 3 chapter 6 answer key review solution image_2

Starts at 0
Count by 7 as many times as you can
Count the number of times you jumped back 7
You have jumped 4 times
So, there are 4 groups of 7 in 28
28 ÷ 7 = 4

Question 7.
Part B
Write a division equation to represent the model.
Type below:
___________

Answer: 28 ÷ 7 = 4

Question 8.
A workbook is 64 pages long. If each chapter is 8 pages long, how many chapters are there?
_________ chapters

Answer: 8 chapters

Explanation:

A workbook is 64 pages long
If each chapter is 8 pages long
Divide the number of pages by number of pages in each chapter
= 64 ÷ 8 = 64/8 = 8
Therefore there are 8 chapters in the workbook

Question 9.
There are 56 apples packed in 7 baskets with the same number of apples in each basket. How many apples are in each basket?
For numbers, 9a–9d, choose Yes or No to tell whether the equation represents the problem.
a. 56 + 7 = ■
i. yes
ii. no

Answer: No

Explanation:

56 + 7 = 63 ≠ 8
So, the answer is no

Question 9.
b. 7 × ■ = 56
i. yes
ii. no

Answer: Yes

Explanation:

7 × ■ = 56
■ = 56/7 = 8
So, the answer is yes

Question 9.
c. 56 ÷ ■ = 8
i. yes
ii. no

Answer: Yes

Explanation:

56 ÷ ■ = 8
■ = 56/8 = 7
So, the answer is yes

Question 9.
d. 56 − ■ = 8
i. yes
ii. no

Answer: No

Explanation:

56 − ■ = 8
■ = 64 ≠ 7
So, the answer is no

Question 10.
Stefan has 24 photos to display on some posters. Select a way that he could display the photos in equal groups on the posters. Mark all that apply.
Options:
a. 6 photos on each of 4 posters
b. 7 photos on each of 3 posters
c. 4 photos on each of 6 posters
d. 5 photos on each of 5 posters
e. 3 photos on each of 8 posters
f. 7 photos on each of 4 posters

Answer: A, C, E

A. 6 photos on each of 4 posters
6 x 4 = 24 photos ✓

B. 7 photos on each of 3 posters
7 x 3 = 21 ≠ 24 photos

C. 4 photos on each of 6 posters
4 x 6 = 24 photos ✓

D. 5 photos on each of 5 posters
5 x 5 = 25 ≠ 24 photos

E. 3 photos on each of 8 posters
3 x 8 = 24 photos ✓

F. 7 photos on each of 4 posters
7 x 4 = 28 ≠ 24 photos

Review/Test Page No 360

Question 11.
Debbie made this array to model a division equation. Which equation did Debbie model? Mark all that apply.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 46
Options:
a. 14 ÷ 7 = 2
b. 28 ÷ 4 = 7
c. 28 ÷ 7 = 4
d. 14 ÷ 2 = 7

Answer: 28 ÷ 4 = 7

Explanation:

Total Number shaded blocks = 28
Number of equal rows = 4
To write the division equation
we have to divide number of blocks by number of equal rows
28 ÷ 7 = 7
So, the correct answer is option B

Question 12.
Mrs. Edwards made a total of 40 fingers on some gloves she knitted. How many gloves did Mrs. Edwards knit?
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 47
__________ gloves

Answer: 40 ÷ 5 = 8

Explanation:

Mrs. Edwards made a total of 40 fingers on some gloves she knitted
Number in each group = 5
Divide Number of fingers by number in each group
= 40 ÷ 5 = 8
Number of equal groups = 8

Question 13.
Make true equations. Select a number to complete the equation.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 48
7 ÷ 7 = ________
7 ÷ 1 = ________
0 ÷ 7 = ________

Answer:

7 ÷ 7 = 1
7 ÷ 1 = 7
0 ÷ 7 = 0

Explanation:

7 ÷ 7 = 1
Any number divided by the same numbers is always 1. So the quotient is 1
7 ÷ 1 = 7
Any number divided by 1 gives the same number as quotient.
0 ÷ 7 = 0
Zero divided by any number is always 0. So, the quotient is 0.

Question 14.
The coach separated the 18 players at lacrosse practice into 3 different groups. How many players were in each group?
________ players

Answer: 6 in each group

Explanation:

Total number of players = 18
Number of equal groups = 3
To find the number in the equal group you have to divide the total number of players by number of equal groups
= 18 ÷ 3 = 6
Therefore there are 6 players in each group

Review/Test Page No 361

Question 15.
Write a division equation to represent the repeated subtraction.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 49
Type below:
________

Answer: 32 ÷ 8 = 4

Explanation:

Step 1:

Start at 32

Step 2:

Subtract with 8 until you get 0

Step 3:

Count the number of times you subtract with 8
Since you subtract 4 times
There are 4 groups of 8 in 32
32 ÷ 8 = 4
Thirty two divided by eight equals four

Question 16.
Write related facts for the array. Explain why there are not more related facts.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 50
Type below:
________

Answer:

There are 6 rows of 6 squares.
The related facts are:
6 x 6 = 36; 36 ÷ 6 = 6
An array represents a multiplication because it has rows and columns and the total number of cells is the product of its rows and columns.
Also, the division is related to multiplication.
So, the only related facts are multiplication and division.

Question 17.
Darius bakes 18 muffins for his friends. He gives each of his friends an equal number of muffins and has none left over.
Part A
Draw a picture to show how Darius divided the muffins and complete the sentence.
Darius gave muffins to ________ friends.
Type below:
________

Answer:

If one muffin for 18 friends

18 = 1 × 18

Go math grade 3 key chapter 6 understand division review solution image _ 3a

If 2 muffins for 9 friends

18 = 2 × 9

Chapter 6 Go Math Answer Key Grade 3 review solution image_3b

If 3 muffins for 6 friends

18 = 3 × 6

Go Math Grade 3 Chapter 6 answer key review solution image_3c

Six muffins for 3 friends

18 = 6 × 3

If 9 muffins for 2 friends

Answer key for HMH Go Math Grade 3 Chapter 6 Review solution image_3d

So, Darius gave muffins to 2, 3, 6, 9, 18 friends

Question 17.
Part B
Could Darius have given all of his muffins equally to 4 of his friends? Explain why or why not.
Type below:
________

Answer: No

No, because if he divides 18 muffins to 4 people, then they get 4 muffins each, and two are not given.
4 × 4 + 2 = 18

Review/Test Page No 362

Question 18.
Circle numbers to complete the related facts.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 51 × 8 = 72   72 ÷ Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 52 = 8
______                                              _______

Answer: 9 × 8 = 72; 72 ÷ 9 = 8

Grade 3 Go Math Answer Key Chapter 6 Review solution img_5a × 8 = 72; 72 ÷ Chapter 6 Go Math HMH Answer Key Grade 3 Review solution img_5b = 8

Question 19.
Use the numbers to write a related multiplication and division facts.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 53
Type below:
__________

Answer: 45 ÷ 9 = 5; 45 ÷ 5 = 9

Explanation:

The multiplication and division facts for 45, 9 and 5 are
45 ÷ 5 = 9
45 ÷ 9 = 5
9 × 5 = 45

Question 20.
Tyrone took 16 pennies from his bank and put them in 4 equal stacks. How many pennies did Tyrone put in each stack? Show your work.
Go Math Grade 3 Answer Key Chapter 6 Understand Division Review/Test img 54
__________ pennies

Answer: 4 pennies

Go Math Grade 3 Chapter 6 Key Review solution image_4

16 ÷ 4 = 4 pennies

Explanation:

Total number of pennies = 16
Number of equal stacks = 4
Divided number of pennies by number of equal stacks to know the pennies in each stack
16 ÷ 4 = 4

Try to solve exercise questions and cross check your answers from Go Math Grade 3 Answer Key Chapter 6 Understand Division Extra Practice. This way you can assess your strengths and weaknesses and concentrate on the areas you are lagging.

Detailed Solutions are provided in the 3rd Grade Go Math Answer Key Chapter 6 Understand Division making it easy for you to understand.

Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers

go-math-grade-5-chapter-2-divide-whole-numbers-answer-key

Trying to Score Better Scores in Grade 5 Maths? Utilize Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers and make the most out of them. Begin your practice right away using the Go Math Grade 5 Answer Key and understand the concepts. HMH Go Math Grade 5 Practice Tests along with questions and answers exist here. Attain more knowledge using the Go Math Grade 5 Chapter 2 Divide Whole Numbers Solution Key and cross-check the Solutions from it after your practice sessions.

Go Math Grade 5 Chapter 2 Divide Whole Numbers Answer Key

Apply Maths in your Real-Time and get the Tips & Tricks to Solve Various Problems using  HMH Go Math Grade 5 Answer Key. We have provided shortcuts to solve all the Problems in Go Math Chapter 2 Divide Whole Numbers. Try to utilize the resource available Go Math Grade 5 Chapter 2 Divide Whole Numbers Answer Key and make your preparation way more effective.

Lesson 1: Place the First Digit

Lesson 2: Divide by 1-Digit Divisors

Lesson 3: Investigate • Division with 2-Digit Divisors

Lesson 4: Partial Quotients

Mid-Chapter Checkpoint

Lesson 5: Estimate with 2-Digit Divisors

Lesson 6: Divide by 2-Digit Divisors

Lesson 7: Interpret the Remainder

Lesson 8: Adjust Quotients

Lesson 9: Problem Solving • Division

Review/Test

Place the First Digit – Share and Show – Page No. 63

Divide.

Question 1.
3)\(\overline { 579 } \)
_____

Answer:
193

Explanation:
Divide integers 57/3 = 19
Multiply 19 x 3 = 57; Subtract 57 – 57 = 0
Write down 9 and divide integers 9/3 = 3.
Multiply 3 x 3 = 9. Subtract 9 – 9 = 0.
The remainder is 0.
So, 193 is the answer.

Question 2.
5)\(\overline { 1,035 } \)
_____

Answer:
207

Explanation:
Divide integers 10/5 = 2
Multiply 2 x 5 = 10; Subtract 10 – 10 = 0
Write down 35 and divide integers 35/5 = 7.
Multiply 7 x 5 = 35. Subtract 35 – 35 = 0.
The remainder is 0.
So, 207 is the answer.

Question 3.
8)\(\overline { 1,766 } \)
_____ R _____

Answer:
220 R 6

Explanation:
Divide integers 17/8 = 2
Multiply 2 x 8 = 16; Subtract 17 – 16 = 1
Write down 16 and divide integers 16/8 = 2.
Multiply 2 x 8 = 16. Subtract 16 – 16 = 0.
Write down 6; 6 < 8. There are not enough tens
So, the remainder is 6
So, 220 is the answer.

On Your Own

Divide.

Question 4.
8)\(\overline { 275 } \)
_____ R _____

Answer:
43 R 3

Explanation:
Divide integers 27/8 = 3
Multiply 8 x 3 = 24; Subtract 27 – 24= 3
Write down 3 and divide integers 35/8 = 4.
Multiply 8 x 4 = 32. Subtract 35 – 32 = 3.
The remainder is 3.
So, 43 is the answer.

Question 5.
3)\(\overline { 468 } \)
_____

Answer:
155 R 3

Explanation:
Divide integers 46/3 = 15
Multiply 3 x 15 = 45; Subtract 46 – 45= 1
Write down 18 and divide integers 18/3 = 5.
Multiply 3 x 5 = 15. Subtract 18 – 15 = 3.
The remainder is 3.
So, 155 is the answer.

Question 6.
4)\(\overline { 3,220 } \)
_____

Answer:
805

Explanation:
Divide integers 32/4 = 8
Multiply 4 x 8 = 32; Subtract 32 – 32 = 0
Write down 20 and divide integers 20/4 = 5.
Multiply 4 x 5 = 20. Subtract 20 – 20= 0.
The remainder is 0.
So, 805 is the answer.

Question 7.
6)\(\overline { 618 } \)
_____

Answer:
103

Explanation:
Divide integers 61/6 = 10
Multiply 6 x 10 = 60; Subtract 61 – 60 = 1
Write down 18 and divide integers 18/6 = 3.
Multiply 6 x 3 = 18. Subtract 18 – 18 = 0.
The remainder is 0.
So, 103 is the answer.

Question 8.
4)\(\overline { 716 } \)
_____

Answer:
179

Explanation:
Divide integers 71/4 = 17
Multiply 4 x 17 = 68; Subtract 71 – 68 = 3
Write down 36 and divide integers 36/4 = 9.
Multiply 4 x 9 = 36. Subtract 36 – 36 = 0.
The remainder is 0.
So, 179 is the answer.

Question 9.
9)\(\overline { 1,157 } \)
_____ R _____

Answer:
128 R 5

Explanation:
Divide integers 11/9 = 1
Multiply 9 x 1 = 9; Subtract 11 – 9 = 2
Write down 25 and divide integers 25/9 = 2.
Multiply 9 x 2 = 18. Subtract 25 – 18 = 7.
Write down 77 and divide integers 77/9 = 8.
Multiply 9 x 8 = 72. Subtract 77 – 72= 5.
The remainder is 5.
So, 128 is the answer.

Question 10.
6)\(\overline { 6,827 } \)
_____ R _____

Answer:
1,137 R 5

Explanation:
Divide integers 6/6 = 1
Multiply 6 x 1 = 6; Subtract 6 – 6 = 0
Write down 82 and divide integers 82/6 = 13.
Multiply 6 x 13 = 78. Subtract 82 – 78 = 4.
Write down 47 and divide integers 47/6 = 7.
Multiply 6 x 7 = 42. Subtract 47 – 42= 5.
The remainder is 5.
So, 1,137 is the answer.

Question 11.
7)\(\overline { 8,523 } \)
_____ R _____

Answer:
1,217 R 4

Explanation:
Divide integers 8/7 = 1
Multiply 7 x 1 = 7; Subtract 8 – 7 = 1
Write down 15 and divide integers 15/7 = 2.
Multiply 7 x 2 = 14. Subtract 15 – 14 = 1.
Write down 12 and divide integers 12/7 = 1.
Multiply 7 x 1 = 7. Subtract 12 – 7= 5.
Write down 53 and divide integers 53/7 = 7.
Multiply 7 x 7 = 49. Subtract 53 – 49= 4.
The remainder is 4.
So, 1,217 is the answer.

Practice: Copy and Solve Divide.

Question 12.
645 ÷ 8 = _____ R _____

Answer:
645 ÷ 8 = 80 R 5

Explanation:
Divide integers 64/8 = 8
Multiply 8 x 8 = 64; Subtract 64 – 64 = 0
Write down 05; 5 < 8; There are not enough tens
The remainder is 5.
So, 80 is the answer.

Question 13.
942 ÷ 6 = _____

Answer:
157

Explanation:
Divide integers 9/6 = 1
Multiply 6 x 1 = 6; Subtract 9 – 6 = 3
Write down 34 and divide integers 34/6 = 5.
Multiply 6 x 5 = 30. Subtract 34 – 30 = 4.
Write down 42 and divide integers 42/6 = 7.
Multiply 6 x 7 = 42. Subtract 42 – 42 = 0.
The remainder is 0.
So, 157 is the answer.

Question 14.
723 ÷ 7 = _____ R _____

Answer:
103 R 2

Explanation:
Divide integers 7/7 = 1
Multiply 7 x 1 = 7; Subtract 7 – 7 = 0
Write down 23 and divide integers 23/7 = 3.
Multiply 7 x 3 = 21. Subtract 23 – 21 = 2.
The remainder is 2.
So, 103 is the answer.

Question 15.
3,478 ÷ 9 = _____ R _____

Answer:
386 R 4

Explanation:
Divide integers 34/9 = 3
Multiply 9 x 3 = 27; Subtract 34 – 27 = 7
Write down 77 and divide integers 77/9 = 8.
Multiply 9 x 8 = 72. Subtract 77 – 72 = 5.
Write down 58 and divide integers 58/9 = 6.
Multiply 9 x 6 = 54. Subtract 58 – 54= 4.
The remainder is 4.
So, 386 is the answer.

Question 16.
3,214 ÷ 5 = _____ R _____

Answer:
642 R 4

Explanation:
Divide integers 32/5 = 6
Multiply 5 x 6 = 30; Subtract 32 – 30 = 2
Write down 21 and divide integers 21/5 = 4.
Multiply 5 x 4 = 20. Subtract 21 – 20 = 1.
Write down 14 and divide integers 14/5 = 2.
Multiply 5 x 2 = 10. Subtract 14 – 10 = 4.
The remainder is 4.
So, 642 is the answer.

Question 17.
492 ÷ 4 = _____

Answer:
123

Explanation:
Divide integers 4/4 = 1
Multiply 4 x 1 = 4; Subtract 4 – 4 = 0
Write down 9 and divide integers 9/4 = 2.
Multiply 4 x 2 = 8. Subtract 9 – 8 = 1.
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12. Subtract 12 – 12 = 0.
The remainder is 0.
So, 123 is the answer.

Question 18.
2,403 ÷ 9 = _____

Answer:
267

Explanation:
Divide integers 24/9 = 2
Multiply 9 x 2 = 18; Subtract 24 – 18 = 6
Write down 60 and divide integers 60/9 = 6.
Multiply 9 x 6 = 54. Subtract 60 – 54 = 6.
Write down 63 and divide integers 63/9 = 7.
Multiply 9 x 7 = 63. Subtract 63 – 63 = 0.
The remainder is 0.
So, 267 is the answer.

Question 19.
2,205 ÷ 6 = _____ R _____

Answer:
367 R 3

Explanation:
Divide integers 22/6 = 3
Multiply 6 x 3 = 18; Subtract 22 – 18 = 4
Write down 40 and divide integers 40/6 = 6.
Multiply 6 x 6 = 36; Subtract 40 – 36 = 4
Write down 45 and divide integers 45/6 = 7.
Multiply 6 x 7 = 42; Subtract 45 – 42 = 3
The remainder is 3.
So, 367 is the answer.

Question 20.
2,426 ÷ 3 = _____ R _____

Answer:
808 R 2

Explanation:
Divide integers 24/3 = 8
Multiply 3 x 8 = 24; Subtract 24 – 24 = 0
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
The remainder is 2.
So, 808 is the answer.

Question 21.
1,592 ÷ 8 = _____ R _____

Answer:
199

Explanation:
Divide integers 15/8 = 1
Multiply 8 x 1 = 8; Subtract 15 – 8 = 7
Write down 79 and divide integers 79/8 = 9.
Multiply 8 x 9 = 72; Subtract 79 – 72 = 7
Write down 72 and divide integers 72/8 = 9.
Multiply 8 x 9 = 72; Subtract 72 – 72 = 0
The remainder is 0.
So, 199 is the answer.

Question 22.
926 ÷ 4 = _____ R _____

Answer:
231 R 2

Explanation:
Divide integers 9/4 = 2
Multiply 4 x 2 = 8; Subtract 9 – 8 = 1
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12; Subtract 12 – 12 = 0
Write down 6 and divide integers 6/4 = 1.
Multiply 4 x 1 = 4; Subtract 6 – 4 = 2
The remainder is 2.
So, 231 is the answer.

Question 23.
6,033 ÷ 5 = _____ R _____

Answer:
1,206 R 3

Explanation:
Divide integers 6/5 = 1
Multiply 5 x 1 = 5; Subtract 6 – 5 = 1
Write down 10 and divide integers 10/5 = 2.
Multiply 5 x 2 = 10; Subtract 10 – 10 = 0
Write down 33 and divide integers 33/5 = 6.
Multiply 5 x 6 = 30; Subtract 33 – 30 = 3
The remainder is 3.
So, 1206 is the answer.

Place the First Digit – UNLOCK the Problem – Page No. 64

Question 24.
Rosa has a garden divided into sections. She has 125 daisy plants. If she plants an equal number of the daisy plants in each section of daisies, will she have any left over? If so, how many daisy plants will be left over?
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers Divide Whole Numbers; Place the First Digit img 1
a. What information will you use to solve the problem?
Type below:
__________

Answer:
We can use the fact that she has 125 daisy plants and she plants an equal number of the daisy plants in each of 3 sections.

Question 24.
b. How will you use division to find the number of daisy plants left over?
Type below:
__________

Answer:
We have to do 125/3
Divide integers 12/3 = 4
Multiply 3 x 4 = 12; Subtract 12 – 12 = 0
Write down 5 and divide integers 5/3 = 1.
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
The remainder is 2.
41 daisy plants in each section.
2 daisy plants left over

Question 24.
c. Show the steps you use to solve the problem. Estimate: 120 ÷ 3 = _____
Type below:
__________

Answer:
Divide integers 12/3 = 4
Multiply 3 x 4 = 12; Subtract 12 – 12 = 0
The remainder is 0.
So, 40 is the answer.

Question 24.
d. Complete the sentences:
Rosa has _____ daisy plants.
She puts an equal number in each of _____ sections.
Each section has _____ plants.
Rosa has _____ daisy plants left over.
Type below:
__________

Answer:
Rose has 125 daisy planes.
She puts an equal number in each of 3 sections.
Each section has 41 plants.
Rosa has 2 daisy plants left over.

Question 25.
One case can hold 3 boxes. Each box can hold 3 binders. How many cases are needed to hold 126 binders?
_____ cases

Answer:
14 cases

Explanation:
One case can hold 3 boxes. Each box can hold 3 binders. 3 x 3 = 9.
For 12 binders,
126/ (3 x 3) = 126/9 = 14

Question 26.
Test Prep In which place is the first digit in the quotient 1,497 ÷ 5?
Options:
a. thousands
b. hundreds
c. tens
d. ones

Answer:
b. hundreds

Explanation:
1,497 ÷ 5 = 499. the first digit 4 is in hundreds place.

Divide by 1-Digit Divisors – Share and Show – Page No. 67

Divide. Check your answer.

Question 1.
8)\(\overline { 624 } \)
Check
_____

Answer:
78

Explanation:
Divide integers 62/8 = 7
Multiply 8 x 7 = 56; Subtract 62 – 56 = 6
Write down 64 and divide integers 64/8 = 8.
Multiply 8 x 8 = 64. Subtract 64 – 64 = 0.
The remainder is 0.
So, 78 is the answer.
Check:
78 x 8 = 624;
624 = 624

Question 2.
4)\(\overline { 3,220 } \)
Check
_____

Answer:
805

Explanation:
Divide integers 32/4 = 8
Multiply 4 x 8 = 32; Subtract 32 – 32 = 0
Write down 20 and divide integers 20/4 = 5.
Multiply 4 x 5 = 20. Subtract 20 – 20 = 0.
The remainder is 0.
So, 805 is the answer.
Check:
805 x 4 = 3,220;
3,220 = 3,220.

Question 3.
4)\(\overline { 1,027 } \)
Check
_____ R _____

Answer:
256 R 3

Explanation:
Divide integers 10/4 = 2
Multiply 4 x 2 = 8; Subtract 10 – 8 = 2
Write down 22 and divide integers 22/4 = 5.
Multiply 4 x 5 = 20. Subtract 22 – 20= 2.
Write down 27 and divide integers 27/4 = 6.
Multiply 4 x 6 = 24. Subtract 27 – 24 = 3.
The remainder is 3.
So, 256 R 3.
Check:
256 x 4 = 1,024;
1,024 + 3 = 1,027.
1,027 = 1,027

On Your Own

Divide.

Question 4.
6)\(\overline { 938 } \)
_____ R _____

Answer:
156 R 2

Explanation:
Divide integers 9/6 = 1
Multiply 6 x 1 = 6; Subtract 9 – 6 = 3
Write down 33 and divide integers 33/6 = 5.
Multiply 6 x 5 = 30. Subtract 33 – 30 = 3.
Write down 38 and divide integers 38/6 = 6.
Multiply 6 x 6 = 36. Subtract 38 – 36 = 2.
The remainder is 2.
So, 156 R 2.

Question 5.
4)\(\overline { 762 } \)
_____ R _____

Answer:
190 R 2

Explanation:
Divide integers 7/4 = 1
Multiply 4 x 1 = 4; Subtract 7 – 4 = 3
Write down 36 and divide integers 36/4 = 9.
Multiply 4 x 9 = 36. Subtract 36 – 36 = 0.
Write down 2. 2 < 4; There are not enough tens
The remainder is 2.
So, 190 R 2.

Question 6.
3)\(\overline { 5,654 } \)
_____ R _____

Answer:
1884 R 2

Explanation:
Divide integers 5/3 = 1
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
Write down 25 and divide integers 25/3 = 8.
Multiply 3 x 8 = 24. Subtract 25 – 24 = 1.
Write down 14 and divide integers 14/3 = 4.
Multiply 3 x 4 = 12. Subtract 14 – 12 = 2.
The remainder is 2.
So, 1884 R 2.

Question 7.
8)\(\overline { 475 } \)
_____ R _____

Answer:
59 R 3

Explanation:
Divide integers 47/8 = 5
Multiply 8 x 5 = 40; Subtract 47 – 40 = 7
Write down 75 and divide integers 75/8 = 9.
Multiply 9 x 8 = 72. Subtract 75 – 72 = 3.
The remainder is 3.
So, 59 R 3.

Practice: Copy and Solve Divide.

Question 8.
4)\(\overline { 671 } \)
_____ R _____

Answer:
167 R 3

Explanation:
Divide integers 6/4 = 1
Multiply 4 x 1 = 4; Subtract 6 – 4 = 2
Write down 27 and divide integers 27/4 = 6.
Multiply 4 x 6 = 24. Subtract 27 – 24 = 3.
Write down 31 and divide integers 31/4 = 7.
Multiply 4 x 7 = 28. Subtract 31 – 28 = 3.
The remainder is 3.
So, 167 R 3.

Question 9.
9)\(\overline { 2,023 } \)
_____ R _____

Answer:
224 R 7

Explanation:
Divide integers 20/9 = 2
Multiply 9 x 2 = 18; Subtract 20 – 18 = 2
Write down 22 and divide integers 22/9 = 2.
Multiply 9 x 2 = 18. Subtract 22 – 18 = 4.
Write down 43 and divide integers 43/9 = 4.
Multiply 9 x 4 = 36. Subtract 43 – 36 = 7.
The remainder is 7.
So, 224 R 7.

Question 10.
3)\(\overline { 4,685 } \)
_____ R _____

Answer:
1,561 R 2

Explanation:
Divide integers 4/3 = 1
Multiply 3 x 1 = 3; Subtract 4 – 3 = 1
Write down 16 and divide integers 16/3 = 5.
Multiply 3 x 5 = 15. Subtract 16 – 15 = 1.
Write down 18 and divide integers 18/3 = 6.
Multiply 3 x 6 = 18. Subtract 18 – 18 = 0.
Write down 5 and divide integers 5/3 = 1.
Multiply 3 x 1 = 3. Subtract 5 – 3 = 2.
The remainder is 2.
So, 1,561 R 2.

Question 11.
8)\(\overline { 948 } \)
_____ R _____

Answer:
118 R 4

Explanation:
Divide integers 9/8 = 1
Multiply 8 x 1 = 8; Subtract 9 – 8 = 1
Write down 14 and divide integers 14/8 = 1.
Multiply 8 x 1 = 8. Subtract 14 – 8 = 6.
Write down 68 and divide integers 68/8 = 8.
Multiply 8 x 8 = 64. Subtract 68 – 64 = 4.
The remainder is 4.
So, 118 R 4.

Question 12.
1,326 ÷ 4 = _____ R _____

Answer:
331 R 2

Explanation:
Divide integers 13/4 = 3
Multiply 4 x 3 = 12; Subtract 13 – 12 = 1
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12. Subtract 12 – 12 = 0.
Write down 6 and divide integers 6/4 = 1.
Multiply 4 x 1 = 4. Subtract 6 – 4 = 2.
The remainder is 2.
So, 331 R 2.

Question 13.
5,868 ÷ 6 = _____

Answer:
978

Explanation:
Divide integers 58/6 = 9
Multiply 6 x 9 = 54; Subtract 58 – 54 = 4
Write down 46 and divide integers 46/6 = 7.
Multiply 6 x 7 = 42. Subtract 46 – 42 = 4.
Write down 48 and divide integers 48/6 = 8.
Multiply 6 x 8 = 48. Subtract 48 – 48 = 0.
The remainder is 0.
So, 978.

Question 14.
566 ÷ 3 = _____ R _____

Answer:
188 R 2

Explanation:
Divide integers 5/3 = 1
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
The remainder is 2.
So, 188 R 2.

Question 15.
3,283 ÷ 9 = _____ R _____

Answer:
364 R 7

Explanation:
Divide integers 32/9 = 3
Multiply 9 x 3 = 27; Subtract 32 – 27 = 5
Write down 58 and divide integers 58/9 = 6.
Multiply 9 x 6 = 54. Subtract 58 – 54 = 4.
Write down 43 and divide integers 43/9 = 4.
Multiply 9 x 4 = 36. Subtract 43 – 36 = 7.
The remainder is 7.
So, 364 R 7.

Algebra Find the value of n in each equation. Write what n represents in the related division problem.

Question 16.
n = 4 × 58
Value of n = _______
Represents: _______

Answer:
Value of n = 232
Represents: dividend

Explanation:
n = 4 × 58;
232 = 4 x 58;
n is the dividend

Question 17.
589 = 7 × 84 + n
Value of n = _______
Represents: _______

Answer:
Value of n = 1
Represents: remainder

Explanation:
589 = 7 × 84 + n
589 = 588 + n;
589 – 588 = n;
1 = n
n is the remainder

Question 18.
n = 5 × 67 + 3
Value of n = _______
Represents: _______

Answer:
Value of n = 338
Represents: dividend

Explanation:
n = 5 × 67 + 3
n = 335 + 3
n = 338
n is the dividend

Divide by 1-Digit Divisors – Problem Solving – Page No. 68

Use the table to solve 19–20.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers Divide Whole Numbers; Divide by 1-Digit Divisors img 2

Question 19.
If the Welcome gold nugget were turned into 3 equal-sized gold bricks, how many troy ounces would each brick weigh?
_____ troy ounces

Answer:
739 troy ounces

Explanation:
Welcome gold nugget = 2,217 troy ounces.
If it turned into 3 equal-sized gold bricks, 2,217/3 = 739.
739 troy ounces

Question 20.
Pose a Problem Look back at Problem 19. Write a similar problem by changing the nugget and the number of bricks. Then solve the problem.
Type below:
__________

Answer:
571 troy ounces

Explanation:
If Welcome Stranger nugget were turned into 4 equal-sized gold bricks, how many troy ounces would each brick weigh?
Welcome Stranger nugget = 2,284.
If it turned into 4 equal-sized gold bricks, 2,217/3 = 571.
571 troy ounces

Question 21.
There are 246 students going on a field trip to pan for gold. If they are going in vans that hold 9 students each, how many vans are needed? How many students will ride in the van that isn’t full?
The number of vans: _________
_________ students in the van that isn’t full

Answer:
The number of vans: 27
3 students will ride in the van that isn’t full

Explanation:
There are 246 students going on a field trip to pan for gold. If they are going in vans that hold 9 students each, 246/9 = 27 R 3
The number of vans: 27
3 students will ride in the van that isn’t full
Question 22.
One crate can hold 8 cases of trading cards. How many crates are needed to hold 128 cases of trading cards?
_____ crates

Answer:
16 crates

Explanation:
One crate can hold 8 cases of trading cards. To hold 128 cases of trading cards, 128/8 = 16 crates needed.

Question 23.
Test Prep At a bake sale, a fifth-grade class sold 324 cupcakes in packages of 6. How many packages of cupcakes did the class sell?
Options:
a. 1,944
b. 108
c. 64
d. 54

Answer:
d. 54

Explanation:
At a bake sale, a fifth-grade class sold 324 cupcakes in packages of 6. 324/6 = 54

Division with 2-Digit Divisors – Share and Show – Page No. 71

Use the quick picture to divide.

Question 1.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers Divide Whole Numbers; Division with 2-Digit Divisors img 3
143 ÷ 13 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 1
143 ÷ 13 = 11

Explanation:
143 = 100 + 40 + 3
Model the first partial quotient by making a rectangle with the hundred and 3 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10) = 100 + 30 = 130.
The rectangle shows 10 groups of 13.
Model the second partial quotient by making a line with the ten and 3 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1) = 10 + 3 = 13
130 + 13 = 143;
So, the answer is 10 + 1 = 11

Divide. Use base-ten blocks.

Question 2.
168 ÷ 12 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 2
168 ÷ 12 = 14

Explanation:
168 ÷ 12
Model the first partial quotient by making a rectangle with the hundred and 2 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10) = 100 + 20 = 120.
The rectangle shows 10 groups of 12.
Model the second partial quotient by making a line with the ten and 2 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1) = 10 + 2 = 12.
Repeat the above step more three times to get
120 + 12 + 12 + 12 + 12 = 168;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 3.
154 ÷ 14 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 3
154 ÷ 14 = 11

Explanation:
154 ÷ 14
Model the first partial quotient by making a rectangle with the hundred and 4 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10) = 100 + 40 = 140.
The rectangle shows 10 groups of 14.
Model the second partial quotient by making a line with the ten and 4 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1) = 10 + 4 = 14.
Repeat the above step more three times to get
140 + 14 = 154;
So, the answer is 10 + 1 = 11

Question 4.
187 ÷ 11 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 4
187 ÷ 11 = 17

Explanation:
187 ÷ 11 =
Model the first partial quotient by making a rectangle with the hundred and 1 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10) = 100 + 10 = 110.
The rectangle shows 10 groups of 11.
Model the second partial quotient by making a line with the ten and 1 ones. In the Record section, cross out the ten and ones you use.
10 + (1) = 10 + 1 = 11.
Repeat the above step more six times to get
110 + 11 + 11 + 11 + 11 + 11 + 11 + 11 = 187;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 17

Divide. Draw a quick picture.

Question 5.
165 ÷ 11 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 5
165 ÷ 11 = 15

Explanation:
165 ÷ 11
Model the first partial quotient by making a rectangle with the hundred and 1 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10) = 100 + 10 = 110.
The rectangle shows 10 groups of 11.
Model the second partial quotient by making a line with the ten and 1 ones. In the Record section, cross out the ten and ones you use.
10 + (1) = 10 + 1 = 11.
Repeat the above step more four times to get
110 + 11 + 11 + 11 + 11 + 11 = 165;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 = 15

Question 6.
216 ÷ 18 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 6
216 ÷ 18 = 12

Explanation:
216 ÷ 18
Model the first partial quotient by making a rectangle with the hundred and 8 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10 + 10 + 10 + 10 + 10) = 100 + 80 = 180.
The rectangle shows 10 groups of 18.
Model the second partial quotient by making a line with the ten and 8 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = 10 + 8 = 18.
Repeat the above step to get
180 + 18 + 18  = 216;
So, the answer is 10 + 1 + 1 = 12

Question 7.
196 ÷ 14 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 7
196 ÷ 14 = 14

Explanation:
196 ÷ 14
Model the first partial quotient by making a rectangle with the hundred and 4 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10) = 100 + 40 = 140.
The rectangle shows 10 groups of 14.
Model the second partial quotient by making a line with the ten and 4 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1) = 10 + 4 = 14.
Repeat the above step more three times to get
140 + 14 + 14 + 14 + 14  = 196;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 8.
195 ÷ 15 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 8
195 ÷ 15 = 13

Explanation:
195 ÷ 15
Model the first partial quotient by making a rectangle with the hundred and 5 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10 + 10) = 100 + 50 = 150.
The rectangle shows 10 groups of 15.
Model the second partial quotient by making a line with the ten and 5 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1 + 1) = 10 + 5 = 15.
Repeat the above step more three times to get
150 + 15 + 15 + 15  = 195;
So, the answer is 10 + 1 + 1 + 1 = 13

Question 9.
182 ÷ 13 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 9
182 ÷ 13 = 14

Explanation:
182 ÷ 13
Model the first partial quotient by making a rectangle with the hundred and 3 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 ) = 100 + 30 = 130.
The rectangle shows 10 groups of 13.
Model the second partial quotient by making a line with the ten and 3 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1) = 10 + 3 = 13.
Repeat the above step more four times to get
130 + 13 + 13 + 13 + 13 = 182;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 10.
228 ÷ 12 = _____

Answer:
grade 5 chapter 2 Division with 2-Digit Divisors image 10
228 ÷ 12 = 19

Explanation:
228 ÷ 12
Model the first partial quotient by making a rectangle with the hundred and 2 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10) = 100 + 20 = 120.
The rectangle shows 10 groups of 12.
Model the second partial quotient by making a line with the ten and 2 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1) = 10 + 2 = 12.
Repeat the above step more eight times to get
120 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 228;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 19

Division with 2-Digit Divisors – Connect to Social Studies – Page No. 72

Pony Express

The Pony Express used men riding horses to deliver mail between St. Joseph, Missouri, and Sacramento, California, from April, 1860 to October, 1861. The trail between the cities was approximately 2,000 miles long. The first trip from St. Joseph to Sacramento took 9 days 23 hours. The first trip from Sacramento to St. Joseph took 11 days 12 hours.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers Divide Whole Numbers; Division with 2-Digit Divisors img 4

Solve.

Question 11.
Suppose two Pony Express riders rode a total of 165 miles. If they replaced each horse with a fresh horse every 11 miles, how many horses would they have used?
_____ horses

Answer:
16 horses

Explanation:
Suppose two Pony Express riders rode a total of 165 miles. If they replaced each horse with a fresh horse every 11 miles. Then, 16 horses used.

Question 12.
Suppose a Pony Express rider was paid $192 for 12 weeks of work. If he was paid the same amount each week, how much was he paid for each week of work?
$ _____

Answer:
$16

Explanation:
Suppose a Pony Express rider was paid $192 for 12 weeks of work.
For each week. $192/12 = $16.

Question 13.
Suppose three riders rode a total of 240 miles. If they used a total of 16 horses, and rode each horse the same number of miles, how many miles did they ride before replacing each horse?
_____ miles

Answer:
15 miles

Explanation:
Assuming each horse was only ridden once then a total of 16 horses were ridden for a total of 240 miles
240 miles/16 horses = 15 miles/horse
if each horse was ridden more than once before being replaced the distance between replacements could be reduced.
The fact that there were 3 riders is irrelevant.

Question 14.
Suppose it took 19 riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento. If they all rode the same number of hours, how many hours did each rider ride?
_____ hours

Answer:
15 hours

Explanation:
Suppose it took 19 riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento.
(11 x 24 + 21)/19 = (264 + 21)/19 = 285/19 = 15 hours.

Partial Quotients – Share and Show – Page No. 75

Divide. Use partial quotients.

Question 1.
18)\(\overline { 648 } \)
_____

Answer:
36

Explanation:
Multiply 18 x 10 = 180; Subtract: 648 – 180 = 468.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 468 – 180= 288.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 288- 180= 108.
partial quotient = 10
Multiply 18 x 6 = 108; Subtract: 108 – 108 = 0.
partial quotient = 6;
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 6 = 36 R 0

Question 2.
62)\(\overline { 3,186 } \)
_____ R _____

Answer:

Explanation:
Multiply 62 x 10 = 620; Subtract: 3,186 – 620 = 2,566.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 2,566 – 620 = 1,946.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 1,946 – 620 = 1,326.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 1,326 – 620 = 706.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 706 – 620 = 86.
partial quotient = 10
Multiply 62 x 1 = 62; Subtract: 86 – 62 = 24.
partial quotient = 1
The remainder is 24;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10  + 10 + 1 = 51 R 24

Question 3.
858 ÷ 57
_____ R _____

Answer:

Explanation:
Multiply 57 x 10 = 570; Subtract: 858 – 570 = 288.
partial quotient = 10
Multiply 57 x 5 = 285; Subtract: 288 – 285 = 3.
partial quotient = 5
The remainder is 3;
Add partial quotient to find the wholenumber quotient;
10 + 5 = 15 R 3

On Your Own

Divide. Use partial quotients.

Question 4.
73)\(\overline { 584 } \)
_____

Answer:
8

Explanation:
Multiply 73 x 8 = 584; Subtract: 584 – 584 = 0.
partial quotient = 8
The remainder is 0;

Question 5.
51)\(\overline { 1,831 } \)
_____ R _____

Answer:
35 R 46

Explanation:
Multiply 51 x 10 = 510; Subtract: 1,831 – 510 = 1,321.
partial quotient = 10
Multiply 51 x 10 = 510; Subtract: 1,321 – 510 = 811.
partial quotient = 10
Multiply 51 x 10 = 510; Subtract: 811 – 510 = 301.
partial quotient = 10
Multiply 51 x 5 = 255; Subtract: 301 – 255 = 46.
partial quotient = 5
The remainder is 46;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 5 = 35 R 46

Question 6.
82)\(\overline { 2,964 } \)
_____ R _____

Answer:
36 R 12

Explanation:
Multiply 82 x 10 = 820; Subtract: 2,964 – 820 = 2,144.
partial quotient = 10
Multiply 82 x 10 = 820; Subtract: 2,144 – 820 = 1,324.
partial quotient = 10
Multiply 82 x 10 = 820; Subtract: 1,324 – 820 = 504.
partial quotient = 10
Multiply 82 x 6 = 492; Subtract: 504 – 492= 12.
partial quotient = 6
The remainder is 12;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 6 = 36 R 12

Question 7.
892 ÷ 26
_____ R _____

Answer:
34 R 8

Explanation:
Multiply 26 x 10 = 260; Subtract: 892 – 260 = 632.
partial quotient = 10
Multiply 26 x 10 = 260; Subtract: 632 – 260 = 372.
partial quotient = 10
Multiply 26 x 10 = 260; Subtract: 372 – 260 = 112.
partial quotient = 10
Multiply 26 x 4 = 104; Subtract: 112 – 104 = 8.
partial quotient = 4
The remainder is 8;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 4 = 34 R 8

Question 8.
1,056 ÷ 48
_____

Answer:
22

Explanation:
Multiply 48 x 10 = 480; Subtract: 1,056 – 480 = 576.
partial quotient = 10
Multiply 48 x 10 = 480; Subtract: 576 – 480 = 96.
partial quotient = 10
Multiply 48 x 2 = 96; Subtract: 96 – 96 = 0.
partial quotient = 2
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 2 = 22

Question 9.
2,950 ÷ 67
_____ R _____

Answer:
44 R 2

Explanation:
Multiply 67 x 10 = 670; Subtract: 2,950 – 670 = 2,280.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 2,280 – 670 = 1,610.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 1,610 – 670 = 940.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 940 – 670 = 270.
partial quotient = 10
Multiply 67 x 4= 268; Subtract: 270 – 268 = 2.
partial quotient = 4
The remainder is 2;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 4 = 44 R 2

Practice: Copy and Solve Divide. Use partial quotients.

Question 10.
653 ÷ 42
_____ R _____

Answer:
15 R 23

Explanation:
Multiply 42 x 10 = 420; Subtract: 653 – 420 = 233.
partial quotient = 10
Multiply 42 x 5 = 210; Subtract: 233 – 210 = 23.
partial quotient = 5
The remainder is 23;
Add partial quotient to find the wholenumber quotient;
10 + 5 = 15 R 23

Question 11.
946 ÷ 78
_____ R _____

Answer:
12 R 10

Explanation:
Multiply 78 x 10 = 780; Subtract: 946 – 780 = 166.
partial quotient = 10
Multiply 78 x 2 = 156; Subtract: 166 – 156 = 10.
partial quotient = 2
The remainder is 10;
Add partial quotient to find the wholenumber quotient;
10 + 2 = 12 R 10

Question 12.
412 ÷ 18
_____ R _____

Answer:
22 R 16

Explanation:
Multiply 18 x 10 = 180; Subtract: 412 – 180 = 232.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 232 – 180 = 52.
partial quotient = 10
Multiply 18 x 2 = 36; Subtract: 52 – 36 = 16.
partial quotient = 2
The remainder is 16;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 2 = 22 R 16

Question 13.
871 ÷ 87
_____ R _____

Answer:
10 R 1

Explanation:
Multiply 87 x 10 = 870; Subtract: 871 – 870 = 1.
partial quotient = 10
The remainder is 1;
10 R 1

Question 14.
1,544 ÷ 34
_____ R _____

Answer:
45 R 14

Explanation:
Multiply 34 x 10 = 340; Subtract: 1,544 – 340 = 1,204.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 1,204 – 340 = 864.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 864 – 340 = 524.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 524 – 340 = 184.
partial quotient = 10
Multiply 34 x 5 = 170; Subtract: 184 – 170 = 14.
partial quotient = 5
The remainder is 14;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 5 = 45 R 14

Question 15.
2,548 ÷ 52
_____ R _____

Answer:
47 R 14

Explanation:
Multiply 52 x 10 = 520; Subtract: 2,548 – 520 = 2028.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 2028- 520 = 1508.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 1508- 520 = 988.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 988 – 520 = 468.
partial quotient = 10
Multiply 52 x 9 = 468; Subtract: 468 – 468= 0.
partial quotient = 9
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 9 = 49 R 0

Question 16.
2,740 ÷ 83
_____ R _____

Answer:
33 R 1

Explanation:
Multiply 83 x 10 = 830; Subtract: 2,740 – 830= 1910.
partial quotient = 10
Multiply 83 x 10 = 830; Subtract: 1910 – 830= 1080.
partial quotient = 10
Multiply 83 x 10 = 830; Subtract: 1080 – 830= 250.
partial quotient = 10
Multiply 83 x 3 = 249; Subtract: 250 – 249 = 1.
partial quotient = 3
The remainder is 1;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 3 = 33 R 1

Question 17.
4,135 ÷ 66
_____ R _____

Answer:
62 R 43

Explanation:
Multiply 66 x 10 = 660; Subtract: 4,135 – 660 = 3475.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 3475 – 660 = 2815.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 2815 – 660 = 2155.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 2155 – 660 = 1495.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 1495 – 660 = 835.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 835 – 660 = 175.
partial quotient = 10
Multiply 66 x 2 = 132; Subtract: 175 – 132 = 43.
partial quotient = 2
The remainder is 43;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 10 + 10 + 2 = 62 R 43

Partial Quotients – Problem Solving – Page No. 76

Use the table to solve 18–20 and 22.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers Divide Whole Numbers; Partial Quotients img 5

Question 18.
How many years would it take for a person in the United States to eat 855 pounds of apples?
_____ years

Answer:
45 years

Explanation:
Each year a person eats 19 pounds of apples. So, to eat 855 pounds of apples, it takes 855/19 = 45 years.

Question 19.
How many years would it take for a person in the United States to eat 1,120 pounds of turkey?
_____ years

Answer:
80 years

Explanation:
Each year a person eats 14 pounds of turkey. So, to eat 1,120 pounds of turkey, it takes 1,120/14 = 80 years.

Question 20.
If 6 people in the United States each eat the average amount of popcorn for 5 years, how many quarts of popcorn will they eat?
_____ quarts

Answer:
2,040 quarts

Explanation:
1 person eats 68 quarts of popcorn each year. 6 people = 6 x 68 quarts of popcorn = 408 quarts of popcorn for each year.
For 5 years, they will eat popcorn = 5 x 408 = 2,040 quarts

Question 21.
In a study, 9 people ate a total of 1,566 pounds of potatoes in 2 years. If each person ate the same amount each year, how many pounds of potatoes did each person eat in 1 year?
_____ pounds

Answer:
87 pounds

Explanation:
9 people ate a total of 1,566 pounds of potatoes in 2 years. If each person ate the same amount each year, 1,566/2 = 783.
To calculate how many pounds of potatoes did each person eat in 1 year, 783/9 = 87 pounds.

Question 22.
Sense or Nonsense? In the United States, a person eats more than 40,000 pounds of bread in a lifetime if he or she lives to be 80 years old. Does this statement make sense, or is it nonsense? Explain.
__________

Answer:
nonsense; 40,000 pounds / 80 years = 4,000 pounds / 8 years = 2,000 pounds (1 ton) / 4 years = 1,000 pounds / 2 years = 1,000 pounds / 2 years = 500 pounds per year = almost 1 and 1/2 pounds of bread every day of your life.

Question 23.
Test Prep The school auditorium has 448 seats arranged in 32 equal rows. How many seats are in each row?
Options:
a. 14,336
b. 480
c. 416
d. 14

Answer:
d. 14

Explanation:
The school auditorium has 448 seats arranged in 32 equal rows.
Each row = 448/32 = 14

Mid-Chapter Checkpoint – Page No. 77

Concepts and Skills

Question 1.
Explain how estimating the quotient helps you place the first digit in the quotient of a division problem.
Type below:
__________

Answer:
Let’s do 5980 divided by 347
Estimate: 6000/300 = 20
So, I now know my first digit will go into the 10’s place
or 57890 divided by 34
that is 60,000 divided by 30 = 2000
my first digit goes into the thousands place.

Question 2.
Explain how to use multiplication to check the answer to a division problem.
Type below:
__________

Answer:
Take 739/9 = 82 R 1.
Check: 9 x 82 + 1 = 739.
divisor x quotient + remainder = dividend.

Divide.

Question 3.
633 ÷ 3 = _____

Answer:
211

Explanation:
Divide integers 6/3 = 2
Multiply 3 x 2 = 6; Subtract 6 – 6 = 0
Write down 3 and divide integers 3/3 = 1.
Multiply 3 x 1 = 3. Subtract 3 – 3 = 0.
Write down 3 and divide integers 3/3 = 1.
Multiply 3 x 1 = 3. Subtract 3 – 3 = 0.
The remainder is 0.
So, 211 is the answer.

Question 4.
487 ÷ 8 = _____ R _____

Answer:
60 R 7

Explanation:
Divide integers 48/8 = 6
Multiply 8 x 6 = 48; Subtract 48 – 48 = 0
Write down 7;7 < 8.
The remainder is 7.
So, 60 R 7.

Question 5.
1,641 ÷ 4 = _____ R _____

Answer:
410 R 1

Explanation:
Divide integers 16/4 = 4
Multiply 4 x 4 = 16; Subtract 16 – 16 = 0
Write down 4 and divide integers 4/4 = 1.
Multiply 4 x 1 = 4; Subtract 4 – 4 = 0
Write down 1; 1<4
The remainder is 1.
So, 410 R 1.

Question 6.
2,765 ÷ 9 = _____ R _____

Answer:
307 R 2

Explanation:
Divide integers 27/9 = 3
Multiply 9 x 3 = 27; Subtract 27 – 27 = 0
Write down 65 and divide integers 65/9 = 7.
Multiply 9 x 7 = 63. Subtract 65 – 63 = 2.
The remainder is 2.
So, 307 R 2.

Divide. Use partial quotients.

Question 7.
156 ÷ 13 = _____

Answer:
12

Explanation:
Multiply 13 x 10 = 130; Subtract: 156 – 130 = 26.
partial quotient = 10
Multiply 13 x 2 = 26; Subtract: 26 – 26 = 0.
partial quotient = 2
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 +2 = 12 R 0

Question 8.
318 ÷ 53 = _____

Answer:
6

Explanation:
Multiply 53 x 6 = 318; Subtract: 318 – 318= 0.
partial quotient = 6
The remainder is 0;
quotient = 6

Question 9.
1,562 ÷ 34 =
_____ r _____

Answer:
45 R 32

Explanation:
Multiply 34  x 10 = 340; Subtract: 1,562 – 340 = 1,222.
partial quotient = 10
Multiply 34  x 10 = 340; Subtract: 1,222 – 340 = 882.
partial quotient = 10
Multiply 34  x 10 = 340; Subtract: 882 – 340 = 542.
partial quotient = 10
Multiply 34  x 10 = 340; Subtract: 542 – 340 = 202.
partial quotient = 10
Multiply 34  x 5 = 170; Subtract: 202 – 170 = 32.
partial quotient = 5
The remainder is 32;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 5 = 45 R 32

Question 10.
4,024 ÷ 68 =
_____ r _____

Answer:
59 R 12

Explanation:
Multiply 68 x 10 = 680; Subtract: 4,024 – 680 = 3,344.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 3,344 – 680= 2664.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 2664 – 680 = 1984.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 1984 – 680= 1304.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 1304 – 680 = 624.
partial quotient = 10
Multiply 68 x 9 = 612; Subtract: 624 – 612 = 12.
partial quotient = 9
The remainder is 12;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 10 + 9 = 59 R 12

Mid-Chapter Checkpoint – Page No. 78

Question 11.
Emma is planning a party for 128 guests. If 8 guests can be seated at each table, how many tables will be needed for seating at the party?
_____ tables

Answer:
16 tables

Explanation:
Emma is planning a party for 128 guests. If 8 guests can be seated at each table 128/8 = 16.

Question 12.
Tickets for the basketball game cost $14 each. If the sale of the tickets brought in $2,212, how many tickets were sold?
_____ tickets

Answer:
158 tickets

Explanation:
Tickets for the basketball game cost $14 each. If the sale of the tickets brought in $2,212, $2,212/$14 = 158

Question 13.
Margo used 864 beads to make necklaces for the art club. She made 24 necklaces with the beads. If each necklace has the same number of beads, how many beads did Margo use for each necklace?
_____

Answer:
36 beads

Explanation:
Margo used 864 beads to make necklaces for the art club. She made 24 necklaces with the beads. If each necklace has the same number of beads, 864/24 = 36 beads

Question 14.
Angie needs to buy 156 candles for a party. Each package has 8 candles. How many packages should Angie buy?
_____ packages

Answer:
20 packages

Explanation:
Angie needs to buy 156 candles for a party. Each package has 8 candles.
156/8 = 20

Question 15.
Max delivers 8,520 pieces of mail in one year. About how many pieces of mail does he deliver in 2 months? Explain your steps.
_____ pieces

Answer:
1,420 pieces

Explanation:
Max delivers 8,520 pieces of mail in one year.
So, for 12 months, 8,520/12 = 710.
To deliver in 2 months, 710 x 2 = 1,420

Share and Show – Page No. 81

Use compatible numbers to find two estimates.

Question 1.
22)\(\overline { 154 } \)
140 ÷ 20 = _____
160 ÷ 20 = _____
Estimate: _____ ; _____

Answer:
140 ÷ 20 = 7
160 ÷ 20 = 8
Estimate: 7 ; 8

Explanation:
Two sets of compatible numbers to find two different estimates are
140 ÷ 20
14 ÷ 2 = 7
140 ÷ 20 = 7
160 ÷ 20
16 ÷ 2 = 8
160 ÷ 20  = 8

Question 2.
68)\(\overline { 503 } \)
Estimate: _____ ; _____

Answer:
476 ÷ 68= 7
544 ÷ 68 = 8
Estimate: 7 ; 8

Explanation:
Multiples of 68:
68 136 204 272 340 408 476 544
Find multiples that are close to the dividend. Use either or both numbers to estimate the quotient.
476/68 = 7
544/68 = 8
The quotient is between 7 and 8.

Question 3.
81)\(\overline { 7,052 } \)
Estimate: _____ ; _____

Answer:
6400 ÷ 80 = 80
7200 ÷ 80 = 90
Estimate: 80 ; 90

Explanation:
6400/80
64/8 = 8
640 / 80 = 8
6400/80 = 800
7200/80
72/8 = 9
720/80 =9
7200/80 = 90
Estimate: 80, 90

Question 4.
33)\(\overline { 291 } \)
Estimate: _____ ; _____

Answer:
240 ÷ 30= 8
270 ÷ 30 = 9
Estimate: 8 ; 9

Explanation:
240/30
24/3 = 8
240/30 = 8
270/30
27/3 = 9
270/30 = 9
Estimate: 8, 9

Question 5.
58)\(\overline { 2,365 } \)
Estimate: _____ ;

Answer:
2400 ÷ 60= 40
3000 ÷ 60 = 50
Estimate: 40 ; 50

Explanation:
2400/60
24/6 = 4
240/60 = 4
2400/60 = 40
3000/60
30/6 = 5
300/60 = 5
3000/60 = 50
Estimate: 40, 50

Question 6.
19)\(\overline { 5,312 } \)
Estimate: _____ ; _____

Answer:
5300 ÷ 20= 7
5320 ÷ 20 = 8
Estimate: 265 ; 266

Explanation:
5300/20
5300/20 = 265
5320/20
5320/20 = 266

On Your Own

Use compatible numbers to find two estimates.

Question 7.
42)\(\overline { 396 } \)
Estimate: _____ ; _____

Answer:
360 ÷ 40 = 9
400 ÷ 40 = 10
Estimate: 9 ; 10

Explanation:
360/40 = 9
400/40 = 10
Estimate: 9,10

Question 8.
59)\(\overline { 413 } \)
Estimate: _____ ; _____

Answer:
420 ÷ 60= 7
480 ÷ 60 = 8
Estimate: 7 ; 8

Explanation:
420/60 = 7
480/60 = 8

Question 9.
28)\(\overline { 232 } \)
Estimate: _____ ; _____

Answer:
240 ÷ 30 = 8
270÷ 30 = 9
Estimate: 8 ; 9

Explanation:
240/30 = 8
270/30 = 9
Estimate: 8 ; 9

Question 10.
22)\(\overline { 368 } \)
Estimate: _____ ; _____

Answer:
320 ÷ 20= 16
340 ÷ 20 = 17
Estimate: 16 ; 17

Explanation:
320/20 = 16
340/20 = 17
Estimate: 16 ; 17

Question 11.
78)\(\overline { 375 } \)
Estimate: _____ ; _____

Answer:
320 ÷ 80 = 4
400 ÷ 80 = 5
Estimate: 4 ; 5

Explanation:
320/80 = 4
400/80 = 5
Estimate: 16 ; 17

Question 12.
88)\(\overline { 6,080 } \)
Estimate: _____ ; _____

Answer:
6210÷ 90= 69
6300 ÷ 90 = 70
Estimate: 69 ; 70

Explanation:
6210/90 = 69
6300/90 = 70

Question 13.
5,821 ÷ 71
Estimate: _____ ; _____

Answer:
5180 ÷ 70 = 74
5250÷ 70 = 75
Estimate: 74 ; 75

Explanation:
5180/70 = 74
5250/70 = 75
Estimate: 74 ; 75

Question 14.
1,565 ÷ 67
Estimate: _____ ; _____

Answer:
1610 ÷ 70 = 23
1680 ÷ 70 = 24
Estimate: 23 ; 24

Explanation:
1610/70 = 23
1680/70 = 24
Estimate: 23 ; 24

Question 15.
7,973 ÷ 91
Estimate: _____ ; _____

Answer:
476 ÷ 90 = 87
544 ÷ 90 = 88
Estimate: 87 ; 88

Explanation:
6960/90 = 87
7920/90 = 88
Estimate: 87 ; 88

Use compatible numbers to estimate the quotient.

Question 16.
19)\(\overline { 228 } \)
Estimate: _____

Answer:
240 ÷ 20 = 12
260 ÷ 20 = 13
Estimate: 12 ; 13

Explanation:
240/20 = 12
260/20 = 13
Estimate: 12 ; 13

Question 17.
25)\(\overline { $595 } \)
Estimate: $ _____

Answer:
575 ÷ 25 = 23
600 ÷ 25 = 24
Estimate: 23 ; 24

Explanation:
575/25 = 23
600/25 = 24
Estimate: 23 ; 24

Question 18.
86)\(\overline { 7,130 } \)
Estimate: _____

Answer:
7380 ÷ 90 = 82
7470 ÷ 90 = 83
Estimate: 82 ; 83

Explanation:
7380/90 = 82
7470/90 = 83
Estimate: 82 ; 83

Question 19.
83)\(\overline { 462 } \)
Estimate: _____

Answer:
400 ÷ 80 = 5
480 ÷ 80 = 6
Estimate: 5 ; 6

Explanation:
400/80 = 5
480/80 = 6
Estimate: 5 ; 6

Question 20.
27)\(\overline { 9,144 } \)
Estimate: _____

Answer:
10,140 ÷ 30 = 338
10,170 ÷ 30 = 339
Estimate: 338 ; 339

Explanation:
10,140/30 = 338
10,170/30 = 339
Estimate: 338 ; 339

Question 21.
68)\(\overline { 710 } \)
Estimate: _____

Answer:
700 ÷ 70 = 10
770 ÷ 70 = 11
Estimate: 10 ; 11

Explanation:
700/70 = 10
770/70 = 11
Estimate: 10 ; 11

Question 22.
707 ÷ 36
Estimate: _____

Answer:
760 ÷ 40 = 19
800 ÷ 40 = 20
Estimate: 19 ; 20

Explanation:
760/40 = 19
800/40 = 20
Estimate: 19 ; 20

Question 23.
1,198 ÷ 41
Estimate: _____

Answer:
1160 ÷ 40 = 29
1200 ÷ 40 = 30
Estimate: 29 ; 30

Explanation:
1160/40 = 29
1200/40 = 30
Estimate: 29 ; 30

Question 24.
5,581 ÷ 72
Estimate: _____

Answer:
5390 ÷ 70 = 77
5460 ÷ 70 = 78
Estimate: 77 ; 78

Explanation:
5390/70 = 77
5460/70 = 78
Estimate: 77 ; 78

Problem Solving – Page No. 82

Use the picture to solve 25–26.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers img 6

Question 25.
About how many meters tall is each floor of the Williams Tower?
_____ m

Answer:
4.29 meters

Explanation:
Williams Tower has 275 meters and 64 floors.
275/64 = 4.29 meters

Question 26.
About how many meters tall is each floor of the Chrysler Building?
_____ m

Answer:
4.142 m

Explanation:
Chrysler Building has 319 meters and 77 floors
319/77 = 4.142

Question 27.
Eli needs to save $235. To earn money, he plans to mow lawns and charge $21 for each. Write two estimates Eli could use to determine the number of lawns he needs to mow. Decide which estimate you think is the better one for Eli to use. Explain your reasoning.
Type below:
__________

Answer:
220/20 = 11

Explanation:
Calculate $235/$21
210/21 = 10
220/20 = 11
number 220 is closer to 235. So, the better estimate is 220/20 = 11.

Question 28.
Explain how you know whether the quotient of 298 ÷ 31 is closer to 9 or to 10.
Type below:
__________

Answer:
270/30 = 9
310/31 = 10
298 is closer to 270. So, the quotient is closer to 9 than 10.

Question 29.
Test Prep Anik built a tower of cubes. It was 594 millimeters tall. The height of each cube was 17 millimeters. About how many cubes did Anik use?
Options:
a. 10
b. 16
c. 30
d. 300

Answer:
c. 30

Explanation:
594/17
540/18 = 30
600/15 = 40
So, Anik use 30 cubes

Share and Show – Page No. 85

Divide. Check your answer.

Question 1.
28)\(\overline { 620 } \)
_____ R _____

Answer:
22 R 4

Explanation:
Divide integers 62/28 = 2
Multiply 28 x 2 = 56; Subtract 62 – 56 = 6
Write down 60 and divide integers 60/28 = 2.
Multiply 28 x 2 = 56. Subtract 60 – 56 = 4.
The remainder is 4.
So, 22 R 4.
Check:
22 x 28 = 616;
616 + 4 = 620
620 = 620

Question 2.
64)\(\overline { 842 } \)
_____ R _____

Answer:
13 R 10

Explanation:
Divide integers 84/64 = 1
Multiply 64 x 1 = 64; Subtract 84 – 64 = 20
Write down 202 and divide integers 202/64 = 3.
Multiply 64 x 3 = 192. Subtract 202 – 192  = 10.
The remainder is 10.
So, 13 R 10.
Check:
64 x 13 = 832;
832 + 10 = 842
842 = 842

Question 3.
53)\(\overline { 2,340 } \)
_____ R _____

Answer:
44 R 8

Explanation:
Divide integers 234/53 = 4
Multiply 53 x 4 = 212; Subtract 234 – 212 = 22
Write down 220 and divide integers 220/53 = 4.
Multiply 53 x 4 = 212. Subtract 220 – 212 = 8.
The remainder is 8.
So, 44 R 8.
Check:
53 x 44 = 2332;
2332 + 8 = 2340
2340 = 2340

Question 4.
723 ÷ 31
_____ R _____

Answer:
23 R 10

Explanation:
Divide integers 72/31 = 2
Multiply 31 x 2 = 62; Subtract 72 – 62 = 10
Write down 103 and divide integers 103/31 = 3.
Multiply 31 x 3 = 93. Subtract 103 – 93 = 10.
The remainder is 10.
So, 23 R 10.
Check:
31 x 23 = 713;
713 + 10 = 723
723 = 723

Question 5.
1,359 ÷ 45
_____ R _____

Answer:
30 R 9

Explanation:
Divide integers 135/45 = 3
Multiply 45 x 3 = 62; Subtract 135 – 135 = 0
Write down 9; 9<45
The remainder is 9.
So, 30 R 9.
Check:
45 x 30 = 1350;
1350 + 9 = 1359
1359 = 1359

Question 6.
7,925 ÷ 72
_____ R _____

Answer:
110 R 5

Explanation:
Divide integers 79/72 = 1
Multiply 72 x 1 = 72; Subtract 79 – 72 = 7
Write down 72 and divide integers 72/72= 1.
Multiply 72 x 1 = 72; Subtract 72 – 72 = 0
Write down 5; 5<72
The remainder is 5.
So, 110 R 5.
Check:
72 x 110 = 7920;
7920 + 5 = 7925
7925 = 7925

On Your Own

Divide. Check your answer.

Question 7.
16)\(\overline { 346 } \)
_____ R _____

Answer:

Explanation:
Divide integers 34/16 = 2
Multiply 16 x 2 = 32; Subtract 34 – 32 = 2
Write down 26 and divide integers 26/16= 1.
Multiply 16 x 1 = 16; Subtract 26 – 16 = 10
The remainder is 10.
So, 21 R 10.
Check:
16 x 21 = 336;
336 + 10 = 346
346 = 346

Question 8.
34)\(\overline { 241 } \)
_____ R _____

Answer:
7 R 3

Explanation:
Divide integers 241/34 = 7
Multiply 34 x 7 = 238; Subtract 241 – 238= 3
The remainder is 3.
So, 7 R 3
Check:
34  x 7 = 238;
238 + 3 = 241
241 = 241

Question 9.
77)\(\overline { 851 } \)
_____ R _____

Answer:
11 R 4

Explanation:
Divide integers 85/77 = 1
Multiply 77 x 1 = 77; Subtract 85  – 77 = 8
Write down 81 and divide integers 81/77= 1.
Multiply 77 x 1 = 77; Subtract 81 – 77 = 4
The remainder is 4.
So, 11 R 4.
Check:
77 x 11 = 847;
847 + 4 = 851
851 = 851

Question 10.
21)\(\overline { 1,098 } \)
_____ R _____

Answer:
52 R 6

Explanation:
Divide integers 109/21 = 5
Multiply 21 x 5 = 105; Subtract 109 – 105= 4
Write down 48 and divide integers 48/21 = 2.
Multiply 21 x 2 = 42; Subtract 48 – 42 = 6
The remainder is 6.
So, 52 R 6.
Check:
21 x 52 = 1092;
1092 + 6 = 1098
1098 = 1098

Question 11.
32)\(\overline { 6,466 } \)
_____ R _____

Answer:
202 R 2

Explanation:
Divide integers 64/32= 2
Multiply 32 x 2 = 64; Subtract 64 – 64 = 0
Write down 66 and divide integers 66/32 = 2.
Multiply 32 x 2 = 64; Subtract 66 – 64 = 2
The remainder is 2.
So, 202 R 2.
Check:
32 x 202 = 6464;
6464 + 2 = 6466
6466 = 6466

Question 12.
45)\(\overline { 9,500 } \)
_____ R _____

Answer:
211 R 5

Explanation:
Divide integers 95/45 = 2
Multiply 45 x 2 = 90; Subtract 95 – 90 = 5
Write down 50 and divide integers 50/45 = 1.
Multiply 45 x 1 = 45; Subtract 50 – 45 = 5
Write down 50 and divide integers 50/45 = 1.
Multiply 45 x 1 = 45; Subtract 50 – 45 = 5
The remainder is 5.
So, 211 R 5.
Check:
45 x 211 = 9495;
9495 + 5 = 9500
9500 = 9500

Question 13.
483 ÷ 21
_____

Answer:
23

Explanation:
Divide integers 48/21 = 2
Multiply 21 x 2 = 42; Subtract 48 – 42 = 6
Write down 63 and divide integers 63/21 = 3.
Multiply 21 x 3 = 63; Subtract 63 – 63 = 0
The remainder is 0.
So, 23 R 0.
Check:
23 x 21 = 483;
483 = 483

Question 14.
2,292 ÷ 19
_____ R _____

Answer:
120 R 12

Explanation:
Divide integers 22/19 = 1
Multiply 19 x 1 = 19; Subtract 22  – 19 = 3
Write down 39 and divide integers 39/19 = 2.
Multiply 19 x 2 = 38; Subtract 39 – 38 = 1
Write down 12; 12<19
The remainder is 12.
So, 120 R 12.
Check:
19 x 120 = 2280;
2280 + 12 = 2,292
2,292 = 2,292

Question 15.
4,255 ÷ 30
_____ R _____

Answer:
141 R 25

Explanation:
Divide integers 42/30 = 1
Multiply 30 x 1 = 30; Subtract 42 – 30 = 12
Write down 125 and divide integers 125/30 = 4.
Multiply 30 x 4 = 120; Subtract 125 – 120 = 5
Write down 55 and divide integers 55/30 = 1.
Multiply 30 x 1 = 30; Subtract 55 – 30 = 25
The remainder is 25.
So, 141 R 25.
Check:
30 x 141 = 4230;
4230 + 25 = 4,255
4,255 = 4,255

Practice: Copy and Solve Divide. Check your answer.

Question 16.
775 ÷ 35
_____ R _____

Answer:
22 R 5

Explanation:
Divide integers 77/35 = 2
Multiply 35 x 2 = 70; Subtract 77 – 70 = 7
Write down 75 and divide integers 75/35 = 2.
Multiply 35 x 2 = 70; Subtract 75 – 70 = 5
The remainder is 5.
So, 22 R 5.
Check:
22 x 35 = 770;
770 + 5 = 775
775 = 775

Question 17.
820 ÷ 41
_____

Answer:
20

Explanation:
Divide integers 82/41 = 2
Multiply 41 x 2 = 82; Subtract 82 – 82= 0
The remainder is 0.
So, 20 R 0.
Check:
41 x 20 = 820;
820 = 820

Question 18.
805 ÷ 24
_____ R _____

Answer:
33 R 13

Explanation:
Divide integers 80/24 = 3
Multiply 24 x 3 = 72; Subtract 80 – 72 = 8
Write down 85 and divide integers 85/24 = 3.
Multiply 24 x 3 = 72; Subtract 85 – 72 = 13
The remainder is 13.
So, 33 R 13.
Check:
24 x 33 = 792;
792 + 13 = 805
805 = 805

Question 19.
1,166 ÷ 53
_____ R _____

Answer:
22 R 0

Explanation:
Divide integers 116/53 = 2
Multiply 53 x 2 = 106; Subtract 116 – 106= 10
Write down 106 and divide integers 106/53 = 2.
Multiply 53 x 2 = 106; Subtract 106 – 106= 0
The remainder is 0.
So, 22 R 0.
Check:
53 x 22 = 1166;
1166 = 1166

Question 20.
1,989 ÷ 15
_____ R _____

Answer:
132 R 9

Explanation:
Divide integers 19/15 = 1
Multiply 15 x 1 = 15; Subtract 19 – 15 = 4
Write down 48 and divide integers 48/15 = 3.
Multiply 15 x 3 = 45; Subtract 48 – 45 = 3
Write down 39 and divide integers 39/15 = 2.
Multiply 15 x 2 = 30; Subtract 39 – 30= 9
The remainder is 9.
So, 132 R 9.
Check:
15 x 132 = 1980;
1980 + 9 = 1989
1989 = 1989

Question 21.
3,927 ÷ 35
_____ R _____

Answer:
112 R 7

Explanation:
Divide integers 39/35 = 1
Multiply 35 x 1 = 35; Subtract 39 – 35 = 4
Write down 42 and divide integers 42/35 = 1.
Multiply 35 x 1 = 35; Subtract 42 – 35 = 7
Write down 77 and divide integers 77/35 = 2.
Multiply 35 x 2 = 70; Subtract 77 – 70 = 7
The remainder is 7.
So, 112 R 7.
Check:
35 x 112 = 3920;
3920 + 7 = 3927
3927 = 3927

Problem Solving – Page No. 86

Use the list at the right to solve 22–24.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers img 7

Question 22.
A smoothie shop receives a delivery of 980 ounces of grape juice. How many Royal Purple smoothies can be made with the grape juice?
_____ smoothies

Answer:
45 smoothies

Explanation:
A smoothie shop receives a delivery of 980 ounces of grape juice.
980 ounces of grape juice/22 ounces of grape juice = 45

Question 23.
The shop has 1,260 ounces of cranberry juice and 650 ounces of passion fruit juice. If the juices are used to make Crazy Cranberry smoothies, which juice will run out first? How much of the other juice will be left over?
Type below:
_________

Answer:
The shop has 1,260 ounces of cranberry juice and 650 ounces of passion fruit juice. If the juices are used to make Crazy Cranberry smoothies, passion fruit juice will run out first.
Because 650<1,260. So, passion fruit juice will run out first.
1,260 – 650 =610 Crazy Cranberry juice will be left over.

Question 24.
In the refrigerator, there are 680 ounces of orange juice and 410 ounces of mango juice. How many Orange Tango smoothies can be made? Explain your reasoning.
_____ smoothies

Answer:
In the refrigerator, there are 680 ounces of orange juice and 410 ounces of mango juice.
So, 410 Orange Tango smoothies can be made. Because there are 410 ounces of mango juices available.

Question 25.
Test Prep James has 870 action figures. He decides to divide them equally among 23 boxes. How many action figures will James have left over?
Options:
a. 19
b. 23
c. 31
d. 37

Answer:
d. 37

Explanation:
James has 870 action figures. He decides to divide them equally among 23 boxes.
870/23 = 37

Share and Show – Page No. 89

Interpret the remainder to solve.

Question 1.
Erika and Bradley want to hike the Big Cypress Trail. They will hike a total of 75 miles. If Erika and Bradley plan to hike for 12 days, how many miles will they hike each day?
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers img 8
a. Divide to find the quotient and remainder.
_____ R _____

Answer:
6 R 3

Explanation:
75/12 = 6
The remainder is 3
6 R 3

Question 1.
b. Decide how to use the quotient and remainder to answer the question.
Type below:
_________

Answer:
75/12 = 6  1/4
So, Each day they will hike 6\(\frac{1}{4}\) miles.

Question 2.
What if Erika and Bradley want to hike 14 miles each day? How many days will they hike exactly 14 miles?
_____ days

Answer:
196 days

Explanation:
If Erika and Bradley want to hike 14 miles each day, 14 x 14 = 196 days

Question 3.
Dylan’s hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 154 hikers. How many rooms will they need?
_____ rooms

Answer:
11 rooms

Explanation:
Dylan’s hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 154 hikers.
So, 154/15 = 10 and the remainder is 4.
Dylan’s hiking club require 10 rooms for 150 hikers and other room for 4 hikers. So, in total they need 10 + 1 = 11 rooms.

On Your Own

Interpret the remainder to solve.

Question 4.
The students in a class of 24 share 84 cookies equally among them. How many cookies did each student eat?
_____ \(\frac{□}{□}\) cookies

Answer:
3\(\frac{1}{2}\) cookies

Explanation:
The students in a class of 24 share 84 cookies equally among them.
So, 84/24 = 3\(\frac{12}{24}\) = 3\(\frac{1}{2}\)

Question 5.
A campground has cabins that can each hold 28 campers. There are 148 campers visiting the campground. How many cabins are full if 28 campers are in each cabin?
_____ cabins

Answer:
5\(\frac{1}{7}\) cabins

Explanation:
A campground has cabins that can each hold 28 campers. There are 148 campers visiting the campground.
184/28 = 5\(\frac{1}{7}\)

Question 6.
A total of 123 fifth-grade students are going to Fort Verde State Historic Park. Each bus holds 38 students. All of the buses are full except one. How many students will be in the bus that is not full?
_____ students

Answer:
9 students

Explanation:
A total of 123 fifth-grade students are going to Fort Verde State Historic Park. Each bus holds 38 students.
123/38 = 3 and the remainder is 9.
3 x 38 = 114 students. 1 bus is not full.
So, 9 students will be in the bus that is not full

Question 7.
What’s the Error? Sheila is going to divide a 36-inch piece of ribbon into 5 equal pieces. She says each piece will be 7 inches long.
Type below:
_________

Answer:
Sheila is going to divide a 36-inch piece of ribbon into 5 equal pieces.
36/5 = 7\(\frac{1}{5}\). She said each piece will be 7 inches long and forgot about \(\frac{1}{5}\) part.

UNLOCK the Problem – Page No. 90

Question 8.
Maureen has 243 ounces of trail mix. She puts an equal number of ounces in each of 15 bags. How many ounces of trail mix does Maureen have left over?
a. What do you need to find?

Answer:
We need to find how many ounces of trail mix does Maureen have left over?

Question 8.
b. How will you use division to find how many ounces of trail mix are left over?
Type below:
_________

Answer:
The division is 243/15

Question 8.
c. Show the steps you use to solve the problem.
Type below:
_________

Answer:
243/15
Divide integers 24/15 = 1
Multiply 15 x 1 = 15; Subtract 24 – 15 = 9
Write down 93 and divide integers 93/3 = 6.
Multiply 15 x 6 = 90. Subtract 93 – 90 = 3.
The remainder is 3.
So, 16 R 3.

Question 8.
d. Complete the sentences.
Maureen has _______ ounces of trail mix.
She puts an equal number in each of _______ bags.
Each bag has _______ ounces.
Maureen has _______ ounces of trail mix left over.
Type below:
_________

Answer:
Maureen has 243 ounces of trail mix.
She puts an equal number in each of 15 bags.
Each bag has 16 ounces.
Maureen has 3 ounces of trail mix left over.

Question 8.
e. Fill in the bubble completely to show your answer.
Options:
a. 3 ounces
b. 15 ounces
c. 16 ounces
d. 17 ounces

Answer:
c. 16 ounces

Question 9.
Mr. Field wants to give each of his 72 campers a certificate for completing an obstacle course. If there are 16 certificates in one package, how many packages will Mr. Field need?
Options:
a. 4
b. 5
c. 16
d. 17

Answer:
b. 5

Explanation:
Mr. Field wants to give each of his 72 campers a certificate for completing an obstacle course. If there are 16 certificates in one package, 72/16 = 4.5

Question 10.
James has 884 feet of rope. There are 12 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive?
Options:
a. 12
b. 73
c. 73 \(\frac{2}{3}\)
d. 74

Answer:
b. 73

Explanation:
James has 884 feet of rope. There are 12 teams of hikers. If James gives an equal amount of rope to each team, 884/12 = 73

Share and Show – Page No. 92

Adjust the estimated digit in the quotient, if needed. Then divide.

Question 1.
4
41)\(\overline { 1,546 }\)
_____ R _____

Answer:
37 R 29

Explanation:
41 x 4 = 164; Subtract: 154 – 164
the estimate too high.
Change the quotient to 3
41 x 3 = 123; Subtract: 154 – 123 = 31
Write down 316 and divide integers 316/41
41 x 7 = 287; Subtract: 316 – 287 = 29
37 R 29

Question 2.
2
16)\(\overline { 416 }\)
_____

Answer:
26

Explanation:
16 x 2 = 32; Subtract: 41 – 32 = 9
Write down 96 and divide integers 96/16
16 x 6 = 96; Subtract: 96 – 96 = 0
26

Question 3.
9
34)\(\overline { 2,831 }\)
_____ R _____

Answer:
83 R 9

Explanation:
34 x 9 = 306; Subtract: 283 – 306
the estimate too high.
Change the quotient to 8
34 x 8 = 272; Subtract: 283 – 272 = 11
Write down 111 and divide integers 111/34
34 x 3 = 102; Subtract: 111 – 102 = 9
83 R 9

Divide.

Question 4.
19)\(\overline { 915 }\)
_____ R _____

Answer:
48 R 3

Explanation:
900/18 = 50
19 x  5 = 95; Subtract: 91 – 95
the estimate too high.
Change the quotient to 4
19 x  4 = 76; Subtract: 91 – 76 = 15
Write down 155 and divide integers 155/19
19 x 7 = 133; Subtract: 155 – 133 = 22
22 > 19;
So Change the quotient to 8
19 x 8 = 152; Subtract: 155 – 152 = 3
48 R 3

Question 5.
28)\(\overline { 1,825 }\)
_____ R _____

Answer:

Explanation:
1800/30 = 60
28 x 6 = 168; Subtract: 182 – 168 = 14
Write down 145 and divide integers 145/28
28 x 5 = 140; Subtract: 145 – 140 = 5
65 R 5

Question 6.
45)\(\overline { 3,518 }\)
_____ R _____

Answer:

Explanation:
3600/40 = 90
45 x 9 = 405; Subtract: 351 – 405
the estimate too high.
Change the quotient to 7
45 x 7 = 315; Subtract: 351 – 315 = 36
Write down 368 and divide integers 368/45
45 x 8 = 360; Subtract: 368 – 315 = 8
78 R 8

On Your Own – Page No. 93

Adjust the estimated digit in the quotient, if needed. Then divide.

Question 7.
2
26)\(\overline { 541 }\)
_____ R _____

Answer:
20 R 21

Explanation:
500/25 = 2
26 x 2 = 52; Subtract: 54 – 52 = 2
Write down 21 and divide integers 21/26
20 R 21

Question 8.
1
43)\(\overline { 688 }\)
_____

Answer:
16

Explanation:
800/40 = 20
43 x 2 = 86; Subtract: 68 – 86
the estimate is too high.
Change the quotient to 1
43 x 1 = 43; Subtract: 68 – 43 = 25
Write down 258 and divide integers 258/43
43 x 6 = 258; Subtract: 258 – 258 = 0
So, 16

Question 9.
6
67)\(\overline { 4,873 }\)
_____ R _____

Answer:
72 R 49

Explanation:
4800/70 = 60
67 x 6 = 402; Subtract: 487 – 402 = 85
the estimate is too low.
Change the quotient to 7
67 x 7 = 469; Subtract: 487 – 469 = 18
Write down 183 and divide integers 183/67
67 x 2 = 134; Subtract: 183 – 134 = 49
72 R 49

Question 10.
15)\(\overline { 975 }\)
_____

Answer:
65

Explanation:
15 x 6 = 90; Subtract 97 – 90 = 7
Write down 75 and divide integers 75/15
15 x 5 = 75; Subtract: 75 – 75 = 0
So, 65

Question 11.
37)\(\overline { 264 }\)
_____ R _____

Answer:
7 R 5

Explanation:
240/40 = 6
37 x 6 = 222; Subtract: 264 – 222 = 42
the estimate is too low.
Change the quotient to 7
37 x 7 = 259; Subtract: 264 – 259 = 5
7 R 5

Question 12.
22)\(\overline { 6,837 }\)
_____ R _____

Answer:
310 R 17

Explanation:
6300/20 = 325
22 x 3 = 66; Subtract: 68 – 66 = 2
Write down 23 and divide integers 23/22
22 x 1 = 22; Subtract: 23 – 22 = 1
Write down 17; 17 < 22
310 R 17

Practice: Copy and Solve Divide.

Question 13.
452 ÷ 31
_____ \(\frac{□}{□}\)

Answer:
14\(\frac{18}{31}\)

Explanation:
Divide integers 45/31 = 1
Multiply 31 x 1 = 31; Subtract 45 – 31 = 14
Write down 142 and divide integers 142/31 = 4.
Multiply 31 x 4 = 124. Subtract 142 – 124 = 18.
The remainder is 18.
So, 14 R 18.
14\(\frac{18}{31}\)

Question 14.
592 ÷ 74
_____

Answer:
8

Explanation:
Divide integers 592/74 = 8
So, 8.

Question 15.
785 ÷ 14
_____ R _____

Answer:
56\(\frac{1}{14}\)

Explanation:
Divide integers 78/14 = 5
Multiply 14 x 5 = 70; Subtract 78 – 70 = 8
Write down 85 and divide integers 85/14 = 6.
Multiply 14 x 6 = 84. Subtract 85 – 84 = 1.
The remainder is 1.
So, 56 R 1.
56\(\frac{1}{14}\)

Question 16.
601 ÷ 66
_____ R _____

Answer:
9 R 7

Explanation:
Divide integers 601/66 = 9
Multiply 66 x 9 = 594 ; Subtract 601 – 594= 7
The remainder is 7.
So, 9 R 7.
9\(\frac{7}{66}\)

Question 17.
1,067 ÷ 97
_____

Answer:
11

Explanation:
Divide integers 106/97 = 1
Multiply 97 x 1 = 97; Subtract 106 – 97 = 9
Write down 97 and divide integers 97/97 = 1
Multiply 97 x 1 = 97; Subtract 97 – 97 = 0
The remainder is 0.
So, 11 is the answer.

Question 18.
2,693 ÷ 56
_____ R _____

Answer:
48 R 5

Explanation:
Divide integers 269/56 = 4
Multiply 56 x 4 = 224; Subtract 269 – 224 = 45
Write down 453 and divide integers 453/56 = 8
Multiply 56 x 8 = 448. Subtract 453 – 448 = 5.
The remainder is 5.
So, 48 R 5.

Question 19.
1,488 ÷ 78
_____ R _____

Answer:
19 R 6

Explanation:
Divide integers 148/78 = 1
Multiply 78 x 1 = 78; Subtract 148 – 78 = 70
Write down 708 and divide integers 708/78 = 9.
Multiply 78 x 9 = 702. Subtract 708 – 702 = 6.
The remainder is 6.
So, 19 R 6.

Question 20.
2,230 ÷ 42
_____ R _____

Answer:
53 R 4

Explanation:
Divide integers 223/42 = 5
Multiply 42 x 5 = 210; Subtract 223 – 210 = 13
Write down 130 and divide integers 130/42 = 3.
Multiply 42 x 3 = 126. Subtract 130 – 126 = 4.
The remainder is 4.
So, 53 R 4.

Question 21.
4,295 ÷ 66
_____ R _____

Answer:
65 R 5

Explanation:
Divide integers 429/66 = 6
Multiply 66 x 6 = 396; Subtract 429 – 396 = 33
Write down 335 and divide integers 335/66 = 5.
Multiply 66 x 5 = 330. Subtract 335 – 330 = 5.
The remainder is 5
So, 65 R 5

Algebra Write the unknown number for each ■.

Question 22.
■ ÷ 33 = 11
■ = _____

Answer:
363

Explanation:
n ÷ 33 = 11
n = 11 x 33 = 363

Question 23.
1,092 ÷ 52 = ■
■ = _____

Answer:
21

Explanation:
1,092 ÷ 52 = 21

Question 24.
429 ÷ ■ = 33
■ = _____

Answer:
13

Explanation:
429 ÷ n = 33
n = 429 ÷ 33
n = 13

UNLOCK the Problem – Page No. 94

Question 25.
A banquet hall serves 2,394 pounds of turkey during a 3-week period. If the same amount is served each day, how many pounds of turkey does the banquet hall serve each day?
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers img 9
a. What do you need to find?
Type below:
_________

Answer:
How many Lbs at turkey they serve each day?

Question 25.
b. What information are you given?
Type below:
_________

Answer:
Every 3 weeks, serves 2,394 lbs.

Question 25.
c. What other information will you use?
Type below:
_________

Answer:
Same each day, 3 weeks = 21 days

Question 25.
d. Find how many days there are in 3 weeks. There are ______ days in 3 weeks.
Type below:
_________

Answer:
There are ______ days in 3 weeks

Explanation:
1 week = 7 days.
3 x 7 = 21 days

Question 25.
e. Divide to solve the problem.
Type below:
_________

Answer:
2394/3 = t
t = 798
798/7 = 114 pounds

Question 25.
f. Fill in the bubble for the correct answer choice.
Options:
a. 50,274 pounds
b. 798 pounds
c. 342 pounds
d. 114 pounds

Answer:
d. 114 pounds

Question 26.
Marcos mixes 624 ounces of lemonade. He wants to fill the 52 cups he has with equal amounts of lemonade. How much lemonade should he put in each cup?
Options:
a. 8 ounces
b. 12 ounces
c. 18 ounces
d. 20 ounces

Answer:
b. 12 ounces

Explanation:
Marcos mixes 624 ounces of lemonade. He wants to fill the 52 cups he has with equal amounts of lemonade. 624/52 = 12 ounces.
12 ounces should he put in each cup

Question 27.
The Box of Sox company packs 18 pairs of socks in a box. How many boxes will the company need to pack 810 pairs of socks?
Options:
a. 40
b. 45
c. 55
d. 56

Answer:
b. 45

Explanation:
The Box of Sox company packs 18 pairs of socks in a box. So, for 810 pairs of socks, 810/18 = 45

Share and Show – Page No. 97

Question 1.
Paula caught a tarpon with a weight that was 10 times as great as the weight of a permit fish she caught. The total weight of the two fish was 132 pounds. How much did each fish weigh?
First, draw one box to represent the weight of the permit fish and ten boxes to represent the weight of the tarpon.
Next, divide the total weight of the two fish by the total number of boxes you drew. Place the quotient in each box.
Last, find the weight of each fish.
The permit fish weighed _____ pounds.
The tarpon weighed _____ pounds.
Type below:
_________

Answer:
The permit fish weighed 12 pounds.
The tarpon weighed 120 pounds.

Explanation:
Let S be the weight of a permit fish Paula caught.
The weight of the tarpon is 10 times as great as the weight of a permit fish she caught = 10 S
The total weight of the two fish was 132 pounds.
S + 10S = 132
11S = 132
S = 132/11 = 12
So, Paula caught a fish with the weight of 12 pounds.
The tarpon weighted 120 pounds.

Question 2.
What if the weight of the tarpon was 11 times the weight of the permit fish, and the total weight of the two fish was 132 pounds? How much would each fish weigh?
permit fish: _________ pounds
tarpon: _________ pounds

Answer:
permit fish: 11 pounds
tarpon: 11 x 11 = 121 pounds

Explanation:
Let S be the weight of a permit fish Paula caught.
The weight of the tarpon is 11 times as great as the weight of a permit fish she caught = 11S
Total weight is 132
11S + S = 132
12S = 132
S = 132/12 = 11.
permit fish: 11 pounds
tarpon: 11 x 11 = 121 pounds

Question 3.
Jon caught four fish that weighed a total of 252 pounds. The kingfish weighed twice as much as the amberjack and the white marlin weighed twice as much as the kingfish.
The weight of the tarpon was 5 times the weight of the amberjack. How much did each fish weigh?
amberjack: _________ pounds
kingfish: _________ pounds
marlin: _________ pounds
tarpon: _________ pounds

Answer:
amberjack: 21 pounds
kingfish: 42 pounds
marlin: 84 pounds
tarpon: 105 pounds

Explanation:
Let S be the weight of the amberjack.
The kingfish weighed twice as much as the amberjack = 2S
The white marlin weighed twice as much as the kingfish = 2 X 2S = 4S
The weight of the tarpon was 5 times the weight of the amberjack = 5S
Total weight = 252 pounds.
2S + 4S + 5S + S = 252
12S = 252
S = 252/12
S = 21.
The kingfish weighed twice as much as the amberjack = 2S = 2 x 21 = 42 pounds.
The white marlin weighed twice as much as the kingfish = 2 X 2S = 4S = 4 x 21 = 84 pounds.
The weight of the tarpon was 5 times the weight of the amberjack = 5S = 5 x 21 = 105 pounds.

On Your Own – Page No. 98

Use the table to solve 4–7.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers img 10

Question 4.
Kevin is starting a saltwater aquarium with 36 fish. He wants to start with 11 times as many damselfish as clown fish. How many of each fish will Kevin buy? How much will he pay for the fish?
Type below:
_________

Answer:
Kevin is starting a saltwater aquarium with 36 fish. He uses 1 damselfish and 11 clown fish. So, three groups form for 36 fishes.
1 damselfish and 11 clown fish = $7 + (11 x $20) = 7 + 220 = 227
He buys 3 damselfish and 33 clown fish.
3 x 7 = 21$ for damselfish and 33 x 20 = 660 for clown fish.
Each fish = 681/36 = 19

Question 5.
Kevin used a store coupon to buy a 40-gallon tank, an aquarium light, and a filtration system. He paid a total of $240. How much money did Kevin save by using the coupon?
$ _____

Answer:
$25

Explanation:
40-gallon tank = $170
aquarium light = $30
filtration system = $65
170 + 30 + 65 = 265
He paid a total of $240; 265 -240 = $25
Kevin save by using the coupon $25.

Question 6.
Kevin bought 3 bags of gravel to cover the bottom of his fish tank. He has 8 pounds of gravel left over. How much gravel did Kevin use to cover the bottom of the tank?
_____ pounds

Answer:
37 pounds.

Explanation:
15lb bag of gravel = $13.
3 bags of gravel = 45lb.
He has 8 pounds of gravel left over = 45 – 8 = 37
Kevin use 37 pounds of gravel to cover the bottom of the tank

Question 7.
Pose a Problem Look back at Problem 6. Write a similar problem by changing the number of bags of gravel and the amount of gravel left.
Type below:
_________

Answer:
If he bought 5 bags of gravel to cover the bottom of his fish tank. He has 10 pounds of gravel left over.
5 bags of gravel = 15 x 5 = 75lbs
He has 10 pounds of gravel left over = 75 – 10 lbs = 65 lbs
65lbs

Explanation:

Question 8.
Test Prep Captain James offers a deep-sea fishing tour. He charges $2,940 for a 14-hour trip. How much does each hour of the tour cost?
Options:
a. $138
b. $201
c. $210
d. $294

Answer:
c. $210

Explanation:
Captain James offers a deep-sea fishing tour. He charges $2,940 for a 14-hour trip.
Each hour = $2940/14 = 210

Chapter Review/Test – Vocabulary – Page No. 99

Choose the best term from the box.
Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers Chapter Review/Test img 11

Question 1.
You can to estimate quotients because they are easy
use _________ to compute with mentally

Answer:
Compatible Numbers

Question 2.
To decide where to place the first digit in the
quotient, you can estimate or use _________

Answer:
Place Value

Concepts and Skills

Use compatible numbers to estimate the quotient.

Question 3.
522 ÷ 6 = _____

Answer:
90

Explanation:
522 is close to 540. 540 ÷ 6 = 90
The quotient is about 90

Question 4.
1,285 ÷ 32 = _____

Answer:
40

Explanation:
1,280 ÷ 32 = 40
The quotient is about 40

Question 5.
6,285 ÷ 89 = _____

Answer:
70

Explanation:
6,300 ÷ 90 = 70
The quotient is about 70

Divide. Check your answer.

Question 6.
2)\(\overline { 554 } \) = _____

Answer:
277

Explanation:
Divide integers 5/2 = 2
Multiply 2 x 2 = 4; Subtract 5 – 4 = 1
Write down 15 and divide integers 15/2 = 7.
Multiply 2 x 7 = 14. Subtract 15 – 14 = 1
Write down 14 and divide integers 14/2 = 7.
Multiply 2 x 7 = 14. Subtract 14 – 14 = 0
The remainder is 0.
So, 277 is the answer.

Question 7.
8)\(\overline { 680 } \) = _____

Answer:
85

Explanation:
Divide integers 68/8 = 8
Multiply 8 x 8 = 64; Subtract 68 – 64 = 4
Write down 40 and divide integers 40/8 = 5.
Multiply 8 x 5 = 40. Subtract 40 – 40 = 0
The remainder is 0.
So, 85 is the answer.

Question 8.
5)\(\overline { 462 } \) = _____ R _____

Answer:
92 R 2

Explanation:
Divide integers 46/5 = 9
Multiply 5 x 9 = 45; Subtract 46 – 45 = 1
Write down 12 and divide integers 12/5 = 2.
Multiply 5 x 2 = 10. Subtract 12 – 10 = 2
The remainder is 2.
So, 92 R 2
Check:
(92 x 5) + 2 = 460 + 2 = 462

Question 9.
522 ÷ 18 = _____

Answer:
29

Explanation:
Divide integers 52/18 = 2
Multiply 18 x 2 = 36; Subtract 52 – 36 = 16
Write down 162 and divide integers 162/8 = 9.
Multiply 8 x 9 = 162. Subtract 162 – 162 = 0
The remainder is 0
So, 29 is the answer.

Question 10.
529 ÷ 37 = _____ R _____

Answer:
14 R 11

Explanation:
Divide integers 52/37 = 1
Multiply 37 x 1 = 37; Subtract 52 – 37 = 15
Write down 159 and divide integers 159/37 = 4.
Multiply 37 x 4 = 148. Subtract 159 – 148 = 11
The remainder is 11.
So, 14 R 11
Check:
(14 x 37) + 11 = 518 + 11 = 529

Question 11.
987 ÷ 15 = _____ R _____

Answer:
65 R 12

Explanation:
Divide integers 98/15 = 6
Multiply 15 x 6 = 90; Subtract 98 – 90 = 8
Write down 87 and divide integers 87/15 = 5.
Multiply 15 x 5 = 75. Subtract 87 – 75 = 12
The remainder is 12.
So, 65 R 12
Check:
(15 x 65) + 12 = 975 + 12 = 987

Question 12.
1,248 ÷ 24 = _____

Answer:
52

Explanation:
Divide integers 124/24 = 5
Multiply 24 x 5 = 120; Subtract 124 – 120 = 4
Write down 48 and divide integers 48/24 = 2.
Multiply 24 x 2 = 48. Subtract 48 – 48 = 0
The remainder is 0
So, 52 is the answer.

Question 13.
5,210 ÷ 17 = _____ R _____

Answer:
306 R 8

Explanation:
Divide integers 52/17 = 3
Multiply 17 x 3 = 51; Subtract 52 – 51 = 1
Write down 110 and divide integers 110/17 = 6.
Multiply 17 x 6 = 102. Subtract 110 – 102 = 8
The remainder is 8.
So, 306 R 8
Check:
(306 x 17) + 8 = 5202 + 8 = 5210

Question 14.
8,808 ÷ 42 = _____ R _____

Answer:
209 R 30

Explanation:
Divide integers 88/42 = 2
Multiply 42 x 2 = 84; Subtract 88 – 84 = 4
Write down 408 and divide integers 408/42 = 9.
Multiply 42 x 9 = 378. Subtract 408 – 378 = 30
The remainder is 30.
So, 209 R 30
Check:
(209 x 42) + 30 = 8778 + 30 = 8808

Chapter Review/Test – Page No. 100

Fill in the bubble completely to show your answer.

Question 15.
Samira bought 156 ounces of trail mix. She wants to divide the amount equally into 24 portions. How many ounces of trail mix will be in each portion?
Options:
A. 6 ounces
B. 6 \(\frac{1}{2}\) ounces
C. 7 ounces
D. 12 ounces

Answer:
B. 6 \(\frac{1}{2}\) ounces

Explanation:
Samira bought 156 ounces of trail mix. She wants to divide the amount equally into 24 portions.156/24 = 6.5 = 6 \(\frac{1}{2}\) ounces

Question 16.
A school band performed 6 concerts. Every seat for each performance was sold. If a total of 1,248 seats were sold for all 6 concerts, how many seats were sold for each performance?
Options:
A. 28
B. 200
C. 206
D. 208

Answer:
D. 208

Explanation:
A school band performed 6 concerts. Every seat for each performance was sold. If a total of 1,248 seats were sold for all 6 concerts, then 1,248/6 = 208.

Question 17.
Dylan’s dog weighs 12 times as much as his pet rabbit. The dog and rabbit weigh 104 pounds altogether. How much does Dylan’s dog weigh?
Options:
A. 104 pounds
B. 96 pounds
C. 88 pounds
D. 8 pounds

Answer:
D. 8 pounds

Explanation:
Dylan’s dog weighs 12 times as much as his pet rabbit. The dog and rabbit weigh 104 pounds altogether.
rabbit weight = S
dog weighs = 12S
S + 12S = 104; 13S = 104; S = 104/13 =8.

Question 18.
Jamie is sewing 14 identical costumes for the school play. She needs 210 buttons to complete all of the costumes. How many buttons will she sew onto each costume?
Options:
A. 15
B. 14
C. 11
D. 9

Answer:
A. 15

Explanation:
Jamie is sewing 14 identical costumes for the school play. She needs 210 buttons to complete all of the costumes. 210/14 = 15

Chapter Review/Test – Page No. 101

Fill in the bubble completely to show your answer.

Question 19.
A book publishing company is shipping an order of 300 books. The books are packaged in boxes that each can hold 24 books. How many boxes are needed to ship the order of books?
Options:
A. 10
B. 11
C. 12
D. 13

Answer:
D. 13

Explanation:
A book publishing company is shipping an order of 300 books. The books are packaged in boxes that each can hold 24 books.
300/24 = 12.5. That is 12 and above boxes. So, the answer is 13

Question 20.
Richard is planning a trip to Italy. He thinks he will need $2,750 for the trip. If the trip is 40 weeks away, which is the best estimate of how much money Richard needs to save each week?
Options:
A. $60
B. $70
C. $600
D. $700

Answer:
B. $70

Explanation:
Richard is planning a trip to Italy. He thinks he will need $2,750 for the trip. If the trip is 40 weeks away, $2,750/40 = $68.75. That is equal to $70

Question 21.
A school club raises $506 to spend on a field trip. There are 23 people going on the trip. How much money did the club raise for each person going?
Options:
A. $27
B. $22
C. $18
D. $12

Answer:
B. $22

Explanation:
A school club raises $506 to spend on a field trip. There are 23 people going on the trip. $506/23 = $22.

Question 22.
A local orange grower processes 2,330 oranges from his grove this year. The oranges are packaged in crates that each hold 96 oranges. All but one crate is full. How many oranges are in this last crate?
Options:
A. 24
B. 25
C. 26
D. 27

Answer:
C. 26

Explanation:
2330 oranges / 96 orange/crate = 24.2708333 crates the decimal portion is the fraction of 96 in the last crate= 96 x .2708333 = 26 oranges in the last crate.

Chapter Review/Test – Page No. 102

Constructed Response

Question 23.
On Monday, 1,900 bottles of perfume are delivered to a warehouse. The bottles are packed in boxes. Each box can hold 32 bottles. How many boxes were delivered? Explain how you found your answer.
_____ boxes

Answer:
I need to divide 1,900 by 32, which is 59 r12. That means the bottles will completely fill 59 boxes. But there will be 12 bottles left over. These would be packed in another box, which makes a total of 60 boxes.

Performance Task

Question 24.
Quincy needs 322 yards of ribbon to decorate quilts for a craft fair.The ribbon comes in rolls of 15 yards.
A. How many rolls of ribbon should Quincy buy? Explain your answer.
_____ rolls

Answer:
I need to divide 322 by 15. The answer is 21  R 7. Since he can’t buy a part of a roll, I need to add 1 to the quotient. So, the final answer is 22.

Question 24.
B. Alice needs twice as many yards of ribbon as Quincy. How many rolls of ribbon does Alice need? Explain your answer.
_____ rolls

Answer:
Twice the length of 322 yards is 644 yards. If I divide 644 by 15, the answer is 42 R 14. Alice needs to buy 43 rolls of ribbon. The remainder doubled is still less than the amount In 1 roll.

Question 24.
C Elena needs yellow, red, and blue ribbon. She needs 285 yards of the three colors combined. Suggest numbers of rolls of each color that would give her enough ribbon. (HINT: Break apart the 285 yards into any combination of 3 groups that total this amount.)
Type below:
_________

Answer:
Sample 1: If Elena wants the same amounts, she will need 95 yards of each color. 95 divided by 15 is 6 R 5, so she will need 7 rolls of each color.
Sample 2: If she wants 109 yards of yellow, 100 yards of red, and 85 yards of blue, she will need 7 rolls of yellow, 7 rolls of red, and 6 rolls of blue.

Conclusion

We wish Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers has helped you in your preparation. We have provided step by step solutions to all the questions in Chapter 2 by which you can score well.  Bookmark our site to know more about Class-Specific Go Math Answer Keys.