Go Math Answer Key – Big Ideas Math Answers

Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem

April 7, 2022March 28, 2022 by Go Math Answer Key

$go-math-grade-8-chapter-12-the-pythagorean-theorem-answer-key$

One has to learn the concepts if he/she wants to become a master in maths. The fundamentals in Go Math Grade 8 Answer Key Chapter 12 The Pythagorean theorem will help you to learn the subject. You need to practice from the beginning itself. We will help you to achieve your dreams by providing simple methods to solve the problems in an easy manner. Download Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem free pdf to help you to gain a grip over the subject.

Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem

Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem will help you to complete your homework in time without any mistakes. The main aim of the ccssmathanswers.com site is to provide quick and simple methods to all the students of 8th grade. The solutions to all the questions in Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem are prepared by the math experts. Tap the links and practice the problems provided in the HMH Go Math 8th Grade Solution Key Chapter 12 The Pythagorean Theorem.

Chapter 12- Lesson 1:

Guided Practice – The Pythagorean Theorem – Page No. 378
12.1 Independent Practice – The Pythagorean Theorem – Page No. 379
FOCUS ON HIGHER ORDER THINKING – The Pythagorean Theorem – Page No. 380

Chapter 12- Lesson 2:

Guided Practice – Converse of the Pythagorean Theorem – Page No. 384
12.2 Independent Practice – Converse of the Pythagorean Theorem – Page No. 385
Converse of the Pythagorean Theorem – Page No. 386

Chapter 12- Lesson 3:

Guided Practice – Distance Between Two Points – Page No. 390
12.3 Independent Practice – Distance Between Two Points – Page No. 391
Distance Between Two Points – Page No. 392
Ready to Go On? – Model Quiz – Page No. 393
Selected Response – Mixed Review – Page No. 394

Guided Practice – The Pythagorean Theorem – Page No. 378

Question 1.
Find the length of the missing side of the triangle
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 1$
a² + b² = c² → 24² + ? = c² → ? = c²
The length of the hypotenuse is _____ feet.
_____ feet

Answer: The length of the hypotenuse is 26 feet.

Explanation: According to Pythagorean Theorem, we shall consider values of a = 24ft, b = 10ft.
Therefore c = √(a² +b²)
c = √(24²+ 10²)
= √(576 + 100)
= √676 = 26ft

Question 2.
Mr. Woo wants to ship a fishing rod that is 42 inches long to his son. He has a box with the dimensions shown.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 2$
a. Find the square of the length of the diagonal across the bottom of the box.
________ inches

Answer: 1700 inches.

Explanation: Here we consider the length of the diagonal across the bottom of the box as d.
Therefore, according to Pythagorean Theorem
W²+ l²= d²40²+ 10² = d²1600 + 100 = d²
1700 = d²

Question 2.
b. Find the length from a bottom corner to the opposite top corner to the nearest tenth. Will the fishing rod fit?
________ inches

Answer: 42.42 inches.

Explanation: We denote by r, the length from the bottom corner to the opposite top corner. We use our Pythagorean formula to find r.
h²+ s²= r²
10²+ 1700 = r²100 + 1700 = r²1800 = r², r = √1800 => 42.42 inches

ESSENTIAL QUESTION CHECK-IN

Question 3.
State the Pythagorean Theorem and tell how you can use it to solve problems.

Answer:
Pythagorean Theorem: In a right triangle, the sum of squares of the legs a and b is equal to the square of the hypotenuse c.
a²+ b²= c²We can use it to find the length of a side of a right triangle when the lengths of the other two sides are known.

12.1 Independent Practice – The Pythagorean Theorem – Page No. 379

Find the length of the missing side of each triangle. Round your answers to the nearest tenth.

Question 4.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 3$
________ cm

Answer: 8.9 cm.

Explanation: According to Pythagorean theorem we consider values of a = 4cm, b = 8cm.
c²= a² + b²
= 4² + 8²= 16 + 64
c²= 80, c= √80 => 8.944
After rounding to nearest tenth value c= 8.9cm

Question 5.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 4$
________ in.

Answer: 11.5 in.

Explanation: According to Pythagorean theorem we consider values of b = 8in, c= 14in
c²= a² + b²14²= a² + 8²
196 = a² + 64
a² = 196 – 64
a = √132 => 11.4891
a = 11.5 in

Question 6.
The diagonal of a rectangular big-screen TV screen measures 152 cm. The length measures 132 cm. What is the height of the screen?
________ cm

Answer: 75.4 cm

Explanation: Let’s consider the diagonal of the TV screen as C = 152cm, length as A = 132 cm, and height of the screen as B.

As C²= A² + B² 152²= 132²+ B²
23,104 = 17,424 + B²
B² = 23,104 – 17,424
B = √5680 => 75.365
So the height of the screen B = 75.4cm

Question 7.
Dylan has a square piece of metal that measures 10 inches on each side. He cuts the metal along the diagonal, forming two right triangles. What is the length of the hypotenuse of each right triangle to the nearest tenth of an inch?
________ in.

Answer: 14.1in.

Explanation:

Using the Pythagorean Theorem, we have:
a²+ b² = c²
10²+ 10²= c²
100 + 100 = c²
200 = c²We are told to round the length of the hypotenuse of each right triangle to the nearest tenth of an inch, therefore: c = 14.1in

Question 8.
Represent Real-World Problems A painter has a 24-foot ladder that he is using to paint a house. For safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. To the nearest tenth of a foot, how high can the ladder safely reach?
________ ft

Answer: 22.6 ft.

Explanation: Consider the below diagram. Length of the ladder C = 24ft, placed at a distance from the base B = 8ft, let the safest height be A.

By using Pythagorean Theorem:
C² = A²+ B²
24²= A² + 8²
576 = A²+ 64
A²= 576 – 64 => 512
A = √512 => 22.627
After rounding to nearest tenth, value of A = 22.6ft

Question 9.
What is the longest flagpole (in whole feet) that could be shipped in a box that measures 2 ft by 2 ft by 12 ft?
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 5$
________ ft

Answer: The longest flagpole (in whole feet) that could be shipped in this box is 12 feet.

Explanation: From the above diagram we have to find the value of r, which gives us the length longest flagpole that could be shipped in the box. Where width w = 2ft, height h = 2ft and length l = 12ft.

First find s, the length of the diagonal across the bottom of the box.
w²+ l²= s²
2²+ 12²= s²
4 + 144 = s²148 = s²We use our expression for s to find r, since triangle with sides s, r, and h also form a right-angle triangle.
h²+ s²= r²
2²+ 148 = r²
4 + 148 = r²152 = r²r = 12.33ft.

Question 10.
Sports American football fields measure 100 yards long between the end zones, and are 53 $\frac{1}{3}$ yards wide. Is the length of the diagonal across this field more or less than 120 yards? Explain.
____________

Answer: The diagonal across this field is less than 120 yards.

Explanation: From the above details we will get a diagram as shown below.
Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem

We are given l = 100 and w = 53 = . If we denote with d the diagonal of the field, using the Pythagorean Theorem, we have:
l²+ w²= d²
100²+ (160/3)²= d²10000 + (25600/9) = d²
9*10000 + 9*(25600/9) = 9* d²
90000 + 25600 = 9 d²
(115600/9) = d²
(340/9) = d²
d = 113.3
Hence the diagonal across this field is less than 120 yards.

Question 11.
Justify Reasoning A tree struck by lightning broke at a point 12 ft above the ground as shown. What was the height of the tree to the nearest tenth of a foot? Explain your reasoning.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 6$
________ ft

Answer: The total height of the tree was 52.8ft

Explanation:

By using the Pythagorean Theorem
a²+ b²= c²12²+ 39²= c²
144 + 1521 = c²
1665 = c²We are told to round the length of the hypotenuse to the nearest tenth of a foot, therefore: c = 40.8ft.
Therefore, the total height of the tree was:
height = a+c
height = 12 +40.8
height = 52.8 feet

FOCUS ON HIGHER ORDER THINKING – The Pythagorean Theorem – Page No. 380

Question 12.
Multistep Main Street and Washington Avenue meet at a right angle. A large park begins at this corner. Joe’s school lies at the opposite corner of the park. Usually Joe walks 1.2 miles along Main Street and then 0.9 miles up Washington Avenue to get to school. Today he walked in a straight path across the park and returned home along the same path. What is the difference in distance between the two round trips? Explain.
________ mi

Answer: Joe walks 1.2 miles less if he follows the straight path across the park.

Explanation: Using the Pythagorean Theorem, we find the distance from his home to school following the straight path across the park:
a²+ b²= c²1.2²+ 0.9²= c²
1.44 + 0.81 = c²
2.25 = c²
1.5 = c
Therefore, the distance of Joe’s round trip following the path across the park is 3 miles (d_home-school+ d_school-home = 1.5 + 1.5). Usually, when he walks along Main Street and Washington Avenue, the distance of his round trip is 4.2 miles (d_home-school+ d_school-home = (1.2 + 0.9) + (0.9+1.2)). As we can see, Joe walks 1.2 miles less if he follows the straight path across the park.

Question 13.
Analyze Relationships An isosceles right triangle is a right triangle with congruent legs. If the length of each leg is represented by x, what algebraic expression can be used to represent the length of the hypotenuse? Explain your reasoning.

Answer: c = x√ 2

Explanation: From the Pythagorean Theorem, we know that if a and b are legs and c is the hypotenuse, then a²+ b²= c². In our case, the length of each leg is represented by x, therefore we have:
a²+ b²= c²x²+ x² = c²2x²= c²c = x√ 2

Question 14.
Persevere in Problem Solving A square hamburger is centered on a circular bun. Both the bun and the burger have an area of 16 square inches.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 1: The Pythagorean Theorem img 7$
a. How far, to the nearest hundredth of an inch, does each corner of the burger stick out from the bun? Explain.
________ in

Answer: Each corner of the burger sticks out 0.57 inches from the bun.

Explanation: Frist, we need to find the radius r of the circular bun. We know that its area A is 16 square inches, therefore:

A = πr²16 = 3.14*r²r²= (16/3.14)
r = 2.26

Then, we need to find the side s of the square hamburger. We know that its area A is 16 square inches, therefore:
A = s²
16 = s²
s = 4
Using the Pythagorean Theorem, we have to find diagonal d of the square hamburger:
s²+ s² = d²
4² + 4²= d²
16 + 16 = d²
32 = d²d = 5.66
To find how far does each corner of the burger stick out from the bun, we denote this length by a and we get:
a = (d/2) – r => (5.66/2) – 2.26
a = 0.57.
Therefore, Each corner of the burger sticks out 0.57 inches from the bun.

Question 14.
b. How far does each bun stick out from the center of each side of the burger?
________ in

Answer: Each bun sticks out 0.26 inches from the center of each side of the burger.

Explanation:

We found that r = 2.26 and s = 4. To find how far does each bun stick out from the center of each side of the burger, we denote this length by b and we get:
b = r – (s/2) = 2.26 – (4/2)
b = 0.26 inches.

Question 14.
c. Are the distances in part a and part b equal? If not, which sticks out more, the burger or the bun? Explain.

Answer: The distances a and b are not equal. From the calculations, we found that the burger sticks out more than the bun.

Guided Practice – Converse of the Pythagorean Theorem – Page No. 384

Question 1.
Lashandra used grid paper to construct the triangle shown.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 8$
a. What are the lengths of the sides of Lashandra’s triangle?
_______ units, _______ units, _______ units,

Answer: The length of Lashandra’s triangle is 8 units, 6 units, 10 units.

Question 1.
b. Use the converse of the Pythagorean Theorem to determine whether the triangle is a right triangle.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 9$
The triangle that Lashandra constructed is / is not a right triangle.
_______ a right triangle

Answer: Lashandra’s triangle is right angled triangle as it satisfied Pythagorean theorem

Explanation:
Verifying with Pythagorean formula a²+ b²= c²8^{2 +}6²= 10²64 + 36 =100
100 = 100.

Question 2.
A triangle has side lengths 9 cm, 12 cm, and 16 cm. Tell whether the triangle is a right triangle.
Let a = _____, b = _____, and c = ______.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 10$
By the converse of the Pythagorean Theorem, the triangle is / is not a right triangle.
_______ a right triangle

Answer: The given triangle is not a right-angled triangle

Explanation: Verifying with Pythagorean formula a²+ b²= c²
9²+ 12²= 16²81 + 144 = 256
225 ≠ 256.
Hence given dimensions are not from the right angled triangle.

Question 3.
The marketing team at a new electronics company is designing a logo that contains a circle and a triangle. On one design, the triangle’s side lengths are 2.5 in., 6 in., and 6.5 in. Is the triangle a right triangle? Explain.
_______

Answer: It is a right-angled triangle.

Explanation: Let a = 2.5, b = 6 and c= 6.5
Verifying with Pythagorean formula a²+ b²= c²2.5²+ 6²= 6.5²6.25 + 36 = 42.25
42.25 = 42.25.
Hence it is a right-angled triangle.

ESSENTIAL QUESTION CHECK-IN

Question 4.
How can you use the converse of the Pythagorean Theorem to tell if a triangle is a right triangle?

Answer: Knowing the side lengths, we substitute them in the formula a²+ b²= c², where c contains the biggest value. If the equation holds true, then the given triangle is a right triangle. Otherwise, it is not a right triangle.

12.2 Independent Practice – Converse of the Pythagorean Theorem – Page No. 385

Tell whether each triangle with the given side lengths is a right triangle.

Question 5.
11 cm, 60 cm, 61 cm
______________

Answer: Since 11²+ 60²= 61², the triangle is a right-angled triangle.

Explanation: Let a = 11, b = 60 and c= 61
Using the converse of the Pythagorean Theorem a²+ b²= c²11²+ 60²= 61²121 + 3600 = 3721
3721 = 3721.
Since 11²+ 60²= 61², the triangle is a right-angled triangle.

Question 6.
5 ft, 12 ft, 15 ft
______________

Answer: Since 5²+ 12²≠ 15², the triangle is not a right-angled triangle.

Explanation: Let a = 5, b = 12 and c= 15
Using the converse of the Pythagorean Theorem a²+ b²= c² 5²+ 12²= 15²25 + 144 = 225
169 ≠ 225.
Since 5²+ 12²≠ 15², the triangle is not a right-angled triangle.

Question 7.
9 in., 15 in., 17 in.
______________

Answer: Since 9²+ 15²≠ 17², the triangle is not a right-angled triangle.

Explanation: Let a = 9, b = 15 and c= 17
Using the converse of the Pythagorean Theorem a²+ b²= c²9²+ 15²= 17²81 + 225 = 225
306 ≠ 225.
Since 9²+ 15²≠ 17², the triangle is not a right-angled triangle.

Question 8.
15 m, 36 m, 39 m
______________

Answer: Since 15²+ 36²= 39², the triangle is a right-angled triangle.

Explanation: Let a = 15, b = 36 and c= 39
Using the converse of the Pythagorean Theorem a²+ b²= c²15²+ 36²= 39²225 + 1296 = 1521
1521 = 1521.
Since 15²+ 36²= 39², the triangle is a right-angled triangle.

Question 9.
20 mm, 30 mm, 40 mm
______________

Answer: Since 20²+ 30²≠ 40², the triangle is not a right-angled triangle.

Explanation: Let a = 20, b = 30 and c= 40
Using the converse of the Pythagorean Theorem a²+ b²= c²20²+ 30²= 40²400 + 900 = 1600
1300 ≠ 1600.
Since 20²+ 30²≠ 40², the triangle is not a right-angled triangle.

Question 10.
20 cm, 48 cm, 52 cm
______________

Answer: Since 20²+ 48²= 52², the triangle is a right-angled triangle.

Explanation: Let a = 20, b = 48 and c= 52
Using the converse of the Pythagorean Theorem a²+ b²= c²20²+ 48²= 52²400 + 2304 = 2704
2704 = 2704.
Since 20²+ 48²= 52², the triangle is a right-angled triangle.

Question 11.
18.5 ft, 6 ft, 17.5 ft
______________

Answer: Since 6²+ 17.5²= 18.5², the triangle is a right-angled triangle.

Explanation: Let a = 6, b = 17.5 and c= 18.5
Using the converse of the Pythagorean Theorem a²+ b²= c²6²+ 17.5²= 18.5²36 + 306.25 = 342.25
342.5 = 342.25.
Since 6²+ 17.5²= 18.5², the triangle is a right-angled triangle.

Question 12.
2 mi, 1.5 mi, 2.5 mi
______________

Answer: Since 2²+ 1.5²= 2.5², the triangle is a right-angled triangle.

Explanation: Let a = 2, b = 1.5 and c= 2.5
Using the converse of the Pythagorean Theorem a²+ b²= c² 2²+ 1.5²= 2.5²4 + 2.25 = 6.25
6.25 = 6.25.
Since 2²+ 1.5²= 2.5², the triangle is a right-angled triangle.

Question 13.
35 in., 45 in., 55 in.
______________

Answer: Since 35²+ 45²≠ 55², the triangle is not a right-angled triangle.

Explanation: Let a = 35, b = 45 and c= 55
Using the converse of the Pythagorean Theorem a²+ b²= c²35²+ 45²= 55²1225 + 2025 = 3025
3250 ≠ 3025.
Since 35²+ 45²≠ 55², the triangle is not a right-angled triangle.

Question 14.
25 cm, 14 cm, 23 cm
______________

Answer: Since 14²+ 23²≠ 25², the triangle is not a right-angled triangle.

Explanation: Let a = 14, b = 23 and c= 25 (longest side)
Using the converse of the Pythagorean Theorem a²+ b²= c²14²+ 23²= 25²196 + 529 = 625
725 ≠ 625.
Since 14²+ 23²≠25², the triangle is not a right-angled triangle.

Question 15.
The emblem on a college banner consists of the face of a tiger inside a triangle. The lengths of the sides of the triangle are 13 cm, 14 cm, and 15 cm. Is the triangle a right triangle? Explain.
________

Answer: Since 13²+ 14²≠ 15², the triangle is not a right-angled triangle.

Explanation: Let a = 13, b = 14 and c= 15
Using the converse of the Pythagorean Theorem a²+ b²= c²13²+ 14²= 15²169 + 196 = 225
365 ≠ 225.
Since 13²+ 14²≠ 15², the triangle is not a right-angled triangle.

Question 16.
Kerry has a large triangular piece of fabric that she wants to attach to the ceiling in her bedroom. The sides of the piece of fabric measure 4.8 ft, 6.4 ft, and 8 ft. Is the fabric in the shape of a right triangle? Explain.
________

Answer: The triangular piece of fabric that Kerry has is in the shape of a right angle since it follows the Pythagorean theorem.

Explanation: Let a = 4.8, b = 6.4 and c= 8
Using the converse of the Pythagorean Theorem a²+ b²= c²4.8²+ 6.4²= 8²23.04 + 40.96 = 64
64 = 64.
Since 4.8²+ 6.4²= 8², the triangle is a right-angled triangle.

Question 17.
A mosaic consists of triangular tiles. The smallest tiles have side lengths 6 cm, 10 cm, and 12 cm. Are these tiles in the shape of right triangles? Explain.
________

Answer: Since 6²+ 10²≠ 12², by the converse of the Pythagorean Theorem, we say that the tiles are not in the shape of right-angled triangle.

Explanation: Let a = 6, b = 10 and c= 12
Using the converse of the Pythagorean Theorem a²+ b²= c² 6²+ 10²= 12²36 + 100 = 144
136 ≠ 144.
Since 6²+ 10²≠ 12², by the converse of the Pythagorean Theorem, we say that the tiles are not in the shape of right-angled triangle.

Question 18.
History In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots as shown. Explain why the rope forms a right angle.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 11$

Answer: The rope has formed a right-angled triangle because the length of its sides follows Pythagorean Theorem.

Explanation: The knots are evenly placed at equal distances
The lengths in terms of knots are a=4 knots, b = 3knots, c = 5 knots
Therefore a²+ b²= c²4²+ 3²= 5²16+9 = 25
25 = 25.
Hence rope has formed a right-angled triangle because the length of its sides follows Pythagorean Theorem.

Converse of the Pythagorean Theorem – Page No. 386

Question 19.
Justify Reasoning Yoshi has two identical triangular boards as shown. Can he use these two boards to form a rectangle? Explain.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 2: Converse of the Pythagorean Theorem img 12$

Answer: Since it was proved that both can form a right-angled triangle, we can form a rectangle by joining them.

Explanation: Given both triangles are identical, if both are right-angled triangles then we can surely join to form a rectangle.
Let’s consider a = 0.75, b= 1 and c=1.25.
By using converse Pythagorean Theorem a²+ b²= c²0.75²+ 1²= 1.25²0.5625 + 1 = 1.5625
1.5625 = 1.5625.
Since it was proved that both can form right angled triangle, we can form a rectangle by joining them.

Question 20.
Critique Reasoning Shoshanna says that a triangle with side lengths 17 m, 8 m, and 15 m is not a right triangle because 17² + 8² = 353, 15² = 225, and 353 ≠ 225. Is she correct? Explain
_______

Answer: She is not right, A triangle with sides 15, 8, and 17 is a right-angled triangle.

Explanation: Lets consider a =15, b= 8 and c = 17 (which is long side)
We will verify by using converse Pythagorean Theorem a²+ b²= c²15²+ 8²= 17²225 + 64 = 289
289 = 289.
Since the given dimensions satisfied Pythagorean Theorem, we can say it is a right-angled triangle. In the given above statement what Shoshanna did was c²+ b²= a², which is not the correct definition of the Pythagorean Theorem.

FOCUS ON HIGHER ORDER THINKING

Question 21.
Make a Conjecture Diondre says that he can take any right triangle and make a new right triangle just by doubling the side lengths. Is Diondre’s conjecture true? Test his conjecture using three different right triangles.
_______

Answer: Yes, Diondre’s conjecture is true. By doubling the sides of a right triangle would create a new right triangle.

Explanation: Given a right triangle, the Pythagorean Theorem holds. Therefore, a²+ b²= c²If we double the side lengths of that triangle, we get:
(2a)²+ (2b)²= (2c)²
4a²+ 4b²= 4c²
4(a²+ b²) = 4c²
a²+ b²= c² As we can see doubling the sides of a right triangle would create a new right triangle.We can test that by using three different right triangles.

The triangle with sides a = 6, b = 8 and c = 10 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 12, b = 16 and c = 20.
12² + 16²= 20²
144 + 256 = 400
400 = 400
Hence proved!
Since 12² + 16²= 20², the new triangle is a right triangle by the converse of the Pythagorean Theorem.

The triangle with sides a = 3, b = 4 and c = 5 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 6, b = 8 and c = 10.
6² + 8²= 10²
36 + 64 = 100
100 = 100
Hence proved!
Since 6² + 8²= 10², the new triangle is a right triangle by the converse of the Pythagorean Theorem.

The triangle with sides a = 12, b = 16 and c = 20 is a right triangle. We double its sides and check if the new triangle is a right triangle. After doubling value of a = 24, b = 32 and c = 40.
24² + 32²= 40²
576 + 1024 = 1600
1600 = 1600
Hence proved!
Since 24² + 32²= 40², the new triangle is a right triangle by the converse of the Pythagorean Theorem.

Question 22.
Draw Conclusions A diagonal of a parallelogram measures 37 inches. The sides measure 35 inches and 1 foot. Is the parallelogram a rectangle? Explain your reasoning.
_______

Answer: Since 12²+ 35²= 37², the triangle is right triangle. Therefore, the given parallelogram is a rectangle.

Explanation: A rectangle is a parallelogram where the interior angles are right angles. To prove if the given parallelogram is a rectangle, we need to prove that the triangle formed by the diagonal of the parallelogram and two sides of it, is a right triangle. Converting all the values into inches, we have a = 12, b = 35 and c = 37. Using the converse of the Pythagorean Theorem, we have:
a²+ b²= c²
12²+ 35²= 37²144 + 1225 = 1369
1369 = 1369.
Since 12²+ 35²= 37², the triangle is right triangle. Therefore, the given parallelogram is a rectangle.

Question 23.
Represent Real-World Problems A soccer coach is marking the lines for a soccer field on a large recreation field. The dimensions of the field are to be 90 yards by 48 yards. Describe a procedure she could use to confirm that the sides of the field meet at right angles.

Answer: To confirm that the sides of the field meet at right angles, she could measure the diagonal of the field and use the converse of the Pythagorean Theorem. If a²+ b²= c²(where a = 90, b = 48 and c is the length of the diagonal), then the triangle is right triangle. This method can be used for every corner to decide if they form right angles or not.

Guided Practice – Distance Between Two Points – Page No. 390

Question 1.
Approximate the length of the hypotenuse of the right triangle to the nearest tenth using a calculator.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 13$
_______ units

Answer: The length of the hypotenuse of the right triangle to the nearest tenth is 5.8 units.

Explanation: From the above figure let’s take
Length of the vertical leg = 3 units
Length of the horizontal leg = 5 units
let length of the hypotenuse = c
By using Pythagorean Theorem a²+ b²= c²c² = 3² + 5²c²= 9 +25
c = √34 => 5.830.
Therefore Length of the hypotenuse of the right triangle to the nearest tenth is 5.8 units.

Question 2.
Find the distance between the points (3, 7) and (15, 12) on the coordinate plane.
_______ units

Answer: Distance between points on the coordinate plane is 13

Explanation: So (x₁, y₁) = (3,7) and (x₂, y₂) = (15, 12)
distance formula d = √( x₂– x₁)²+ √( y₂– y₁)²
d = √(15 -3)²+ √(12 – 7)²
d = √12²+ 5²
d = √144 + 25
d = √169 => 13
Therefore distance between points on the coordinate plane is 13.

Question 3.
A plane leaves an airport and flies due north. Two minutes later, a second plane leaves the same airport flying due east. The flight plan shows the coordinates of the two planes 10 minutes later. The distances in the graph are measured in miles. Use the Pythagorean Theorem to find the distance shown between the two planes.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 14$
_______ miles

Answer: The distance between the two planes is 103.6 miles.

Explanation:
Length of the vertical d_v= √(80 -1)²+ √(1-1)²
= √79²=> 79.
Length of the horizontal d_{h =}√(68 -1)²+ √(1-1)²
= √67²=> 67.
Distance between the two planes D = √(79² + 67²)
= √(6241+4489) => √10730
= 103.5857 => 103.6 miles.

ESSENTIAL QUESTION CHECK-IN

Question 4.
Describe two ways to find the distance between two points on a coordinate plane.

Answer:

Explanation: We can draw a right triangle whose hypotenuse is the segment connecting the two points and then use the Pythagorean Theorem to find the length of that segment. We can also the Distance formula to find the length of that segment.

For example, plot three points; (1,2), (20,2) and (20,12)

Using the Pythagorean Theorem:

The length of the horizontal leg is the absolute value of the difference between the x-coordinates of the points (1,2) and (20,2).
|1 – 20| = 19
The length of the horizontal leg is 19.

The length of the vertical leg is the absolute value of the difference between the y-coordinates of the points (20,2) and (20,12).
|2 – 12| = 10
The length of the vertical leg is 10.

Let a = 19, b = 10 and let c represent the hypotenuse. Find c.
a²+ b²= c²
19²+ 10²= c²
361 + 100 = c²
461 = c²
distance is 21.5 = c

Using the Distance formula:
d= √( x₂– x₁)²+ √( y₂– y₁)²The length of the horizontal leg is between (1,2) and (20,2).
d= √( x₂– x₁)²+ √( y₂– y₁)² = √(20 -1)²+ √(2-2)²
= √(19)²+ √(0)²
= √361 => 19
The length of the vertical leg is between (20,2) and (20,12).
d= √( x₂– x₁)²+ √( y₂– y₁)² = √(20 -20)²+ √(12-2)²
= √(0)²+√(10)²
= √100 => 10
The length of the diagonal leg is between (1,2) and (20,12).
d= √( x₂– x₁)²+ √( y₂– y₁)² = √(20 -1)²+ √(12-2)²
= √(19)²+ √(10)²
= √(361+100) => √461 = 21.5

12.3 Independent Practice – Distance Between Two Points – Page No. 391

Question 5.
A metal worker traced a triangular piece of sheet metal on a coordinate plane, as shown. The units represent inches. What is the length of the longest side of the metal triangle? Approximate the length to the nearest tenth of an inch using a calculator. Check that your answer is reasonable.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 15$
_______ in.

Answer: The length of the longest side of the metal triangle to the nearest tenth is 7.8 units.

Explanation: From the above figure let’s take
Length of the vertical leg = 6 units
Length of the horizontal leg = 5 units
let length of the hypotenuse = c
By using Pythagorean Theorem a²+ b²= c²c² = 6² + 5²c²= 36 +25
c = √61 => 7.8
Therefore Length of the longest side of the metal triangle to the nearest tenth is 7.8 units.

Question 6.
When a coordinate grid is superimposed on a map of Harrisburg, the high school is located at (17, 21) and the town park is located at (28, 13). If each unit represents 1 mile, how many miles apart are the high school and the town park? Round your answer to the nearest tenth.
_______ miles

Answer: The high school and the town park are 13.6 miles apart.

Explanation: The coordinates of the high school are said to be (17,21), where as the coordinates of the park are (28,13). In a coordinate plane, the distance d between the points (17,21) and (28,13) is:

d= √( x₂– x₁)²+ √( y₂– y₁)² = √(28 -17)²+ √(13-21)²
= √(11)²+ √(-8)²
= √(121+64) => √185 = 13.6014

Rounding the answer to the nearest tenth:
d = 13.6.
Taking into consideration that each unit represents 1 mile, the high school and town park are 13.6 miles apart.

Question 7.
The coordinates of the vertices of a rectangle are given by R(- 3, – 4), E(- 3, 4), C (4, 4), and T (4, – 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal $\overline { ET } $.
a. Use the Pythagorean Theorem to find the exact length of $\overline { ET } $.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 16$

Answer: The diagonal ET is about 10.63 units long.

Explanation:
Taking into consideration the triangle TRE, the length of the vertical leg (ER) is 8 units. The length of the horizontal leg (RT) is 7 units. Let a = 8 and b =7. Let c represent the length of the hypotenuse, the diagonal ET. We use the Pythagorean Theorem to find c.
a²+ b²= c²c² = 8² + 7²c²= 64 +49
c = √113 => 10,63.
The diagonal ET is about 10.63 units long.

Question 7.
b. How can you use the Distance Formula to find the length of $\overline { ET } $ ? Show that the Distance Formula gives the same answer.

Answer: The diagonal ET is about 10.63 units long. As we can see the answer is the same as the one we found using the Pythagorean Theorem.

Explanation: Using the distance formula, in a coordinate plane, the distance d between the points E(-3,4) and T(4, -4) is:
d= √( x₂– x₁)²+ √( y₂– y₁)² = √(4 – (-3))²+ √(- 4 – 4)²
= √(7)²+ √(-8)²
= √(49+64) => √113 = 10.63.
The diagonal ET is about 10.63 units long. As we can see the answer is the same as the one we found using the Pythagorean Theorem.

Question 8.
Multistep The locations of three ships are represented on a coordinate grid by the following points: P(- 2, 5), Q(- 7, – 5), and R(2, – 3). Which ships are farthest apart?

Answer: Ships P and Q are farthest apart

Explanation: Distance Formula: In a coordinate plane, the distance d between two points (x₁,y₁) and (x₂,y₂) is:

d= √( x₂– x₁)²+ √( y₂– y₁)²
The distance d₁between the two points P(-2,5) and Q(-7,-5) is:
d_{1 =} √( x_Q– x_P)²+ √( y_Q– y_P)²
= √(-7 – (-2))²+ √(- 5 – 5)²
= √(-5)²+ √(-10)²
= √(25+100) => √125 = 11.18

The distance d₂between the two points Q(-7,-5) and R(2,-3) is:
d_{3 =} √( x_R– x_Q)²+ √( y_R– y_Q)² = √(2 – (-7))²+ √(- 3 – 5)²
= √(9)²+ √(2)²
= √(81+4) => √85 = 9.22

The distance d₃between the two points P(-2,5) and R(2,-3) is:
d_{3 =} √( x_R– x_P)²+ √( y_R– y_P)²
= √(2 – (-2))²+ √(- 3 – 5)²
= √(4)²+ √(-8)²
= √(16+64) => √80 = 8.94.
As we can see, the greatest distance is d₁11.8, which means that ships P and Q are farthest apart.

Distance Between Two Points – Page No. 392

Question 9.
Make a Conjecture Find as many points as you can that are 5 units from the origin. Make a conjecture about the shape formed if all the points 5 units from the origin were connected.

Answer: (0,5), (3,4), (4,3),(5,0),(4,-3),(3,-4),(0,-5),(-3,-4),(-4,-3),(-5,0),(-4,3),(-3,4).

Explanation: Some of the points that are 5 units away from the origin are: (0,5), (3,4), (4,3),(5,0),(4,-3),(3,-4),(0,-5),(-3,-4),(-4,-3),(-5,0),(-4,3),(-3,4) etc, If all the points 5 units away from the origin are connected, a circle would be formed.

Question 10.
Justify Reasoning The graph shows the location of a motion detector that has a maximum range of 34 feet. A peacock at point P displays its tail feathers. Will the motion detector sense this motion? Explain.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 17$

Answer: Considering each unit represents 1 foot, the motion detector, and peacock are 33.5 feet apart. Since the motion detector has a maximum range of 34 feet, it means that it will sense the motion of the peacock’s feathers.

Explanation: The coordinates of the motion detector are said to be (0,25), whereas the coordinates of the peacock are (30,10). In a coordinate plane, the distance d between the points (0,25) and (30,10) is:
d₌ √( x₂– x₁)²+ √( y₂– y₁)²
= √(30 – 0)²+ √(10 – 25)²
= √(30)²+ √(-15)²
= √(900+225) => √1125.
Rounding answer to the nearest tenth:
d = 33.5 feet.
Considering each unit represents 1 foot, the motion detector and peacock are 33.5 feet apart. Since the motion detector has a maximum range of 34 feet, it means that it will sense the motion of the peacock’s feathers.

FOCUS ON HIGHER ORDER THINKING

Question 11.
Persevere in Problem Solving One leg of an isosceles right triangle has endpoints (1, 1) and (6, 1). The other leg passes through the point (6, 2). Draw the triangle on the coordinate plane. Then show how you can use the Distance Formula to find the length of the hypotenuse. Round your answer to the nearest tenth.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 18$

Answer: 7.1 units.

Explanation:

One leg of an isosceles right triangle has endpoints (1,1) and (6,1), which means that the leg is 5 units long. Since the triangle is isosceles, the other leg should be 5 units long too, therefore the endpoints of the second leg that passes through the point (6,2) are (6,1) and (6,6).
In the coordinate plane, the length of the hypotenuse is the distance d between the points (1,1) and (6,6).
d₌ √( x₂– x₁)²+ √( y₂– y₁)²
= √(6 – 1)²+ √(6 – 1)²
= √(5)²+ √(5)²
= √(25+25) => √50.
Rounding answer to nearest tenth:
d = 7.1.
The hypotenuse is around 7.1 units long.

Question 12.
Represent Real-World Problems The figure shows a representation of a football field. The units represent yards. A sports analyst marks the locations of the football from where it was thrown (point A) and where it was caught (point B). Explain how you can use the Pythagorean Theorem to find the distance the ball was thrown. Then find the distance.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Lesson 3: Distance Between Two Points img 19$
_______ yards

Answer: The distance between point A and B is 37 yards

Explanation:

To find the distance between points A and B, we draw segment AB and label its length d. Then we draw vertical segment AC and Horizontal segment CB. We label the lengths of these segments a and b. triangle ACB is a right triangle with hypotenuse AB.
Since AC is vertical segment, its length, a, is the difference between its y-coordinates. Therefore, a = 26 – 14 = 12 units.
Since CB is horizontal segment, its length b is the difference between its x-coordinates. Therefore, b = 75 – 40 = 35units.
We use the Pythagorean Theorem to find d, the length of segment AB.
d²= a²+ b²d²= 12²+ 35²
d² = 144 + 1225
d²= 1369 => d = √1369 => 37
The distance between point A and B is 37 yards

Ready to Go On? – Model Quiz – Page No. 393

12.1 The Pythagorean Theorem

Find the length of the missing side.

Question 1.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Model Quiz img 20$
________ meters

Answer: Length of missing side is 28m

Explanation: Lets consider value of a = 21 and c = 35.
Using Pythagorean Theorem a²+ b²= c²
21²+ b²= 35² 441 + b² = 1225
b²= 784 => b = √784 = 28.
Therefore length of missing side is 28m.

Question 2.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Model Quiz img 21$
________ ft

Answer: Length of missing side is 34ft

Explanation: Let’s consider value of a = 16 and b = 30.
Using Pythagorean Theorem a²+ b²= c²16²+ 30²= c² 256 + 900 = c²
c²= 1156 => c = √1156 = 34.
Therefore length of missing side is 34ft.

12.2 Converse of the Pythagorean Theorem

Tell whether each triangle with the given side lengths is a right triangle.

Question 3.
11, 60, 61
____________

Answer: Since 11²+ 60²= 61², by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.

Explanation: Let a = 11, b = 60 and c= 61
Using the converse of the Pythagorean Theorem a²+ b²= c²11²+ 60²= 61²
121 + 3600 = 3721
3721 = 3721
Since 11²+ 60²= 61², by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle. Question 4.
9, 37, 40
____________

Answer: Since 9²+ 37²≠ 40², by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.

Explanation: Let a = 9, b = 37 and c= 40
Using the converse of the Pythagorean Theorem a²+ b²= c²9²+ 37²= 40²81 + 1369 = 1600
1450 ≠ 3721.
Since 9²+ 37²≠ 40², by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.

Question 5.
15, 35, 38
____________

Answer: Since 15²+ 35²≠ 38², by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.

Explanation: Let a = 15, b = 35 and c= 38
Using the converse of the Pythagorean Theorem a²+ b²= c²15²+ 35²= 38²
225 + 1225 = 1444
1450 ≠ 1444
Since 15²+ 35²≠ 38², by the converse of the Pythagorean Theorem, we say that the given sides are not in the shape of right-angled triangle.

Question 6.
28, 45, 53
____________

Answer: Since 28²+ 45²= 53², by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.

Explanation: Let a = 28, b = 45 and c= 53
Using the converse of the Pythagorean Theorem a²+ b²= c²28²+ 45²= 53²784 + 2025 = 2809
2809 = 2809
Since 28²+ 45²= 53², by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle. Question 7.
Keelie has a triangular-shaped card. The lengths of its sides are 4.5 cm, 6 cm, and 7.5 cm. Is the card a right triangle?
____________

Answer: Since 4.5²+ 6²= 7.5², by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.

Explanation: Let a = 4.5, b = 6 and c= 7.5
Using the converse of the Pythagorean Theorem a²+ b²= c²4.5²+ 6²= 7.5²20.25 + 36 = 56.25
56.25= 56.25
Since 4.5²+ 6²= 7.5², by the converse of the Pythagorean Theorem, we say that the given sides are in the shape of right-angled triangle.

12.3 Distance Between Two Points

Find the distance between the given points. Round to the nearest tenth.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Model Quiz img 22$

Question 8.
A and B
________ units

Answer: Distance between A and B is 6.7 units

Explanation: A= (-2,3) and B= (4,6)

Distance between A and B is d₌ √( x₂– x₁)²+ √( y₂– y₁)²
= √(4 – (-2)²+ √(6 – 3)²
= √(6)²+ √(3)²
= √(36+9) => √45 = 6.7 units

Question 9.
B and C
________ units

Answer: Distance between B and C is 7.07 units

Explanation: B= (4,6) and C= (3,1)

Distance between B and C is d₌ √( x₂– x₁)²+ √( y₂– y₁)²
= √(4 – 3)²+ √(6 – (-1))²
= √(1)²+ √(7)²
= √(1+49) => √50 = 7.07 units

Question 10.
A and C
________ units

Answer: Distance between A and C is 6.403 units

Explanation: A= (-2,3) and C= (3, -1)

Distance between A and C is d₌ √( x₂– x₁)²+ √( y₂– y₁)²
= √(3 – (-2)²+ √(-1 – 3)²
= √(5)²+ √(-4)²
= √(25+16) => √41 = 6.403 units

ESSENTIAL QUESTION

Question 11.
How can you use the Pythagorean Theorem to solve real-world problems?

Answer: We can use the Pythagorean Theorem to find the length of a side of a right triangle when we know the lengths of the other two sides. This application is usually used in architecture or other physical construction projects. For example, it can be used to find the length of a ladder, if we know the height of the wall and distance on the ground from the wall of the ladder.

Selected Response – Mixed Review – Page No. 394

Question 1.
What is the missing length of the side?
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Mixed Review img 23$
A. 9 ft
B. 30 ft
C. 39 ft
D. 120 ft

Answer: C

Explanation:
Given a= 80 ft
b= ?
c= 89 ft
As a²+b²=c²80²+b²= 89²6,400+b²= 7,921
b²= 7,921-6,400
b= √1,521
b= 39 ft.

Question 2.
Which relation does not represent a function?
Options:
A. (0, 8), (3, 8), (1, 6)
B. (4, 2), (6, 1), (8, 9)
C. (1, 20), (2, 23), (9, 26)
D. (0, 3), (2, 3), (2, 0)

Answer: D

Explanation: The value of X is the same for 2 points and 2 values of Y [(2, 3), (2, 0)]. The value of X is repeated for a function to exist, no two points can have the same X coordinates.

Question 3.
Two sides of a right triangle have lengths of 72 cm and 97 cm. The third side is not the hypotenuse. How long is the third side?
Options:
A. 25 cm
B. 45 cm
C. 65 cm
D. 121 cm

Answer: C

Explanation:
Given a= 72 cm
b= ?
c= 97 cm
As a²+b²=c²72²+b²= 97²5,184+b²= 9,409
b²= 9,409-5,184
b= √4,225
b= 65 cm.

Question 4.
To the nearest tenth, what is the distance between point F and point G?
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Mixed Review img 24$
Options:
A. 4.5 units
B. 5.0 units
C. 7.3 units
D. 20 units

Answer: A.

Explanation:
Given F= (-1,6) =(x1,y1).
G= (3,4) = (x2,y2).
The difference between F&G points is
d= √(x2-x1)² + (y2-y1)²
= √(3 – (-1))² + (4 – 6)² = √(4)² + (-2)²
= √16+4
= √20
= 4.471
= 4.5 units.

Question 5.
A flagpole is 53 feet tall. A rope is tied to the top of the flagpole and secured to the ground 28 feet from the base of the flagpole. What is the length of the rope?
Options:
A. 25 feet
B. 45 feet
C. 53 feet
D. 60 feet

Answer: D

Explanation:

By Pythagorean theorem
a²+b²=c²53²+28²= C²2,809+784= C²
C²= 9,409-5,184
C²= 3,593
C= √3,593
C= 59.94 feet
=60 feet.

Question 6.
Which set of lengths are not the side lengths of a right triangle?
Options:
A. 36, 77, 85
B. 20, 99, 101
C. 27, 120, 123
D. 24, 33, 42

Answer: D.

Explanation:
Check if side lengths in option A form a right triangle.
Let a= 36, b= 77, c= 85
By Pythagorean theorem
a²+b²=c²36²+77²= 85²
1,296+ 5,929= 7,225
7,225= 7,225
As 36²+77²= 85² the triangle is a right triangle.

Check if side lengths in option B form a right triangle.
Let a= 20, b= 99, c= 101
By Pythagorean theorem
a²+b²=c²20²+99²= 101²
400+ 9,801= 10,201
10,201= 10,201
As 20²+99²= 101² the triangle is a right triangle.

Check if side lengths in option B form a right triangle.
Let a= 27, b= 120, c= 123
By Pythagorean theorem
a²+b²=c²27²+120²= 123²
729+ 14,400= 15,129
15,129= 15,129
As 27²+120²= 123²the triangle is a right triangle.

Check if side lengths in option B form a right triangle.
Let a= 27, b= 120, c= 123
By Pythagorean theorem
a²+b²=c²24²+33²= 42²
576+ 1,089= 1,764.
1,665= 1,764
As 24²+33²is not equal to 42²the triangle is a right triangle.

Question 7.
A triangle has one right angle. What could the measures of the other two angles be?
Options:
A. 25° and 65°
B. 30° and 15°
C 55° and 125°
D 90° and 100°

Answer: A

Explanation:
The sum of all the angles of a triangle is 180
<A+<B+<C= 180°
<A+<B+ 90°= 180°
<A+<B= 180°-90°
<A+<B= 90, here we will verify with the given options.
25°+65°= 90°
So, the measure of the other two angles are 25° and 65°

Mini-Task

Question 8.
A fallen tree is shown on the coordinate grid below. Each unit represents 1 meter.
$Go Math Grade 8 Answer Key Chapter 12 The Pythagorean Theorem Mixed Review img 25$
a. What is the distance from A to B?
_______ meters

Answer: 13.34 m.

Explanation:
A= (-5,3)
B= (8,0)
Distance between A & B is
D= √{8-(-5)² + (0-3)² = √(13)² + (-3)²
= √169+9
= √178
= 13.34 m.

Question 8.
b. What was the height of the tree before it fell?
_______ meters

Answer: 16.3 m.

Explanation:
Length of the broken part= 13.3 m
Length of vertical part= 3 m
Total Length = 13.3 m + 3 m
= 16.3 m.

Final Words

In addition to the exercise problems, we have provided the solutions for the review questions. So all the students are requested to test your knowledge and solve the problems provided at the end of this chapter. Refer HMH Go Math Grade 8 Answer Keu and try to score the highest marks in the exams. Hope you liked the explanations provided in this chapter. Stay tuned to get the solutions according to the list of the chapters of all the grades.

Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume

April 7, 2022March 28, 2022 by Go Math Answer Key

$go-math-grade-7-chapter-9-circumference-area-and-volume-answer-key$

Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume: Get the solutions to all the questions in this article. Download Go Math Grade 7 Answer Key for Chapter 9 Circumference, Area and Volume pdf for free. Know how and where to use the formulas with the help of the HMH Go Math Grade 7 Solution Key Chapter 9 Circumference, Area, and Volume.

Download Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Pdf

The pupils who are in search of solutions of grade 7 chapter 9 circumference, area, and volume can get them on Go Math Answer Key. The students of 7th Grade can know how to find the area, circumference, and volume of various shapes here. Learn the different methods to solve the problems in Chapter 9 Circumference, Area and Volume using the formulas. We have provided the solutions as per the topics in the below sections.

Guided Practice – Page No. 268

Find the circumference of each circle.

Question 1.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 1$
________ in

Answer: 56.57 in

Explanation:
Circumference of the circle = 2πr = 2 x 22/7 x 9 = 56.57 in

Question 2.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 2$
________ cm

Answer: 44 cm

Explanation:
Circumference of the circle = 2πr = 2 x 22/7 x 7 = 44 cm

Find the circumference of each circle. Use 3.14 or $\frac{22}{7}$ for π. Round to the nearest hundredth, if necessary.

Question 3.
______ m

Question 4.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 3$
______ yd

Answer: 30.15 yd

Explanation:
Circumference of the circle = 2πr = 2 x 3.14 x 4.8 = 30.144 yd

Question 5.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 4$
______ in

Answer: 7.5 in

Explanation:
Circumference of the circle = 2πr = 2 x 3.14 x 7.5 = 47.1 in

Question 6.
A round swimming pool has a circumference of 66 feet. Carlos wants to buy a rope to put across the diameter of the pool. The rope costs $0.45 per foot, and Carlos needs 4 feet more than the diameter of the pool. How much will Carlos pay for the rope?
$ ______

Answer: $6.525

Explanation:
Circumference of the swimming pool = 66 feet
πd = 66
22/7 x d = 66
d = 66 x 7/ 22 = 10.5
The diameter of the pool = 10.5 feet
Carlos needs 4 feet more than the diameter of the pool.
Total rope needed = 10.5 + 4 = 14.5 feet
Cost of rope per foot = $0.45
Total cost of the rope = 14.5 x $0.45 = $6.525
Therefore the total cost of the rope = $6.525

Find each missing measurement to the nearest hundredth. Use 3.14 for π.

Question 7.
r =
d =
C = π yd
r = ________ yd
d = ________ yd

Answer:
r = 0.5 yd
d = 1 yd

Explanation:
Circumference = π yd
2πr = π yd
r = 1/2 yd = 0.5 yd
d = 2r = 2 [1/2] = 1 yd

Question 8.
r ≈
d ≈
C = 78.8 ft
r ≈ ________ ft
d ≈ ________ ft

Answer:
r = 495.31 ft
d = 990.62 ft

Explanation:
Circumference = 78.8 ft
2πr = 78.8 ft
r = 2 x 22/7 x 78.8 = 495.31 ft
d = 2 x 495.31 = 990.62 ft

Question 9.
r ≈
d ≈ 3.4 in
C =
r ≈ ________ in
C = ________ in

Answer:
r = 1.7 in
c = 10.68 in

Explanation:
Diameter = 3.4 in
Circumference = πd = 22/7 x 3.4 in = 10.68 in
r = d/2 = 1.7 in

Essential Question Check-In

Question 10.
Norah knows that the diameter of a circle is 13 meters. How would you tell her to find the circumference?
Type below:
____________

Answer: Circumference = 16.82 meters

Explanation:
Given,
Diameter = 13 meters
Circumference = πd = 22/7 x 13 = 16.82 meters

Independent Practice – Page No. 269

For 11–13, find the circumference of each circle. Use 3.14 or $\frac{22}{7}$ for π. Round to the nearest hundredth, if necessary.

Question 11.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 5$
_______ ft

Answer:
Cicumference = 18.526 ft = 19 ft (approx)

Explanation:
Given:
Diameter = 5.9 ft
Cicumference = πd = 3.14 x 5.9 = 18.526 ft = 19 ft (approx)

Question 12.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 6$
_______ cm

Answer:
Cicumference =176 cm

Explanation:
Given:
Radius = 56 cm
Cicumference = πd = 22/7 x 56 = 176 cm

Question 13.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 7$
_______ in

Answer:
Cicumference = 110 in

Explanation:
Given:
Diameter = 35 in
Cicumference = πd = 22/7 x 35 = 110 in

Question 14.
In Exercises 11–13, for which problems did you use $\frac{22}{7}$ for π? Explain your choice.
Type below:
_____________

Answer:
11th question as 3.14 and the 12 and 13 questions as π

Explanation:
We can take 3.14 as π for 11 th question because the diameter is given in decimal points.
And in questions 12 and 13 we need to take π because the radius and diameter are given in whole number form.

Question 15.
A circular fountain has a radius of 9.4 feet. Find its diameter and circumference to the nearest tenth.
d = _________ ft
C = _________ ft

Answer:
d = 19 ft
C = 59 ft

Explanation:
Given:
Radius = 9.4 ft
Diameter = 2r = 2 x 9.4 = 18.8 ft = 19 ft (approx)
Circumference = πd = 22/7 x 18.8 = 59.08 = 59 ft (approx)

Question 16.
Find the radius and circumference of a CD with a diameter of 4.75 inches.
r = _________ in
C = _________ in

Answer:
r = 2.4 in
C = 15 in

Explanation:
Given:
Diameter = 4.75 in
Radius = r/2 = 4.75/2 = 2.37 in = 2.4 in (approx)
Circumference = πd = 22/7 x 4.75 = 14.92 in =15 in (approx)

Question 17.
A dartboard has a diameter of 18 inches. What are its radius and circumference?
r = _________ in
C = _________ in

Answer:
r = 9 in
C = 56.6 in

Explanation:
Given:
Diameter = 18 in
Radius = r/2 = 18/2 = 9 in
Circumference = πd = 22/7 x 18 = 56.57 in = 56.6 in (approx)

Question 18.
Multistep
Randy’s circular garden has a radius of 1.5 feet. He wants to enclose the garden with edging that costs $0.75 per foot. About how much will the edging cost? Explain.
$ _______

Answer:

Explanation:
Given:
The radius of the garden= 1.5 ft
Circumference of the garden = 2πr = 2 x 22/7 x 1.5 = 9.42 ft
Cost of enclosing the garden per foot = $0.75
Total cost of edging = 9.42 x $0.75 = $7.06 = $7 (approx)

Question 19.
Represent Real-World Problems
The Ferris wheel shown makes 12 revolutions per ride. How far would someone travel during one ride?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 8$
_______ ft

Answer: Total distance travelled in one ride is 4,752 ft

Explanation:
Given:
The diameter of the Ferris wheel= 63 ft
Circumference of the Ferris wheel = 2πr = 2 x 22/7 x 63 = 396 ft
Total number of revolutions = 12
Total distance travelled = 12 x 396 = 4,752 ft

Question 20.
The diameter of a bicycle wheel is 2 feet. About how many revolutions does the wheel make to travel 2 kilometres? Explain. Hint: 1 km ≈ 3,280 ft
_______ revolutions

Answer:
1044 revolutions

Explanation:
Given:
Diametre of the bicycle wheel = 2 feet
Total distance travelled = 2 kilometres
We know that,
1 km ≈ 3,280 ft
2 km = 2 x 3,280 = 6,560 ft
Circumference of the bicycle = Distance travelled in one revolution = πd = 22/7 x 2 = 6.28 ft = 6.3 ft
Total number of revolutions = Total distance travelled / distance travelled in one revolution
= 6560 / 6.28 = 1044 revolutions

Question 21.
Multistep
A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.25 mi long. You walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. How much farther does your friend walk?
_______ mi

Answer:

Explanation:
Given,
The diameter of the pond = 0.25 mi
The length of the bridge = The diameter of the pond = 0.25 mi
Then the distance walked by the man = 0.25 mi
Distance travelled by the friend = Halfway around the pond to meet you at the other side of the bridge = πd/2
= 22/7 x 0.25/2 = 0.39 = 0.4 mi
The friend travelled more distance compared to the man
The more distance travelled by the friend = 0.39 – 0.25 = 0.14 mi

Page No. 270

Question 22.
Architecture
The Capitol Rotunda connects the House and the Senate sides of the U.S. Capitol. Complete the table. Round your answers to the nearest foot.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 9$
Type below:
_____________

Answer:
Radius = 48 ft
Diameter = 96 ft

Explanation:
Given
Height = 180 ft
Circumference = 301.5 ft
πd = 301.5
22/7 x d = 301.5
d = 95.93 = 96 ft
r = d/2 = 96/2 = 48 ft

H.O.T.

Focus on Higher Order Thinking

Question 23.
Multistep
A museum groundskeeper is creating a semicircular statuary garden with a diameter of 30 feet. There will be a fence around the garden. The fencing costs $9.25 per linear foot. About how much will the fencing cost altogether?
$ _______

Answer:
The total cost of fencing = $712

Explanation:
Given,
The diameter = 30 ft
Circumference of the garden in the shape of circle = 2πr
Circumference of the semicircle = πr = πd/2 = 22/7 x 30/2 = 47.14ft
Cost of fencing for each foot = $9.25
The total cost of fencing the semicircular garden = 47.14 x $9.25 + 30 x $9.25 = $712 (approx)

Question 24.
Critical Thinking
Sam is placing rope lights around the edge of a circular patio with a diameter of 18 feet. The lights come in lengths of 54 inches. How many strands of lights does he need to surround the patio edge?
_______ strands

Answer: 12 and a half strands of light = 13 strands (approx)

Explanation:
Given,
The diameter of the circular patio = 18 ft = 216 inch
Circumference of the circular patio = πd = 22/7 x 216 = 678.85 inch
The lights will come in a length (in one strand)= 54 inches
Total number of strands of light required for the circular patio
= Circumference of the circular patio/ The lights will come in a length (in one strand) = 678.85/54 = 12.57 = 12 and a half strands of light

Question 25.
Represent Real-World Problems
A circular path 2 feet wide has an inner diameter of 150 feet. How much farther is it around the outer edge of the path than around the inner edge?
_______ feet

Answer: about 12.6 ft

Explanation:
Given,
Width of the circular path = 2 ft
The inner diameter of the circular path = 150 ft
The outer diameter of the circular path = 150 + 2(2) = 154 ft
Inner circumference = πd = 150 π
Outer circumference = πd = 154π
Distance between the outer and inner edge = 154 π – 150 π = 4 π = 12.6 ft

Question 26.
Critique Reasoning
Gear on a bicycle has the shape of a circle. One gear has a diameter of 4 inches, and a smaller one has a diameter of 2 inches. Justin says that the circumference of the larger gear is 2 inches more than the circumference of the smaller gear. Do you agree? Explain your answer.
_______

Answer:
Justin statement is incorrect.

Explanation:
The circumference of the larger gear = πd = 4π
The circumference of the smaller gear = πd = 2π
Since, 2 x 2π = 4π, the circumference of the larger gear is two times the circumference of the smaller gear.
Since = 4π – 2π = 2π = 6.28
Therefore, The larger circumference is not 2 inches more than the smaller circumference

Question 27.
Persevere in Problem Solving
Consider two circular swimming pools. Pool A has a radius of 12 feet, and Pool B has a diameter of 7.5 meters. Which pool has a greater circumference? How much greater? Justify your answers.
_______

Answer:
Pool B about 0.9 meters

Explanation:
Given,
Pool A has a diameter = 24 ft
Pool B has a diameter = 7.5 m
We know that,
1 ft = 0.3 metres
24 ft = 7.2 metres
The pool B has a greater diameter so it has a greater circumference.
Circumference of the pool A = 7.2π
Circumference of the pool B = 7.5π
Difference between the circumferences = 7.5π – 7.2π = 0.9 meters.

Guided Practice – Page No. 274

Find the area of each circle. Round to the nearest tenth if necessary. Use 3.14 for π.

Question 1.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 10$
_______ m²

Answer: 153.9 m²

Explanation:
Given:
Diameter = 14 m
Radius = 14/2 = 7 m
Area of the circle = πr²
= 3.14 x 7 x 7 = 153.86 = 153.9 m²

Question 2.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 11$
_______ mm²

Answer: 452.2 mm²

Explanation:
Given:
Radius =12mm
Area of the circle = πr²
= 3.14 x 12 x 12 = 3.14(144) = 452.2mm²

Question 3.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 12$
_______ yd²

Answer: 314 yd²

Explanation:
Given:
Diameter = 20yd
Radius = 20/2 = 10yd
Area of the circle = πr²
= 3.14 x 10 x 10 = 3.14(100) = 314yd²

Solve. Use 3.14 for π.

Question 4.
A clock face has a radius of 8 inches. What is the area of the clock face? Round your answer to the nearest hundredth.
_______ in²

Answer: 200.96 in²

Explanation:
Given:
Radius = 8inches
Area of the clock face = πr²
= 3.14 x 8 x 8= 3.14(64) = 200.96 in²

Question 5.
A DVD has a diameter of 12 centimeters. What is the area of the DVD? Round your answer to the nearest hundredth.
_______ cm²

Answer: 113.04 cm²

Explanation:
Given:
Diameter = 12 centimeters
Radius = 12/2 = 6 centimeters
Area of the DVD= πr²
= 3.14 x 6 x 6 = 3.14(36) = 113.04 cm²

Question 6.
A company makes steel lids that have a diameter of 13 inches. What is the area of each lid? Round your answer to the nearest hundredth.
_______ in²

Answer: 132.67 in²

Explanation:
Given:
Diameter = 13 inches
Radius = 13/2 = 6.5 inches
Area of each lid= πr²
= 3.14 x 6.5 x 6.5 = 3.14(42.25) = 132.67 in²

Find the area of each circle. Give your answers in terms of π.

Question 7.
C = 4π
A =
Type below:
______________

Answer: 4π

Explanation:
Given:
Circumcenter = 4π
2πr = 4π
Radius = 4/2 = 2 units
Area of the circle = πr²
= π x 2 x 2 = π(4) = 4π square units

Question 8.
C = 12π
A =
Type below:
______________

Answer: 36π

Explanation:
Given:
Circumcenter = 12π
2πr = 12π
Radius =6 units
Area of the circle = πr²
= π x 6 x 6 = π(36) = 36π square units

Question 9.
C = $\frac{π}{2}$
A =
Type below:
______________

Answer: π/16

Explanation:
Given:
Circumcenter = $\frac{π}{2}$
2πr = $\frac{π}{2}$
Radius = 1/4 units
Area of the circle = πr²
= π x 1/4 x 1/4 = π(1/16) = π/16 square units

Question 10.
A circular pen has an area of 64π square yards. What is the circumference of the pen? Give your answer in terms of π
Type below:
______________

Answer: 16π

Explanation:
Given:
Area of the circular pen = 64π square yards
πr² = 64π
r = 8 yards
Circumference of the circle = 2πr = 2 x 8 x π = 16π yards

Essential Question Check-In

Question 11.
What is the formula for the area A of a circle in terms of the radius r?
Type below:
______________

Answer: πr²

Explanation:
Area of a circle = πr²

Independent Practice – Page No. 275

Question 12.
The most popular pizza at Pavone’s Pizza is the 10-inch personal pizza with one topping. What is the area of a pizza with a diameter of 10 inches? Round your answer to the nearest hundredth.
_______ in²

Answer: 78.5 in²

Explanation:
Given:
Diameter = 10 inches
Radius = 10/2 = 5 inches
Area of a pizza = πr²
= 3.14 x 5 x 5 = 3.14(25) = 78.5 in²

Question 13.
A hubcap has a radius of 16 centimeters. What is the area of the hubcap? Round your answer to the nearest hundredth.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 13$
_______ cm²

Answer: 803.84 cm²

Explanation:
Given:
Radius = 16 cm
Area of the circle = πr²
= 3.14 x 16 x 16 = 3.14(256) = 803.84 cm²

Question 14.
A stained glass window is shaped like a semicircle. The bottom edge of the window is 36 inches long. What is the area of the stained glass window? Round your answer to the nearest hundredth.
_______ in²

Answer: 508.68 in²

Explanation:
Area of the semicircle = 1/2 πr² = 1/2(3.14)(18)(18) = 1/2 (3.14)(324) = 1.57(324) = 508.68 in²

Question 15.
Analyze Relationships
The point (3,0) lies on a circle with the centre at the origin. What is the area of the circle to the nearest hundredth?
_______ units²

Answer: 28.26 units²

Explanation:
Radius = 3
Area of the circle = πr² = π(3)² = 3.14(9) = 28.26 units²

Question 16.
Multistep
A radio station broadcasts a signal over an area with a radius of 50 miles. The station can relay the signal and broadcast over an area with a radius of 75 miles. How much greater is the area of the broadcast region when the signal is relayed? Round your answer to the nearest square mile.
_______ mi²

Answer: 9813 mi²

Explanation:
Given:
The radius of a radio station broadcasted the signal (r) = 50 miles
The greatest radius to which the broadcast can be relayed (R) = 75 miles
The greatest area of the broadcast region when the signal is relayed = πR²-πr² = π(75) (75) – π (50) (50)
= 5625π – 2500π
= 3125π
= 3125(3.14) = 9813 mi²(approx)

Question 17.
Multistep
The sides of a square field are 12 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth.
_______ m²

Answer:30.96 m²

Explanation:
Given:
The side of the square = 12 meters
The diameter circular area of the field in the centre = The side of the square = 12 meters
The radius of the field = 12/2 = 6 meters
Area of the field which is not reached by the sprinkler = Area of the square – Area of the circular area
= (side)²-πr² = (12)(12) – π (6) (6)
= 144 – 36 (3.14)
= 144 – 113.04
= 30.96 m²

Question 18.
Justify Reasoning
A small silver dollar pancake served at a restaurant has a circumference of 2π inches. A regular pancake has a circumference of 4π inches. Is the area of the regular pancake twice the area of the silver dollar pancake? Explain.
_______

Answer: No, the area of the regular pancake is 4 times the area of the silver dollar pancake

Explanation:
Silver Dollar pancake:
Circumference of the silver Dollar pancake = 2π inches
2πr = 2π
r = 1 inch
Area of the silver dollar pancake = πr² = π (1) (1) = π in²

Regular pancake:
Circumference of the regular pancake = 4π inches
2πr = 4π
r = 2 inch
Area of the silver dollar pancake = πr² = π (2) (2) = 4π in²

Therefore, the area of the regular pancake is 4 times the area of the silver dollar pancake

Question 19.
Analyze Relationships
A bakery offers a small circular cake with a diameter of 8 inches. It also offers a large circular cake with a diameter of 24 inches. Does the top of the large cake have three times the area of that of the small cake? If not, how much greater is its area? Explain.
_______

Answer: No, the area of the large cake is 9 times the area of the small cake

Explanation:
Small Cake:
The diameter of the small cake= 8 inches
The radius of the small cake = 8/2 = 4 inches
Area of the small cake = πr² = π (4) (4) = 16 π in²

Large Cake:
The diameter of the large cake= 24 inches
The radius of the large cake = 24/2 = 12 inches
Area of the large cake = πr² = π (12) (12) = 144 π in²

Since 144 π/ 16 π = 9
Therefore the

area of the large cake is 9 times the area of the small cake.

Page No. 276

Question 20.
Communicate Mathematical Ideas
You can use the formula A = $\frac{C^{2}}{4π}$ to find the area of a circle given the circumference. Describe another way to find the area of a circle when given the circumference.
Type below:
____________

Answer: Area = C²/4π

Explanation:
Circumference of the circle = 2πr
C = 2πr
Divide both sides by 2π
then, r = C/2π
Area of the circle = πr²
Substitute C/2π for r:
Area = π(c/2π)² = C²/4π

Question 21.
Draw Conclusions
Mark wants to order a pizza. Which is the better deal? Explain.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 14$
_____

Answer: The pizza of 18 inches is a better deal

Explanation:
Given:
The diameter of the pizza = 12 inches
The radius of the pizza = 12/2= 6 inches
Area of the circle = πr²
= (3.14)(6)(6) = 113 (approx) in²
The total cost of the pizza = $10
Cost of the pizza per inch = $10/113 = $0.09 per square inch

The diameter of the pizza = 18 inches
The radius of the pizza = 18/2= 9 inches
Area of the circle = πr²
= (3.14)(9)(9) = 254 (approx) in²
The total cost of the pizza = $20
Cost of the pizza per inch = $20/254 = $0.08 per inch

Question 22.
Multistep
A bear was seen near a campground. Searchers were dispatched to the region to find the bear.
a. Assume the bear can walk in any direction at a rate of 2 miles per hour. Suppose the bear was last seen 4 hours ago. How large an area must the searchers cover? Use 3.14 for π. Round your answer to the nearest square mile.
_____ mi²

Answer: 201mi²

Explanation:
The bear can walk a distance = 2 x 4 = 8 miles
Since it is walking 2 miles per hour for 4 hours
The radius of the bear = 8 miles
Area of the circle = πr²
= (3.14)(8)(8) = 201 (approx) mi²

Question 22.
b. What If? How much additional area would the searchers have to cover if the bear were last seen 5 hours ago?
_____ mi²

Answer: 113mi²

Explanation:
If the bear for 5 hours then,
The bear can walk a distance = 2 x 5 = 10 miles
Since it is walking 2 miles per hour for 5 hours
The radius of the bear = 10 miles
Area of the circle = πr²
= (3.14)(10)(10) = 314 (approx) mi²

The additional area covered by the searches = 314 – 201 = 113 mi²

H.O.T.

Focus on Higher Order Thinking

Question 23.
Analyze Relationships
Two circles have the same radius. Is the combined area of the two circles the same as the area of a circle with twice the radius? Explain.
_____

Answer: No

Explanation:
If the radius of two circles is the same.
then, Let the radii of the circles be 1.
The area of each circle = π square units
The combined area of 2 circles =π+π = 2π square units

If the radius is doubled.
then, Let the radii of the circles be 2
The area of each circle = 4π square units
The combined area of 2 circles = 4π+4π = 8π square units

Therefore the areas of both cases are not the same.

Question 24.
Look for a Pattern
How does the area of a circle change if the radius is multiplied by a factor of n, where n is a whole number?
Type below:
____________

Answer: The new area is then n² times the area of the original circle.

Explanation:
If the radius is multiplied by a factor “n”
then, the new radius = rn
The area of the circle (with radius rn) = π(rn)²= n² (πr²).
Therefore the new area is n² times the area of the original circle.

Question 25.
Represent Real World Problems
The bull’s-eye on a target has a diameter of 3 inches. The whole target has a diameter of 15 inches. What part of the whole target is the bull’s-eye? Explain.
Type below:
____________

Answer: 1/25 of the target

Explanation:
Bull’s eye:
Diameter of Bull’s eye = 3 inches
Radius of Bull’s eye = 3/2 = 1.5 inches
Area of the Bull’s eye = π(r)²= π(1.5)² = 2.25π
Target:
Diameter of the target = 15 inches
Radius of the target = 15/2 = 7.5 inches
Area of the target = π(r)²= π(7.5)² = 56.25π

The part of Bull’s eye in the whole target = 2.25π/ 56.25π = 1/25

Therefore the 1/25th part of the whole target is the Bull’s eye.

Guided Practice – Page No. 280

Question 1.
A tile installer plots an irregular shape on grid paper. Each square on the grid represents 1 square centimeter. What is the area of the irregular shape?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 15$
_____ cm²

Answer: Area of the irregular shape = 34 cm²

Explanation:
STEP1 First divide the irregular shapes into polygons.
STEP2 The irregular shape can be divided into a triangle, rectangle, parallelogram
STEP3 Areas of the polygons
Area of triangle = 1/2 (base x height) = 1/2 (4 x 2) = 4 cm²
Area of the rectangle = length x breadth = 5 x 3 = 15 cm²
Area of the parallelogram = base x height = 5 x 3 = 15 cm²
Area of the irregular shape = (15+15+5) cm²= 34cm²

Question 2.
Show two different ways to divide the composite figure. Find the area both ways. Show your work below.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 16$
_____ cm²

Answer: Area of the figure in both ways = 288 cm²

Explanation:
The first way to divide up the composite shape is to divide it into an 8 by 9 rectangle and a 12 by 18 rectangle.
The area of the first rectangle = Length x breadth = 9 x 8 = 72 cm²
The area of the second rectangle = Length x breadth = 18 x 12 = 216 cm²
The total area of the figure = 72 + 216 = 288 cm²

Question 3.
Sal is tiling his entryway. The floor plan is drawn on a unit grid. Each unit length represents 1 foot. Tile costs $2.25 per square foot. How much will Sal pay to tile his entryway?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 17$
$ _____

Answer: Sal will pay $97.875

Explanation:
Separate this figure into trapezium and parallelogram.
Area of the trapezium = 1/2 (a+b)h = 1/2 (7+4) 5 = 1/2 (11) 5 = 27.5 ft²
Area of the parallelogram = base x height = 4 x 4 = 16 ft²

The total area of the figure = 27.5 + 16 = 43.5ft²
Cost of each square foot = $2.25
Amount paid by Sal = 43.5 x 2.25 = $97.875

Essential Question Check-In

Question 4.
What is the first step in finding the area of a composite figure?
Type below:
______________

Answer:
The first step in finding the area of a composite figure is to divide it up into smaller basic shapes.

Explanation:
The first step in finding the area of a composite figure is to divide it up into smaller basic shapes such as triangles, squares, rectangles, parallelograms, circles and trapezium.
Then calculate the area of each figure and add them to find the area of the figure.

Independent Practice – Page No. 281

Question 5.
A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diameter of the semicircle. What is the total area of the banner? Use 3.14 for π.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 18$
_____ in²

Answer: 941.33 in²

Explanation:
Area of the square = side x side = 26 x 26 = 676 in²
Area of the semicircle =1/2 πr²= 1/2 (3.14) (13) (13) = 1/2 (3.14) (169) = 265.33 in²
Area of the figure = 676 + 265.33 = 941.33 in²

Question 6.
Multistep
Erin wants to carpet the floor of her closet. A floor plan of the closet is shown.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 19$
a. How much carpet does Erin need?
_____ ft²

Answer: 61 ft²

Explanation:
Area of the rectangle = length x breadth = 4 x 10 = 40 ft
Area of the triangle = 1/2 x base x height = 1/2 x 6 x 7 = 21 ft
The total area of the figure = 40+21 = 61 ft²

Question 6.
b. The carpet Erin has chosen costs $2.50 per square foot. How much will it cost her to carpet the floor?
$ _____

Answer: $152.50

Explanation:
Cost per square foot of the carpet = $2.50
The total cost of the carpet on the floor = 61 x $2.50 =$152.50

Question 7.
Multiple Representations
Hexagon ABCDEF has vertices A(-2, 4), B(0, 4), C(2, 1), D(5, 1), E(5, -2), and F(-2, -2). Sketch the figure on a coordinate plane. What is the area of the hexagon?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 20$
_____ units²

Answer: The area of the figure is 30 square units

Explanation:
Separate the figure into a trapezium and a rectangle.
Area of a trapezium = 1/2 (a+b) h= 1/2 (2+4) x 3 = 1/2 (6) 3 = 9 square units
Area of a rectangle = length x breadth = 7 x 3 = 21 square units
The total area of the figure = 9+21 = 30 square units

Question 8.
A field is shaped like the figure shown. What is the area of the field? Use 3.14 for π.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 21$
_____ m²

Answer: 146.24 m²

Explanation:
Divide the figure into a square, triangle and a quarter of a circle.

Area of a square = side x side = 8 x 8 = 64 m²
Area of a quarter of a circle = 1/4 (πr²) = 1/4 (3.14 x 8²)
= 1/4 (200.96) = 50.24 m²
Area of the triangle = 1/2 x base x height = 1/2 x 8 x 8 = 32 m²
Total area of the figure = 64+32+50.24 = 146.24 m²

Question 9.
A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 12 cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.
_____ cm²

Answer: 60.56 cm²

Explanation:
The bookmark is divided into a rectangle, semicircle.
Area of the rectangle = length x breadth = 12 x 4 = 48 cm²
The diameter of the semicircle = The width of the rectangle = 4 cm
The radius of the semicircle = 4/2 = 2 cm
The area of the semicircle = πr² = 3.14 x 2 x 2 = 12.56 cm²
The total area of the bookmark = 12.56 + 48 = 60.56 cm²

Question 10.
Multistep
Alex is making 12 pendants for the school fair. The pattern he is using to make the pennants is shown in the figure. The fabric for the pennants costs $1.25 per square foot. How much will it cost Alex to make 12 pennants?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 22$
$ _____

Answer: $52.50

Explanation:
Each pendant is made up of a rectangle and a triangle.
Area of the rectangle = length x breadth = 3 x 1 = 3 ft²
Area of the triangle = 1/2 x base x height = 1/2 x 1 x 1 = 0.5 ft²
The total area of the pendant = 3+0.5 = 3.5 ft²
Number of pendants = 12
Area of the pendants = 12 x 3.5 = 42 ft²
Cost of each square feet of the pendant = $1.25
Total cost for all the 12 pendants = 12 x $1.25 = $52.50

Question 11.
Reasoning
A composite figure is formed by combining a square and a triangle. Its total area is 32.5 ft². The area of the triangle is 7.5 ft². What is the length of each side of the square? Explain.
_____ ft

Answer: 5 ft

Explanation:
Given:
The area of the composite figure = 32.5 ft²
The area of the triangle = 7.5 ft²
The area of the square = 32.5 – 7.5 = 25
side x side = 25
side² = 25
side = root 25 = 5 ft

H.O.T. – Page No. 282

Focus on Higher Order Thinking

Question 12.
Represent Real-World Problems
Christina plotted the shape of her garden on graph paper. She estimates that she will get about 15 carrots from each square unit. She plans to use the entire garden for carrots. About how many carrots can she expect to grow? Explain.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 23$
______ carrots

Answer: 300 carrots

Explanation:
This shape is divided into two triangles and a square.
Area of figure = 2(1/2 x 2 x 2) + 4(4) = 4 + 16 = 20 square units
Number of carrots per square unit = 300
Total number of carrots = 20 x 15 = 300

Question 13.
Analyze Relationships
The figure shown is made up of a triangle and a square. The perimeter of the figure is 56 inches. What is the area of the figure? Explain.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 24$
_____ in²

Answer: 192 in²

Explanation:
Given:
The perimeter of the figure = 56 inches
The figure is divided into a square and a triangle.
10 + 10 + 3s = 56
3s = 36
s = 12
The area of a triangle = 1/2 x 12 x 8 = 48 in²
The area of a square = 12 x 12 = 144 in²
Total area of the figure = 144 + 48 = 192 in²

Question 14.
Critical Thinking
The pattern for a scarf is shown at right. What is the area of the scarf? Use 3.14 for π.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 25$
_____ in²

Answer: 243 in²

Explanation:
Area of the rectangle in the given figure = 28 x 15 = 420 in²
Area of two semicircles = 2 (1/2 πr² ) = 3.14 x 7.5 x 7.5 = 176.625 in²
Area of the shaded region = 420 – 176.625 = 243 in²(approx)

Question 15.
Persevere in Problem Solving
The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal size. A shade for the window will extend 4 inches beyond the perimeter of the window, shown by the dashed line around the window. Each square in the window has an area of 100 in².
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 26$
a. What is the area of the window? Use 3.14 for π.
_____ in²

Answer: a) 2228 in²

Explanation:
Area of the square = 100 in²
side x side = 100
Side = 10 in
Since the side of each square is 10 in and there are 4 squares.
The side length of the larger square (s) = 40 in
Area of the larger square = side x side = 40 x 40 = 1600 in²
Since the side of each square is 10 in and there are 2 squares.
The radius of the semi-circle = 20 in
Area of the semi-circle = 1/2(πr²) = 1/2(3.14 x 20²) = 628 in²
The area of the window = 1600 + 628 = 2228 in²

Question 15.
b. What is the area of the shade? Round your answer to the nearest whole number.
_____ in²

Answer: b) 3016 in²

Explanation:
The shade extends 4 inches beyond the shapes so the length of the bottom rectangle is 40+4+4 = 48 in
The length extends below the original square.
The height is now = 40+4 = 44 in
The radius of the semi-circle = 20+4 = 24 in
The new area of the figure = 48(44) + 1/2(3.14 x 24²) = 2112 + 904.32 = 3016.32 = 3016 in²

Guided Practice – Page No. 286

Find the surface area of each solid figure.

Question 1.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 27$
Total surface area: _____ ft²

Answer: 150 ft²

Explanation:
The base is a triangle with side lengths of 8 ft, 5 ft, 5 ft so the perimeter of the base = P = 8+5+5 = 18 ft
The height of the prism = 7 ft
The base is a triangle.
Area of the triangle = 1/2 (8) (3) = 12 ft²
The surface area formula for a prism is S = Ph + 2b
P = Perimeter = 18 h = height = 7 b = base = area of the triangle = 12
The surface area of the prism = 18(7) + 2(12) = 126 + 24 = 150 ft²

Question 2.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 28$
Total surface area: _____ m²

Answer: 503 m²

Explanation:
Given:
Dimensions of the cuboid:
Length = 11 m
Breadth = 9 m
Height = 7 m
The surface area of the cuboid = 2(lb+bh+hl) = 2(11 x 9 + 9 x 7 + 7 x 11) = 478m²
The dimensions of the cube:
Length of the side = 2.5 m
The surface area of the cube = 6a² = 6 x 2.5 x 2.5 = 37.5 m²
The surface area of the rectangular prism = 2.5 x 2.5 = 6.25
The surface area of the figure = The overlapping area is the area of the base of the cube
= 37.5 + 478 – 2(6.25) = 503 m²

Essential Question Check-In

Question 3.
How can you find the surface area of a composite solid made up of prisms?
Type below:
_____________

Answer: The surface area of the prisms, add them up, and then subtract the overlapping areas twice.

Explanation:
The surface area of a composite solid is made up of prisms by finding the surface areas of the prisms, adding them up, and then up, and then subtracting the overlapping areas.

Independent Practice – Page No. 287

Question 4.
Carla is wrapping a present in the box shown. How much wrapping paper does she need, not including overlap?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 29$
_____ in²

Answer: 164 in²

Explanation:
The surface area of the cuboid excluding the top = 2h(l+b) + lb = 2 x 4 ( 13 ) + 10 x 3 = 164 in²
The length of the wrapping paper = The surface area of the cuboid excluding the top = 164 in²

Question 5.
Dmitri wants to cover the top and sides of the box shown with glass tiles that are 5 mm square. How many tiles does he need?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 30$
_____ tiles

Answer: 3720 tiles

Explanation:
The surface area of the cuboid excluding the bottom = 2h(l+b) + lb = 2 x 9 (35) + 20 x 15 = 930 cm²
5mm = 0.5 cm
Area of a tile = Area of the square = a² = 0.5cm x 0.5cm = 0.25 cm²
Total number of tiles = 930/0.25 = 3720 tiles

Question 6.
Shera is building a cabinet. She is making wooden braces for the corners of the cabinet. Find the surface area of each brace.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 31$
_____ in²

Answer: 45 in²

Explanation:
The perimeter of the figure = P = 3(3) + 2(1) = 11 in
Base = B = 3(2) = 6 in
Height = h = 3
The surface area of the figure = Ph + 2B = 11 x 3 +2(6) = 33 + 12 = 45 in²

Question 7.
The doghouse shown has a floor, but no windows. Find the total surface area of the doghouse, including the door.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 32$
_____ ft²

Answer: 66ft²

Explanation:
Perimeter of the pentagon base (P) = 2(2.5) + 2(2) + 3 = 5 + 4 + 3 = 12
Area of the pentagon base by adding the area of the triangle and the area of the rectangle (B) = 1/2(3)(2) + 2(3) = 9
Height (h) = 2 + 2 = 4
The surface area of the figure = Ph + 2B = 12(4) + 2(9) = 48 + 18 = 66ft²

Eddie built the ramp shown to train his puppy to do tricks. Use the figure for 8–9.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 33$

Question 8.
Analyze Relationships
Describe two ways to find the surface area of the ramp.
Type below:
____________

Answer: One way is to use the formula S = Ph + 2B. Another way is to find the area of each face of the prism and add them up to get the total surface area.

Explanation:
The very first way to use the formula S = Ph + 2B where the trapeziums are the base. The second way is to find the area of each face of the prism and then add them up to get the total surface area.

Question 9.
What is the surface area of the ramp?
_____ in²

Answer: 3264 in²

Explanation:
P = Perimeter of the figure = 16(3) + 2 (20) + 16 = 104
B = Base of the figure = 1/2 (12) (16 + 3(16)) = 6 (16 + 48) = 6 (64) = 384
h = Height of the figure = 2
Surface area of the figure = Ph + 2B = 104(2) + 2(384) = 2496 + 768 = 3264 in²

Marco and Elaine are building a stand like the one shown to display trophies. Use the figure for 10–11.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 34$

Question 10.
What is the surface area of the stand?
_____ ft²

Answer: 58 ft²

Explanation:
Top:
Perimeter = P = 4(1) = 4
Base = B = 1(1) = 1
Height = h = 3
Top surface area = Ph + 2B = 4(3) + 2(1) = 14 ft²
Bottom :
Perimeter = P = 2(7) + 2(1) = 14 + 2 = 16
Base = B = 7(1) = 7
Height = h = 2
Top surface area = Ph + 2B = 16(2) + 2(7) = 46 ft²
Overlapping area = 1(1) = 1
The surface area of the figure = The surface area of the top + The surface area of the bottom – the overlapping area = 14 + 46 – 2 = 60 – 2 = 58 ft²

Question 11.
Critique Reasoning
Marco and Elaine want to paint the entire stand silver. A can of paint covers 25 square feet and costs $6.79. They set aside $15 for paint. Is that enough? Explain.
_____

Answer: No

Explanation:
Since the surface area is 58 ft², they will need 3 cans of paint. Since each can paints 25 ft² and we cannot buy a fraction of cans.
3 cans would then cost 6.79 x 3 = 20.37 so this is not enough.

Page No. 288

Question 12.
Henry wants to cover the box shown with paper without any overlap. How many square centimeters will be covered with paper?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 35$
_____ cm²

Answer: 2316 cm²

Explanation:
Given:
Length = 24cm Breadth = 27cm Height = 10cm
P = Perimeter = 2(24) + 2(27) = 48 + 54 = 102
B = Base = 24(27) = 648
h = Height = 10
Surface area of the figure = Ph + 2B = 102(10) + 2(648) = 1020 + 1296 = 2316 cm²

Question 13.
What If?
Suppose the length and width of the box in Exercise 12 double. Does the surface area S double? Explain.
_____

Answer: No

Explanation:
Given :
Length = 24cm x 2 = 48 cm Breadth = 27cm x 2 = 54 cm Height = 10cm
P = 2(48) + 2(54) = 96 + 108 = 204
B = 48(54) = 2592
New Surface area = Ph + 2B = 204(10) + 2(2592) = 2040 + 5184 = 7224 cm²
Double of surface area = 2 (2316) = 4632 cm²
So the new surface area is not double of the initial area.

H.O.T.

Focus on Higher Order Thinking

Question 14.
Persevere in Problem Solving
Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.5 feet and a height of 3.5 feet. Compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism.
Type below:
______________

Answer: The difference would just be the area in the bottom surface. It would be 6.25 ft² less.

Explanation:
The difference in the amount of paint would just be the area of the bottom surface. The area of the bottom surface is (2.5)² = 6.25.
Therefore she would paint 6.25 ft² less if she painted all but the bottom surface compared to painting the entire prism.

Question 15.
Interpret the Answer
The oatmeal box shown is shaped like a cylinder. Use a net to find the surface area S of the oatmeal box to the nearest tenth. Then find the number of square feet of cardboard needed for 1,500 oatmeal boxes. Round your answer to the nearest whole number
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 36$
_____ ft²

Answer: 138.28 in² , 1440 ft²

Explanation:
Given:
Dimensions of the cylinder:
Radius: 2 in
Height: 9 in
The total surface area of the cylinder = 2πr(r+h) = 2 x 22/7 x 2 (2 + 9) = 138.28 in²

The total number of square inches needed for 1,500 oatmeal boxes = 1,500 x 138.28 = 207,300 in²
1 ft = 12 in
(1 ft)² = (12 in)²
1 ft² = 144 in²
The total number of square feet needed for 1,500 oatmeal boxes (to the nearest whole number)
= 207,300/144 = 1440 ft²

Question 16.
Analyze Relationships
A prism is made of centimeter cubes. How can you find the surface area of the prism in Figure 1 without using a net or a formula? How does the surface area change in Figures 2, 3, and 4? Explain.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 37$
Type below:
______________

Answer: The surface area for the first 3 figures are the same. The surface area for figure 4 is greater than the surface area of the figures 1 – 3.

Explanation:
The surface area of the first 3 figures is the same. The 3 new faces on figure 2 have the same areas as the 3 visible faces that were removed when the top corner cube was removed. The surface area is then the same as it is for figure 1. Similarly, the areas of the new visible faces in figure 3 are equal to the areas of the visible faces removed from removing the corner cubes so the surface areas are the same as in figure 1. The surface area for figure 4 is greater than the surface areas of the figures 1 – 3. Removing the cube removed 2 of the visible faces (one from the top and one from the front side) but added 4 visible faces so the surface area increases.

Guided Practice – Solving Volume Problems – Page No. 292

Question 1.
Find the volume of the triangular prism.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Lesson 5: Solving Volume Problems img 38$
_____ ft³

Answer: 84 ft³

Explanation:
Base area of the prism = 1/2 x 8 x 3 = 12 ft²
Height of the prism = 7 ft
Volume of the prism = (12 x 7) ft³

Question 2.
Find the volume of the trapezoidal prism.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Lesson 5: Solving Volume Problems img 39$
_____ m³

Answer: 330 m³

Explanation:
Base area of the prism = 1/2 x (15 + 5) x 3 = 30 m²
Height of the prism = 11 m
Volume of the prism = (30 x 11) m³ = 330 m³

Question 3.
Find the volume of the composite figure.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Lesson 5: Solving Volume Problems img 40$
_____ ft²

Answer: Composite figure: 360 ft³

Explanation:
The volume of the triangular prism:
The base area of the prism = 1/2 x 4 x 6 = 12 ft²
Height = 6 ft
The volume of the triangular prism = 12 x 6 = 72 ft³

The volume of the rectangular prism:
The base area of the prism = 4 x 6 = 24 ft²
Height = 12 ft
The volume of the triangular prism = 12 x 24 = 288 ft³

Volume of the composite figure = (288 + 72)ft³ = 360 ft³

Find the volume of each figure.

Question 4.
The figure shows a barn that Mr. Fowler is building for his farm.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Lesson 5: Solving Volume Problems img 41$
_____ ft³

Answer: 40,000 ft³

Explanation:
Triangular prism:
B = Base area = 1/2 x 10 (40) = 200 cm²
Height = 50 cm
The volume of the triangular prism = Bh = 200 x 50 = 10,000 cm³
Rectangular prism:
B = Base area =40 x 15 = 600 cm²
Height = 50 cm
The volume of the triangular prism = Bh = 600 x 50 = 30,000 cm³
Total volume of the prism = 10,000 + 30,000 = 40,000 cm³

Question 5.
The figure shows a container, in the shape of a trapezoidal prism, that Pete filled with sand.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Lesson 5: Solving Volume Problems img 42$
_____ cm³

Answer: 385 cm³

Explanation:
B = Base area = 1/2 x 5 (10 + 12) = 55 cm²
Height = 7 cm
The volume of the container = Bh = 55 x 55 = 385 cm³

Essential Question Check-In

Question 6.
How do you find the volume of a composite solid formed by two or more prisms?
Type below:
______________

Answer: Finding the volume of each figure adding them up to get the volume of the composite solid.

Explanation:
To find the volume of the composite figure that can be divided into 2 or more prisms, find the volume of each prism and add them up to get the volume of the composite solid.

Independent Practice – Page No. 293

Question 7.
A trap for insects is in the shape of a triangular prism. The area of the base is 3.5 in² and the height of the prism is 5 in. What is the volume of this trap?
_____ in³

Answer: 17.5 in³

Explanation:
The volume of the trap = Base area x height = 3.5 x 5 = 17.5 in³

Question 8.
Arletta built a cardboard ramp for her little brothers’ toy cars. Identify the shape of the ramp. Then find its volume.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 43$
Shape: _________
Area: _________ in³

Answer: 525 in³

Explanation:
Base area = 1/2 x 6 x 25 = 75 in²
Height = 7 in
Volume of the figure = 75 x 7 = 525 in³

Question 9.
Alex made a sketch for a homemade soccer goal he plans to build. The goal will be in the shape of a triangular prism. The legs of the right triangles at the sides of his goal measure 4 ft and 8 ft, and the opening along the front is 24 ft. How much space is contained within this goal?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 44$
_____ ft³

Answer: 384 ft³

Explanation:
Base area = 1/2 x 4 x 8 = 16 ft²
Height = 24 ft
Volume of the figure = 16 x 24 = 384 ft³

Question 10.
A gift box is in the shape of a trapezoidal prism with base lengths of 7 inches and 5 inches and a height of 4 inches. The height of the gift box is 8 inches. What is the volume of the gift box?
_____ in³

Answer: 192 in³

Explanation:
Base area = 1/2 x 4 x (7+5) = 24 in²
Height = 8 in
Volume of the figure = 24 x 8 = 192 Base area = 1/2 x 6 x 25 = 75 in²
Height = 7 in
Volume of the figure = 75 x 7 = 525 in³

Question 11.
Explain the Error
A student wrote this statement: “A triangular prism has a height of 15 inches and a base area of 20 square inches. The volume of the prism is 300 square inches.” Identify and correct the error.
Type below:
____________

Answer: The error is measurement unit.

Explanation:
The volume of the prism is:
base area x height = 20 x 15 = 300 in³

Find the volume of each figure. Round to the nearest hundredth if necessary.

Question 12.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 45$
_____ in³

Answer: 97.2 in³

Explanation:
The volume of the hexagonal prism = 23.4 x 3 = 70.2 in³

Base area of the rectangular prism = 3 x 3 = 9 in²
The volume of the rectangular prism = Bh = 9 x 3 = 27 in³

Total volume of the figure = 70.2 + 27 = 97.2 in³

Question 13.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 46$
_____ m³

Answer: 316.41 m³

Explanation:
The volume of the rectangular prism on the left = Bh = [7.5 x 3.75] (3.75) = 105.47 m³
The volume of the rectangular prism on the right = Bh = [7.5 x 3.75](7.5) = 210.94 m³
Total volume of the composite figure = 105.47 + 210.94 = 316.41 m³

Question 14.
Multi-Step
Josie has 260 cubic centimeters of candle wax. She wants to make a hexagonal prism candle with a base area of 21 square centimeters and a height of 8 centimeters. She also wants to make a triangular prism candle with a height of 14 centimeters. Can the base area of the triangular prism candle be 7 square centimeters? Explain.
_____

Answer: No

Explanation:
The volume of the hexagonal prism = 21 x 8 = 168
The total volume of wax, 260 is equal to the sum of the volumes of each prism.
B is the base area of the triangular prism.
168 + 14B = 260 cm³
14B = 260 – 168
B = 6.6 cm³

Page No. 294

Question 15.
A movie theater offers popcorn in two different containers for the same price. One container is a trapezoidal prism with a base area of 36 square inches and a height of 5 inches. The other container is a triangular prism with a base area of 32 square inches and a height of 6 inches. Which container is the better deal? Explain.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 47$
Type below:
___________

Answer: The triangular prism is a better deal since it has a larger volume

Explanation:
The base area of the trapezoidal prism = 36 in²
The volume of the trapezoidal prism = Bh = 36 x 5 = 175 in³

The base area of the triangular prism = 32 in²
The volume of the rectangular prism = Bh = 32 x 6 = 192 in³

The triangular prism is a better deal since it has a larger volume.

H.O.T.

Focus on Higher Order Thinking

Question 16.
Critical Thinking
The wading pool shown is a trapezoidal prism with a total volume of 286 cubic feet. What is the missing dimension?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 48$
______ ft.

Answer: 3.5 ft

Explanation:
Area of the trapezoidal prism = B = 1/2 x 13 (2+x)
Volume of the figure = 286 cubic feet
V = Bh
286 = 1/2 x 13 (2+x)(8)
5.5 = (2+x)
x = 3.5 ft

Question 17.
Persevere in Problem Solving
Lynette has a metal doorstop with the dimensions shown. Each cubic centimeter of the metal in the doorstop has a mass of about 8.6 grams. Find the volume of the metal in the doorstop. Then find the mass of the doorstop.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 49$
______ grams

Answer: 75 cubic centimeter, 645 grams

Explanation:
V = Bh
B = Area of the triangle of base = 10 cm , height = 6 cm = 1/2 x 10 x 6 = 30 square centimeter
V = 30 x 2.5 = 75 cubic centimeter

1 cubic centimeter = 8.6 grams in mass
V = 75 cubic centimeter x 8.6 = 645 grams

Question 18.
Analyze Relationships
What effect would tripling all the dimensions of a triangular prism have on the volume of the prism? Explain your reasoning.
Type below:
____________

Answer: The volume is 27 times the original volume.

Explanation:
The area of the base = B = 1/2 (3b) (3h) = 9/2 (bh)
H is the height of the prism
The volume would be = 9/2 (bh) x (3H) = 27 [ 1/2 (bhH) ]

Therefore, The volume is 27 times the original volume.

Question 19.
Persevere in Problem Solving
Each of two trapezoidal prisms has a volume of 120 cubic centimetres. The prisms have no dimensions in common. Give possible dimensions for each prism.
Type below:
____________

Answer: A possible combination of dimension could be the height at 8 cm, base at 2 cm and 3 cm

Explanation:
The numbers that multiply to get 120 are 20 and 6 so let the first prism have a base area of 20 square centimetres and the height of 6 cm.
If the base area is 20, the height of the trapezoid and the length of the bases could be 8,2 and 3 respectively.

The other numbers that multiply to get 120 are 4 and 30 so let the second prism have a base area of 30 square centimetres and the height of 4 cm.
If the base area is 30, the height of the trapezoid and the length of the bases could be 10,1 and 5 respectively.

9.1, 9.2 Circumference and Area of Circles – Page No. 295

Find the circumference and area of each circle. Use 3.14 for π. Round to the nearest hundredth if necessary.

Question 1.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 50$
C = _________ m
A = _________ m²

Answer:
C = 43.96 m
A = 153.86 m²

Explanation:
C = 2 πr = 2 π(7) = 14 (3.14) = 43.96 m
A = πr² = 3.14 (7)² = 153.86 m²

Question 2.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 51$
C = _________ ft
A = _________ ft²

Answer:
C = 37.68 ft
A = 113.04 ft²

Explanation:
Diameter = 12 ft
Radius = d/2 = 12/2 = 6 ft
C = 2 πr = 2 π(6) = 6 (3.14) = 37.68 ft
A = πr² = 3.14 (6)² = 113.04 ft²

9.3 Area of Composite Figures

Find the area of each figure. Use 3.14 for π.

Question 3.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 52$
______ m²

Answer: 180.48 m²

Explanation:
Area of the triangle = 1/2 x 16 x 10 = 80 m²
Area of the semicircle = 1/2 πr² = 1/2 (3.14) (8)² = 100.48 m²
The total area of the figure = 80 + 100.48 = 180.48 m²

Question 4.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 53$
______ cm²

Answer: 200 cm²

Explanation:
Area of the parallelogram = 4.5(20) = 90 cm²
Area of the rectangle = 20(5.5) = 110 cm²
The total area of the figure = 90 + 110 = 200 cm²

9.4, 9.5 Solving Surface Area and Volume Problems

Find the surface area and volume of each figure.

Question 5.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 54$
S = _________ cm²
V = _________ cm³

Answer:
S = 132 cm²
V = 60 cm³

Explanation:
Perimeter = 3+4+5 = 12 cm
Base area = Area of the triangle = 1/2 x 3 x 4 = 6
S = Ph + 2B = 12(10) + 2(6) = 120 +12 = 132 cm²

V = Bh = 6 x 10 = 60 cm³

Question 6.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 55$
S = _________ yd²
V = _________ yd³

Answer:
S = 54.5 yd²
V = 27.5 yd³

Explanation:
Perimeter = 2(2.5) + 2(2) + 4 = 13 cm
Base area = Area of the triangle + Area of the rectangle = 1/2 x 1.5 x 4 + 4(2)= 11
S = Ph + 2B = 13(2.5) + 2(11) = 32.5 +22 = 54.5 yd²

V = Bh = 11 x 2.5 = 27.5 yd³

Essential Question

Question 7.
How can you use geometry figures to solve real-world problems?
Type below:
______________

Answer: We can solve real-world problems by finding surface area and volume.
Example: We can find the amount of liquid in a tank by calculating its volume.

Explanation:
Real-world problems by finding surface area and volume.
Example1: We can find the amount of liquid in a tank by calculating its volume.
Example2: We can find the surface area of the house and find the amount of paint required to paint the house.

Page No. 296

Question 1.
What is the circumference of the circle?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 56$
a. 34.54 m
b. 69.08 m
c. 379.94 m
d. 1519.76 m

Answer: b. 69.08 m

Explanation:
Circumference = 2 πr = 2 π(11) = 22 (3.14) = 69.08 m

Question 2.
What is the area of the circle?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 57$
Options:
a. 23.55 m²
b. 47.1 m²
c. 176.625 m²
d. 706.5 m²

Answer: c. 176.625 m²

Explanation:
Diameter = 15 m
Radius = 7.5 m
Area of the circle = πr² = 3.14 (7.5)² = 176.625 m²

Question 3.
What is the area of the figure?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 58$
Options:
a. 28.26 m²
b. 36 m²
c. 64.26 m²
d. 92.52 m²

Answer: c. 64.26 m²

Explanation:
Area of the square = 6 x 6 = 36 m²
Radius = 6 m
Area of the quarter circle = 1/4 πr² = 1/4 x 3.14 (6)² = 28.26 m²
The total area of the figure = 36 + 28.26 = 64.26 m²

Question 4.
A one-year membership to a health club costs $480. This includes a $150 fee for new members that is paid when joining. Which equation represents the monthly cost x in dollars for a new member?
Options:
a. 12x + 150 = 480
b. $\frac{x}{12}$ + 150 = 480
c. 12x + 480 = 150
d. $\frac{x}{12}$ + 480 = 150

Answer: a. 12x + 150 = 480

Explanation:
If x is the monthly fee, then 12x is the total monthly fees.
The joining fee = $150
Total cost = $480
then,
12x + 150 = 480

Question 5.
What is the volume of the prism?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 59$
Options:
a. 192 ft³
b. 48 ft³
c. 69 ft³
d. 96 ft³

Answer: d. 96 ft³

Explanation:
B = Base area of the triangle = 1/2 x 8 x 2 = 8 ft²
Height = 12 ft
Volume of the triangular orism = Bh = 8(12) = 96 ft³

Question 6.
A school snack bar sells a mix of granola and raisins. The mix includes 2 pounds of granola for every 3 pounds of raisins. How many pounds of granola are needed for a mix that includes 24 pounds of raisins?
Options:
a. 16 pounds
b. 36 pounds
c. 48 pounds
d. 120 pounds
e. 120 pounds

Answer: a. 16 pounds

Explanation:
2/3 is equal to x/24 then 3 times 8 is equal to 24 and if 2 times 8 is equal to 16.

Question 7.
Find the percent change from $20 to $25.
Options:
a. 25% decrease
b. 25% increase
c. 20% decrease
d. 20% increase

Answer: b. 25% increase

Explanation:
25 – 20 = 5 divide by 20 = 1/4
When we find the percentage we get 25.
So we can say that there is an increase in 25%

Question 8.
Each dimension of the smaller prism is half the corresponding dimension of the larger prism.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 60$
a. What is the surface area of the figure?
_____ in²

Answer: 856 in²

Explanation:
Height of the top prism = 10/2 = 5
Length of the top prism = 16/2 = 8
Width of the top prism = 8/2 = 4
Perimeter = 2l + 2w = 2(8) + 2(4) = 16 + 8 = 24 in
B = lw = 8(4) = 32 in
Surface area of top prism= Ph + 2B = 24(5) + 2(32) = 184 in²

Height of the prism = 10
Length of the prism = 16
Width of the prism = 8
Perimeter = 2l + 2w = 2(16) + 2(8) = 32 + 16 = 48 in
B = lw = 16(8) = 128 in
Surface area of bottom prism= Ph + 2B = 48(10) + 2(128) = 736 in²

Area of overlapping region = 32 in²

The total surface area of the prism
= Surface area of top prism + Surface area of bottom prism – 2[Area of overlapping region ]
= 184 + 736 – 2(32) = 856 in²

Question 8.
b. What is the volume of the figure?
_____ in³

Answer: 1440 in³

Explanation:
Volume of top prism = Bh = 32(5) = 160 in³
Volume of bottom prism = Bh = 128(10) = 1280 in³
The total volume of the figure = 160 + 1280 = 1440 in³

EXERCISES – Page No. 298

Question 1.
In the scale drawing of a park, the scale is 1 cm: 10 m. Find the area of the actual park.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 61$
_____ m²

Answer: 450 m²

Explanation:
Multiply the dimensions of the scale drawing by 10 since 1 cm = 10 m
3cm by 1.5 cm = 30m by 15 m
Area = 30(15) = 450 m²

Question 2.
Find the value of y and the measure of ∠YPS.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 62$
y = __________ °
mYPS = __________ °

Answer: y = 8
mYPS = 40 °

Explanation:
140 + 5y = 180 [sum of angle on a line = 180°]
5y = 40
y = 8

mYPS = mRPZ = 5y [vertically opposite angles]
mYPS = 5(8) = 40°

Question 3.
Kanye wants to make a triangular flower bed using logs with the lengths shown below to form the border. Can Kanye form a triangle with the logs without cutting any of them? Explain.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 63$
_____

Answer: No

Explanation:
A side of a triangle must be greater than the difference of the other two sides and smaller than the sum of the other 2 sides.
The sum of the first 2 sides = 3+4 = 7 < 8
Therefore, he cannot form a triangle unless he cuts the logs.

Question 4.
In shop class, Adriana makes a pyramid with a 4-inch square base and a height of 6 inches. She then cuts the pyramid vertically in half as shown. What is the area of each cut surface?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 64$
_____ in²

Answer: 12 in²

Explanation:
Base = 4 in
Height = 6 in
Area of the triangle = 1/2 x 6 x 4 = 12 in²

Page No. 300

Find the circumference and area of each circle. Round to the nearest hundredth.

Question 1.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 65$
C = __________ in
A = __________ in²

Answer:
C = 69.08 in
A = 379.94 in²

Explanation:
Diameter = 22 in
Radius = d/2 = 22/2 = 11 in
C = 2 πr = 2 π(11) = 22 (3.14) = 69.08 in
A = πr² = 3.14 (11)² = 379.94 in²

Question 2.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 66$
C = __________ m
A = __________ m²

Answer:
C = 28.26 m
A = 63.59m²

Explanation:
Radius = 4.5 m
C = 2 πr = 2 π(4.5) = 9 (3.14) = 28.26 m
A = πr² = 3.14 (4.5)² = 63.59 m²

Find the area of each composite figure. Round to the nearest hundredth if necessary.

Question 3.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 67$
______ in²

Answer: 99 in²

Explanation:
Area of the square = 9 x 9 = 81 in²
Base of the triangle = 13 – 9 = 4 in
Area of the triangle = 1/2 x 4 x 9 = 18 in²
The total area of the figure = 81 + 18 = 99 in²

Question 4.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 68$
______ cm²

Answer: 420.48 cm²

Explanation:
Area of the rectangle = 16 x 20 = 320 cm²
Diameter = 16 cm
Radius = 16/2 = 8 cm
Area of the semi circle = 1/2 πr² = 1/2 x 3.14 (8)² = 100.48 cm²
The total area of the figure = 320 + 100.48 = 420.48 cm²

Find the volume of each figure.

Question 5.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 69$
______ in³

Answer: 420 in³

Explanation:
B = 7(5) = 35 in²
V = Bh = 35 x 12 = 420 in³

Question 6.
The volume of a triangular prism is 264 cubic feet. The area of a base of the prism is 48 square feet. Find the height of the prism.
______ in

Answer: 5.5 ft

Explanation:
V = Bh
264 = 48h
h = 264/48 = 5.5ft

Page No. 301

A glass paperweight has a composite shape: a square pyramid fitting exactly on top of an 8 centimeter cube. The pyramid has a height of 3 cm. Each triangular face has a height of 5 centimeters.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 70$

Question 7.
What is the volume of the paperweight?
______ cm³

Answer: 576 cm³

Explanation:
Pyramid:
B = 8 x 8 = 64 cm²
V = 1/3 Bh = 1/3 x 64 x 3 = 64 cm³
Prism:
B = 8 x 8 = 64 cm²
V = Bh = 64 x 8 = 512 cm³

The total volume of the figure = 64 + 512 = 576 cm³

Question 8.
What is the total surface area of the paperweight?
______ cm²

Answer: 400 cm²

Explanation:
Pyramid:
P = 4(8) = 32 cm
S = 1/2 Pl + B = 80 + 64 = 144 cm²

Prism:
P = 4(8) = 32 cm
S = Ph + 2B = 32(8) + 2(64) = 384 cm²
The total surface area of the prism
= Area of the prism + Area of the pyramid – 2[Area of the overlapping region]
= 144 + 384 – 2(64) = 400

Unit 4 Performance Tasks

Question 9.
Product Design Engineer
Miranda is a product design engineer working for a sporting goods company. She designs a tent in the shape of a triangular prism. The dimensions of the tent are shown in the diagram.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 71$
a. How many square feet of material does Miranda need to make the tent (including the floor)? Show your work.
______ ft²

Answer: 261 3/4 ft²

Explanation:
P = 2 x 7 1/2 + 8 = 22 1/2
B = 4/2 (8) (6) = 24
S = Ph + 2B = 22 1/2 x 9 1/2 + 2(24) = 213 3/4 + 48 = 261 3/4 ft²

Question 9.
b. What is the volume of the tent? Show your work.
______ ft³

Answer: 228 ft³

Explanation:
V = Bh = 24 x 9 1/2 = 228 ft³

Question 9.
c. Suppose Miranda wants to increase the volume of the tent by 10%. The specifications for the height (6 feet) and the width (8 feet) must stay the same. How can Miranda meet this new requirement? Explain
Type below:
____________

Answer: Increase the height to 10.45 ft

Explanation:
New volume = 1.10 x 228 = 250.8
250.8 = 24h
h = 10.45 ft

Unit 4 Performance Tasks (cont’d) – Page No. 302

Question 10.
Li is making a stand to display a sculpture made in art class. The stand will be 45 centimeters wide, 25 centimeters long, and 1.2 meters high.
a. What is the volume of the stand? Write your answer in cubic centimeters.
______ cm³

Answer: 135,000 cm³

Explanation:
B = 45 x 25 = 1125 cm²
V = Bh = 1125 x 120 = 135,000 cm³

Question 10.
b. Li needs to fill the stand with sand so that it is heavy and stable. Each piece of wood is 1 centimeter thick. The boards are put together as shown in the figure, which is not drawn to scale. How many cubic centimeters of sand does she need to fill the stand? Explain how you found your answer.
______ cm³

Answer: 116,702 cm³

Explanation:
Width = 45 – 2(1) = 43 ft
Length = 25 – 2(1) =23ft
Height = 120-2(1) = 118ft
B = 43 x 23 = 989 ft²
V = Bh = 989 x 118 = 116,702 ft³

Selected Response – Page No. 303

Question 1.
A school flag is in the shape of a rectangle with a triangle removed as shown.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 72$
What is the measure of angle x?
Options:
a. 50°
b. 80°
c. 90°
d. 100°

Answer: d. 100°

Explanation:
x = 50 + 50 = 100° [ Sum of two angles created by the 2 lines]

Question 2.
On a map with a scale of 2 cm = 1 km, the distance from Beau’s house to the beach is 4.6 centimetres. What is the actual distance?
Options:
a. 2.3 km
b. 4.6 km
c. 6.5 km
d. 9.2 km

Answer: a. 2.3 km

Explanation:
2/1 = 4.6/x
x = 4.6/2 = 2.3 km

Question 3.
Lalasa and Yasmin are designing a triangular banner to hang in the school gymnasium. They first draw the design on paper. The triangle has a base of 5 inches and a height of 7 inches. If 1 inch on the drawing is equivalent to 1.5 feet on the actual banner, what will the area of the actual banner be?
Options:
a. 17.5 ft²
b. 52.5 ft²
c. 39.375 ft²
d. 78.75 ft²

Answer: c. 39.375 ft²

Explanation:
1in = 1.5ft
The base of the triangle = 5 in = 1.5(5) ft = 7.5 ft
Height = 7 in = 7(1.5) ft = 10.5 ft
Area of the triangle = 1/2 x 7.5 x 10.5 = 39.375 ft²

Question 4.
Sonya has four straws of different lengths: 2 cm, 8 cm, 14 cm, and 16 cm. How many triangles can she make using the straws?
Options:
a. no triangle
b. one triangle
c. two triangles
d. more than two triangles

Answer: b. one triangle

Explanation:
The third side of a triangle must be smaller than the sum of the other two sides to form a triangle.
2+8 = 10<14
2+8 = 10<16
8+14 = 22>14
8+14 = 22>16
2+14 = 16=16
2+16 = 18>16

Therefore, only one triangle can be formed using the sides 8, 14, 16.

Question 5.
A one-topping pizza costs $15.00. Each additional topping costs $1.25. Let x be the number of additional toppings. You have $20 to spend. Which equation can you solve to find the number of additional toppings you can get on your pizza?
Options:
a. 15x + 1.25 = 20
b. 1.25x + 15 = 20
c. 15x − 1.25 = 20
d. 1.25x − 15 = 20

Answer: b. 1.25x + 15 = 20

Explanation:
If x is the number of additional toppings, then 1.25 x is the cost of the additional toppings.
This gives the total cost is 1.25x + 15
then,
1.25x + 15 = 20

Question 6.
A bank offers a home improvement loan with simple interest at an annual rate of 12%. J.T. borrows $14,000 over a period of 3 years. How much will he pay back altogether?
Options:
a. $15680
b. $17360
c. $19040
d. $20720

Answer: c. $19040

Explanation:
Simple interest = 14,000 x 0.12 x 2 = $5,040
Amount = $14,000 + $5,040 = $19040

Question 7.
What is the volume of a triangular prism that is 75 centimeters long and that has a base with an area of 30 square centimeters?
Options:
a. 2.5 cm³
b. 750 cm³
c. 1125 cm³
d. 2250 cm³

Answer: d. 2250 cm³

Explanation:
V = Bh = 30(75) = 2250cm³

Question 8.
Consider the right circular cone shown.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 73$
If a vertical plane slices through the cone to create two identical half cones, what is the shape of the cross section?
Options:
a. a rectangle
b. a square
c. a triangle
d. a circle

Answer: c. a triangle

Explanation:
Slicing through the vertex to create 2 identical half cones would create a cross-section that is a triangle.

Page No. 304

Question 9.
The radius of the circle is given in meters. What is the circumference of the circle? Use 3.14 for π.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 74$
a. 25.12 m
b. 50.24 m
c. 200.96 m
d. 803.84 m

Answer: b. 50.24 m

Explanation:
Circumference = 2 πr = 2 π(8) = 16 (3.14) = 50.24 m

Question 10.
The dimensions of the figure are given in millimeters. What is the area of the two-dimensional figure?
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 75$
Options:
a. 39 mm²
b. 169 mm²
c. 208 mm²
d. 247 mm²

Answer: c. 208 mm²

Explanation:
Area of the square = 13 x 13 = 169 mm²
Area of the triangle = 1/2 x 13 x 6 = 39 mm²
The total area of the figure = 169 + 39 = 208 mm²

Question 11.
A forest ranger wants to determine the radius of the trunk of a tree. She measures the circumference to be 8.6 feet. What is the trunk’s radius to the nearest tenth of a foot?
Options:
a. 1.4 ft
b. 2.7 ft
c. 4.3 ft
d. 17.2 ft

Answer: a. 1.4 ft

Explanation:
Circumference = 2 πr = 8.6 ft
r = 8.6/2 π = 1.4 ft

Question 12.
What is the measure in degrees of an angle that is supplementary to a 74° angle?
Options:
a. 16°
b. 74°
c. 90°
d. 106°

Answer: d. 106°

Explanation:
Sum of supplementary angles = 180°
x + 74° = 180°
x = 106°

Question 13.
What is the volume in cubic centimeters of a rectangular prism that has a length of 6.2 centimeters, a width of 3.5 centimeters, and a height of 10 centimeters?
Options:
a. 19.7 cm³
b. 108.5 cm³
c. 217 cm³
d. 237.4 cm³

Answer: c. 217 cm³

Explanation:
V = Bh
B = 6.2 x 3.5 = 21.7 cm²
h = 10 cm
V = 21.7 x 10 = 217 cm³

Question 14.
A patio is the shape of a circle with diameter shown.
$Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume img 76$
What is the area of the patio? Use 3.14 for π.
Options:
a. 9 m²
b. 28.26 m²
c. 254.34 m²
d. 1017.36 m²

Answer: c. 254.34 m²

Explanation:
Diameter = 18 m
Radius = 18/2 = 9 m
Area of the patio = πr² = 3.14 (9)² = 254.34 m²

Question 15.
Petra fills a small cardboard box with sand. The dimensions of the box are 3 inches by 4 inches by 2 inches.
a. What is the volume of the box?
______ in³

Answer: 24 in³

Explanation:
V = Bh
B = 3 x 4 = 12 in²
V = 12 x 2 = 24 in³

Question 15.
b. Petra decides to cover the box by gluing on wrapping paper. How much wrapping paper does she need to cover all six sides of the box?
______ in²

Answer: 76 in²

Explanation:
P = 2(3) + 2(4) = 6 + 8 = 14 in
S = Ph + 2B = 14 x 2 + 2 x 24 = 76 in²

Question 15.
c. Petra has a second, larger box that is 6 inches by 8 inches by 4 inches. How many times larger is the volume of this second box? The surface area?
Volume is _________ times greater.
Surface area is _________ times greater

Answer: Surface area is about 2.7 times larger

Explanation:
B = 6 x 8 = 48 in²
V = Bh = 48 x 4 = 192 in³
192/24 = 8
P = 2(6) + 2(8) = 12 + 16 = 28
S = Ph + 2B = 28(4) + 2(48) = 112 + 96 = 208 in²
208/76 = 2.7

Conclusion:

We wish the information provided in this article regarding the Go Math Grade 7 Chapter 9 Circumference, Area, and Volume is beneficial for all the students. Make use of the given links and practice well for the exams. If you have any quieries about HMH Go Math 7th Grade Chapter 9 Circumference, Area, and Volume you can post your comments in the below section.

Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review/Test

April 7, 2022March 28, 2022 by Go Math Answer Key

$go-math-grade-4-chapter-3-multiply-2-digit-numbers-review-test-answer-key$

Students of 4th grade can collect chapter 3 Multiply 2-Digit Numbers Go Math Homework Review/Test Answer key from this page in pdf format. All you have to do is click on the links provided over here and practice more from the HMH Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review/Test. However, students can score good marks in the exam.

Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review/Test

Moreover, educators and instructors can also make use of this Go Math Grade 4 Answer Key Homework FL Review/Test as a test paper to keep the exam and verify their student’s knowledge. We as a team designed this guide by providing detailed solutions for each and every question from Practice Tests, Chapter Tests, Cumulative Practice. Practice regularly by using the 4th Grade Go Math Chapter 3 Answer Key Review/Test and also use it as a quick reference to assess your knowledge after preparing the concepts within it.

Chapter 3: Review/Test

Review/Test – Page No. 131
Review/Test – Page No. 132
Review/Test – Page No. 133
Review/Test – Page No. 134

Review/Test – Page No. 131

Concepts and Skills

Question 1.
Explain how to find 14 × 19 by breaking apart the factors into tens and ones and finding the sum of the four partial products.

Answer: 266.

Explanation:
We can break 14 and 19 as 10+4 and 10+9 and to get the answer we will multiply both of the first two numbers by the other two. So we will multiply 10(10+9) and 4(10+9), then the values will be (100+90) and (40+36). By adding both we will get 100+90+40+36= 266

Question 2.
Explain how to find 40 × 80 using mental math.

Answer: 3600.

Explanation:
By using mental math we will multiply 4×8= 36 and then we will add zeros, so the answer will be 3600.

Estimate the product. Choose a method.

Question 3.
80 × 26

Answer: 2,080.

Explanation:
80
×26
———
480
+160
———–
2,080

Question 4.
19 × $67
$ ____

Answer: $1,273.

Explanation:
By breaking apart the factors into tens and ones and we can find the sum of the four partial products.
19×67= (10+9)×(60+7)
= (10×60)+(10×7)+(9×60)+(9×7)
= 600+70+540+63
= $1,273.

Question 5.
43 × 25

Answer: 1,075.

Explanation:
By breaking apart the factors into tens and ones and we can find the sum of the four partial products.
43 × 25= (40+3)×(20+5)
= (40×20)+(40×5)+(3×20)+(3×5)
= 800+200+60+15
= 1,075.

Question 6.
54 × 83

Answer: 4,482.

Explanation:
By breaking apart the factors into tens and ones and we can find the sum of the four partial products.
54 × 83= (50+4)×(80+3)
= (50×80)+(50×3)+(4×80)+(4×3)
= 4000+150+320+12
= 4,482.

Estimate. Then find the product.

Question 7.
$ 2 4
× 9 6
———–
Estimate: $ ________
Product: $ _________

Answer:
Estimate: $ 2,300
Product: $ 2,304

Explanation:
$ 2 4
× 9 6
———–
14 4
+ 216
———–
2,304

Question 8.
4 4
× 6 0
————
Estimate: _________
Product: _________

Answer:
Estimate: 2,600.
Product: 2,640.

Explanation:
4 4
× 6 0
————
00
+264
———–
2640

Question 9.
9 9
× 1 4
————
Estimate: _________
Product: _________

Answer:
Estimate: 1,400
Product: 1,386

Explanation:
9 9
× 1 4
————
396
+99
———–
1,386.

Question 10.
6 7
× 2 5
————
Estimate: _________
Product: _________

Answer:
Estimate: 1,700
Product: 1,675

Explanation:
6 7
× 2 5
————
335
+134
————
1,675

Question 11.
3 6
× 5 7
————
Estimate: _________
Product: _________

Answer:
Estimate: 2,000.
Product: 2,052.

Explanation:
3 6
× 5 7
————
252
+180
———–
2,052

Question 12.
$ 5 4
× 2 9
————
Estimate: $ _________
Product: $ _________

Answer:
Estimate: 1,600.
Product: 1,566.

Explanation:
$ 5 4
× 2 9
————
486
+108
———–
1,566

Question 13.
7 6
× 3 8
————
Estimate: _________
Product: _________

Answer:
Estimate: 2,900.
Product: 2,888.

Explanation:
7 6
× 3 8
————
608
+228
———–
2,888.

Question 14.
8 5
× 4 6
————
Estimate: _________
Product: _________

Answer:
Estimate: 3,900.
Product: 3,910

Explanation:
8 5
× 4 6
————
510
+340
———-
3,910.

Review/Test – Page No. 132

Fill in the bubble completely to show your answer.

Question 15.
Each month Sid’s parents put $75 into his college fund. How much do his parents put in the fund during 2 years?
Options:
a. $150
b. $450
c. $1,800
d. $15,300

Answer: c.

Explanation:
As Sid’s parents put $75 into his college fund, during two years Sid’s parent’s fund $75×24= $1800.

Question 16.
Mrs. Jenks wrote the correct answer to a homework problem on the board below. Which of the following could have been the homework problem?
$Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review Test img 1$
Options:
a. 5 × 4,000
b. 50 × 400
c. 50 × 40
d. 50 × 4,000

Answer: c.

Explanation:
Mrs. Jenks’s homework problem is 50 × 40 because 50 × 40= 2,000.

Question 17.
George buys 30 cartons of 18 eggs for the Community Pancake Breakfast. How many eggs does he buy?
Options:
a. 340
b. 354
c. 460
d. 540

Answer: d

Explanation:
As George bought 30 cartons of 18 eggs for the Community Pancake Breakfast, the number of eggs George bought is 30×18= 540.

Review/Test – Page No. 133

Fill in the bubble completely to show your answer.

Question 18.
Mrs. Sampson donated a carton of pencils for each of the 35 classes at Lancet Elementary School. Each carton holds 64 pencils. Which is the best estimate for the number of pencils Mrs. Sampson donated?
Options:
a. A 99
b. B 1,800
c. C 2,400
d. D 2,800

Answer: c.

Explanation:
As Mrs. Sampson donated a carton of pencils for each of the 35 classes at Lancet Elementary School, and each carton holds 64 pencils, so Mrs. Sampson donates 35×64= 2,240. And the estimated value is 2,400.

Question 19.
The school’s athletic department ordered 95 dozen badminton feather shuttles. How many feather shuttles were ordered?
Options:
a. A 2,280
b. B 1,140
c. C 1,030
d. D 114

Answer: b

Explanation:
One dozen is equal to 12. As school’s athletic department ordered 95 dozen badminton feather shuttles, so 95 dozens means
95×12= 1,140 badminton feather shuttles.

Question 20.
Jill sold 35 adult tickets and 48 child tickets for a fund-raising dinner. An adult ticket costs $18 and a child ticket costs $14. How much did Jill collect for the tickets?
Options:
a. A $1,354
b. B $1,302
c. C $1,232
d. D $1,102

Answer: b

Explanation:
As Jill sold 35 adult tickets and 48 child tickets for a fund-raising dinner and each adult ticket costs $18 and a child ticket costs $14, so total amount Jill collected is 35×$18= 630 and 48×$18= 672 by adding 630+672= $1,302.

Question 21.
Which shows a way to find 35 × 74?
Options:
a. A (30 × 7) + (30 × 4) + (70 × 3) + (70 × 5)
b. B (30 × 70) + (30 × 4) + (50 × 70) + (50 × 4)
c. C (30 + 70) + (30 + 4) + (70 + 30) + (70 + 5)
d. D (30 × 70) + (30 × 4) + (5 × 70) + (5 × 4)

Answer: d

Explanation:
By breaking apart the factors into tens and ones and finding the sum of the four partial products,
35 × 74= (30 × 70) + (30 × 4) + (5 × 70) + (5 × 4)

Question 22.
New seats are being delivered to the theater. There are 45 new seats for each row in a 15-row section. How many seats are being delivered?
Options:
a. A 60
b. B 400
c. C 675
d. D 1,000

Answer: c

Explanation:
As new seats are being delivered to the theater and there are 45 new seats for each row in a 15-row section, so the total number of new seats is 45×15= 675.

Review/Test – Page No. 134

Constructed Response

Question 23.
Gulfside Gifts has 48 boxes of postcards to sell. There are 24 postcards in each box. If the shop sells 3 boxes of postcards, how many postcards does the shop have left to sell? Explain how you found the answer.
______ remaining cards

Answer: 1,080 remaining cards.

Explanation:
As Gulfside Gifts has 48 boxes of postcards to sell and there are 24 postcards in each box. So total number of post cards are
48×24= 1,152. And the shop sold 3 boxes of postcards i.e 3×24= 72, so shop has left 1,152-72= 1,080 cards are remaining to sell.

Question 24.
Several steps in finding the product of 68 and 34 are shown below. Describe the remaining steps. Use pictures, words, or numbers. Then complete the multiplication.
$Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review Test img 2$
_____

Answer: 2,312.

Explanation:
68
× 34
———-
272
+ 204
———
2,312

Performance Task

Question 25.
A city is having a festival in a local park. Alison’s Bakery has agreed to donate $1,200 worth of baked goods for the event. The city wants to order 12 loaves of holiday bread, 18 dozen biscuits, 12 dozen bagels, and 14 dozen multigrain rolls.
A. Is the cost of the baked goods under the $1,200 donation limit? Use pictures, numbers, or words to explain how you found your answer.
$Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review Test img 3$

Answer: Yes, the donation is under $1,200.

Explanation:
As the city ordered 12 loaves of holiday bread, 18 dozen biscuits, 12 dozen bagels, and 14 dozen multigrain rolls. And holiday bread costs $20, one dozen busicuits costs $12, and one dozen bagels costs $28, 1 dozen multigrain rolls costs $22. So by adding them
(12×20)+(12×18)+(12×28)+(14×22) we will get $1,100 which is less than $1,200

Question 25.
B. If yes, what could the city add to the order? If no, what could the city remove from the order?

Answer: The city can add whatever they want with the remaining $100. As $1,200-$1,100= $100.

Conclusion:

We hope the information shared about the Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review/Test has benefited you in your way. For more problems to practice check out our Go Math Grade 4 Answer Key Homework Practice FL Chapter 3 Multiply 2-Digit Numbers.

Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review/Test

April 7, 2022March 28, 2022 by Go Math Answer Key

$go-math-grade-4-chapter-7-add-and-subtract-fractions-review-test-answer-key$

Develop student’s math skills by referring to our provided Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review/Test. By using these review test solutions, students will surely get to know the weak and strong areas that they need to sharpen. After knowing them they will keep practicing on those areas with the help of HMH Go Math Grade 4 Review/Test Answer Key. Refer to the number of questions in Add and Subtract fractions with step by step explanation on our page.

Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review/Test

Go Math Grade 4 Answer Key Homework FL Review/Test holds all the topics in ch 7 Add and Subtract Fractions you might require as a part of preparation. Following this Go Math Grade 4 Review/Test Answer guide of Ch 7 Add and Subtract Fractions helps you to secure better marks in exams. Get a good grip on the Add and Subtract Fractions concepts & solve the sums within no time.

Chapter 7: Review/Test

Review/Test – Page No. 309
Review/Test – Page No. 310
Review/Test – Page No. 311
Review/Test – Page No. 312

Review/Test – Page No. 309

Choose the best term from the box.
$Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review Test img 1$

Question 1.
A number represented by a whole number and a fraction is a _________________ .
_________

Answer:
A number represented by a whole number and a fraction is a Mixed number.

Question 2.
A fraction that always has a numerator of 1 is a _______________ .
_________

Answer:
A fraction that always has a numerator of 1 is a Unit Fraction.

Write the fraction as a sum of unit fractions.

Question 3.
$\frac{4}{5}$ =

Answer:
$\frac{1}{5}$+$\frac{1}{5}$+$\frac{1}{5}$+$\frac{1}{5}$+$\frac{1}{5}$

Explanation:
For a unit fraction the numerator should be 1, here we can see the numerator as 4 so we will add $\frac{1}{5}$ four times. And the fraction can be written as the sum of a unit fraction as
$\frac{1+1+1+1}{5}$
= $\frac{1}{5}$+$\frac{1}{5}$+$\frac{1}{5}$+$\frac{1}{5}$+$\frac{1}{5}$.

Question 4.
$\frac{5}{10}$ =

Answer:
$\frac{1}{10}$+$\frac{1}{10}$+$\frac{1}{10}$+$\frac{1}{10}$+$\frac{1}{10}$

Explanation:
For a unit fraction the numerator should be 1, here we can see the numerator as 4 so we will add $\frac{1}{5}$ four times. And the fraction can be written as the sum of a unit fraction as
$\frac{1+1+1+1}{10}$
= $\frac{1}{10}$+$\frac{1}{10}$+$\frac{1}{10}$+$\frac{1}{10}$+$\frac{1}{10}$.

Write the mixed number as a fraction.

Question 5.
1 $\frac{3}{8}$ =
$\frac{□}{□}$

Answer: So the answer is $\frac{11}{8}$.

Explanation:
To convert a mixed number as a fraction, we will multiply the whole number by the fraction’s denominator, and then we will add to the numerator and the result will be on the top of the denominator.
1 $\frac{3}{8}$
= (1×8)+3
= 8+3
= 11
So the answer is $\frac{11}{8}$.

Question 6.
4 $\frac{2}{3}$ =
$\frac{□}{□}$

Answer: $\frac{14}{3}$.

Explanation:
To convert a mixed number as a fraction, we will multiply the whole number by the fraction’s denominator, and then we will add to the numerator and the result will be on the top of the denominator.
4 $\frac{2}{3}$
= 4×3
= 12
= 12+2
= 14.
The answer is $\frac{14}{3}$.

Question 7.
2 $\frac{3}{5}$ =
$\frac{□}{□}$

Answer: $\frac{13}{5}$.

Explanation:
To convert a mixed number as a fraction, we will multiply the whole number by the fraction’s denominator, and then we will add to the numerator and the result will be on the top of the denominator.
2 $\frac{3}{5}$
= 2×5
= 10
= 10+3
= 13.
The answer is $\frac{13}{5}$.

Write the fraction as a mixed number.

Question 8.
$\frac{12}{10}$ =
_____ $\frac{□}{□}$

Answer: 1 $\frac{1}{5}$.

Explanation:
To convert the fraction to a mixed number we will divide the numerator with denominator and write the whole number, then the remainder will be written above the denominator.
$\frac{12}{10}$
= 12÷10
= 1 $\frac{2}{10}$
= 1 $\frac{1}{5}$.

Question 9.
$\frac{10}{3}$ =
_____ $\frac{□}{□}$

Answer: 3 $\frac{1}{3}$.

Question 10.
$\frac{15}{6}$ =
_____ $\frac{□}{□}$

Answer: 2 $\frac{1}{2}$.

Explanation:
To convert the fraction to a mixed number we will divide the numerator with denominator and write the whole number, then the remainder will be written above the denominator.
$\frac{15}{6}$
= 15÷6
= 2 $\frac{3}{6}$
= 2 $\frac{1}{2}$.

Find the sum or difference.

Question 11.
$2 \frac{3}{8}+1 \frac{6}{8}$ =
_____ $\frac{□}{□}$

Answer: $\frac{33}{8}$.

Explanation:
$2 \frac{3}{8}+1 \frac{6}{8}$
= $\frac{19}{8}$+$\frac{14}{8}$
= $\frac{33}{8}$.

Question 12.
$\frac{9}{12}-\frac{2}{12}$ =
_____ $\frac{□}{□}$

Answer: $\frac{7}{12}$.

Explanation:
$\frac{9}{12}-\frac{2}{12}$
= $\frac{7}{12}$.

Question 13.
$5 \frac{7}{10}-4 \frac{5}{10}$ =
_____ $\frac{□}{□}$

Answer: $\frac{6}{5}$.

Explanation:
$5 \frac{7}{10}-4 \frac{5}{10}$
= $\frac{57}{10}$–$\frac{45}{10}$
= $\frac{12}{10}$
= $\frac{6}{5}$.

Question 14.
$4 \frac{1}{6}-2 \frac{5}{6}$ =
_____ $\frac{□}{□}$

Answer: $\frac{4}{3}$.

Explanation:
$4 \frac{1}{6}-2 \frac{5}{6}$
= $\frac{25}{6}$–$\frac{17}{6}$
= $\frac{8}{6}$
= $\frac{4}{3}$.

Question 15.
$3 \frac{2}{5}-1 \frac{4}{5}$ =
_____ $\frac{□}{□}$

Answer: $\frac{8}{5}$.

Explanation:
$3 \frac{2}{5}-1 \frac{4}{5}$
= $\frac{17}{5}$–$\frac{9}{5}$
= $\frac{8}{5}$.

Question 16.
$\frac{4}{12}+\frac{6}{12}$ =
$\frac{□}{□}$

Answer: $\frac{5}{6}$.

Explanation:
$\frac{4}{12}+\frac{6}{12}$
= $\frac{10}{12}$
= $\frac{5}{6}$.

Use the properties and mental math to find the sum.

Question 17.
(1 $\frac{2}{5}$ + $\frac{1}{5}$) + 2 $\frac{3}{5}$ =
_______ $\frac{□}{□}$

Answer: $\frac{21}{5}$.

Explanation:
(1 $\frac{2}{5}$ + $\frac{1}{5}$) + 2 $\frac{3}{5}$
= ( $\frac{7}{5}$ + $\frac{1}{5}$) + $\frac{13}{5}$
= $\frac{21}{5}$.

Question 18.
2 $\frac{4}{6}$ + (2 $\frac{3}{6}$ + 2 $\frac{2}{6}$) =
_______ $\frac{□}{□}$

Answer: $\frac{45}{6}$.

Explanation:
2 $\frac{4}{6}$ + (2 $\frac{3}{6}$ + 2 $\frac{2}{6}$)
= $\frac{16}{6}$ + ($\frac{15}{6}$) + $\frac{14}{6}$)
= $\frac{16}{6}$ +($\frac{29}{6}$)
= $\frac{45}{6}$.

Question 19.
$\frac{3}{10}$ + (2 $\frac{4}{10}$ + $\frac{7}{10}$) =
_______ $\frac{□}{□}$

Answer: $\frac{34}{10}$.

Explanation:
$\frac{3}{10}$ + (2 $\frac{4}{10}$ + $\frac{7}{10}$)
= $\frac{3}{10}$ + ($\frac{24}{10}$ + $\frac{7}{10}$)
= $\frac{3}{10}$ + ( $\frac{31}{10}$)
= $\frac{34}{10}$.

Review/Test – Page No. 310

Fill in the bubble completely to show your answer.

Question 20.
Eddie cut 2 $\frac{2}{4}$ feet of balsa wood for the length of a kite. He cut $\frac{3}{4}$ foot for the width of the kite. How much longer is the length of the kite than the width?
Options:
a. 1 $\frac{1}{4}$ feet
b. 1 $\frac{3}{4}$ feet
c. 2 feet
d. 3 $\frac{1}{4}$ feet

Answer: b

Explanation:
The length of Eddie cut is 2 $\frac{2}{4}$ feet and the width is $\frac{3}{4}$ feet, so the difference in the length and width is 2 $\frac{2}{4}$– $\frac{3}{4}$
= $\frac{10}{4}$–$\frac{3}{4}$
= $\frac{7}{4}$
= 1 $\frac{3}{4}$ feet.

Question 21.
On a trip to the art museum, Lily rode the subway for $\frac{7}{10}$ mile and walked for $\frac{3}{10}$ mile. How much farther did she ride on the subway than walk?
Options:
a. $\frac{3}{10}$ mile
b. $\frac{4}{10}$ mile
c. $\frac{7}{10}$ mile
d. 1 mile

Answer: d

Explanation:
As Lily rode $\frac{7}{10}$ mile and walked for $\frac{3}{10}$ mile, so she ride total of
$\frac{7}{10}$+ $\frac{3}{10}$
= 1 mile.

Question 22.
Pablo is training for a marathon. He ran 5 $\frac{4}{8}$ miles on Friday, 6 $\frac{5}{8}$ miles on Saturday, and 7 $\frac{4}{8}$ miles on Sunday. How many miles did he run on all three days ?
Options:
a. 1 $\frac{5}{8}$ miles
b. 12 $\frac{1}{8}$ miles
c. 19 $\frac{4}{8}$ miles
d. 19 $\frac{5}{8}$ miles

Answer: d

Explanation:
Pablo ran 5 $\frac{4}{8}$ miles on Friday and 6 $\frac{5}{8}$ miles on Saturday, 7 $\frac{4}{8}$ miles on Sunday. So total he ran on three days is
5 $\frac{4}{8}$+ 6 $\frac{5}{8}$+7 $\frac{4}{8}$
= $\frac{44}{8}$+ $\frac{53}{8}$+ $\frac{60}{8}$
= $\frac{157}{8}$
= 19 $\frac{5}{8}$ miles.

Question 23.
Cindy has two jars of paint.
$Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review Test img 2$
Which fraction below represents how much paint Cindy has?
Options:
a. $\frac{1}{8}$
b. $\frac{4}{8}$
c. $\frac{5}{8}$
d. $\frac{7}{8}$

Answer: c

Explanation:
The first jar contains $\frac{3}{8}$ and in the second jar $\frac{2}{8}$ of paint. So total paint Cindy contains
$\frac{3}{8}$+$\frac{2}{8}$
= $\frac{5}{8}$.

Review/Test – Page No. 311

Question 24.
Cole grew 2 $\frac{3}{4}$ inches last year. Kelly grew the same amount. Which fraction below represents the number of inches that Kelly grew last year?
Options:
a. $\frac{3}{4}$
b. $\frac{5}{4}$
c. $\frac{11}{4}$
d. $\frac{14}{4}$

Answer: c

Explanation:
As Cole grew 2 $\frac{3}{4}$ inches and Kelly has same amount which is 2 $\frac{3}{4}$ inches, so the fraction is
$\frac{11}{4}$ inches.

Question 25.
Olivia’s dog is 4 years old. Her cat is 1 $\frac{1}{2}$ years younger. How old is Olivia’s cat?
Options:
a. 5 $\frac{1}{2}$ years old
b. 3 $\frac{1}{2}$ years old
c. 2 $\frac{1}{2}$ years old
d. 1 $\frac{1}{2}$ years old

Answer: c

Explanation:
Olivia’s dog is 4 years old and her cat is 1 $\frac{1}{2}$ years younger, so Olivia’s cat is
= 4- 1 $\frac{1}{2}$
= $\frac{8}{2}$ – $\frac{3}{2}$
= $\frac{5}{2}$
= 2 $\frac{1}{2}$ years old.

Question 26.
Lisa mixed 4 $\frac{4}{6}$ cups of orange juice with 3 $\frac{1}{6}$ cups of milk to make a health shake. She drank 3 $\frac{3}{6}$ cups of the health shake. How much of the health shake did Lisa not drink?
Options:
a. $\frac{2}{6}$ cup
b. 4 $\frac{2}{6}$ cups
c. 7 $\frac{5}{6}$ cups
d. 11 $\frac{2}{6}$ cups

Answer: b

Explanation:
Lisa mixed 4 $\frac{4}{6}$ cups of orange juice with 3 $\frac{1}{6}$ cups of milk to make a health shake, so total health shake is 4 $\frac{4}{6}$+3 $\frac{1}{6}$
= $\frac{28}{6}$+ $\frac{19}{6}$
= $\frac{47}{6}$ cups of health shake. As she drank 3 $\frac{3}{6}$ cups of health shake, so
= $\frac{47}{6}$– 3 $\frac{3}{6}$
= $\frac{47}{6}$– $\frac{21}{6}$
= $\frac{26}{6}$
= 4 $\frac{2}{6}$ cups.

Question 27.
Keiko entered a contest to design a new school flag. Five twelfths of her flag has stars and $\frac{3}{12}$ has stripes. What fraction of Keiko’s flag has stars and stripes?
Options:
a. $\frac{8}{12}$
b. $\frac{8}{24}$
c. $\frac{2}{12}$
d. $\frac{2}{24}$

Answer: a

Explanation:
As Keiko’s flag has Five-twelfths of stars and $\frac{3}{12}$ of strips, so the fraction of Keiko’s flag has stars and stripes is
$\frac{5}{12}$+$\frac{3}{12}$
= $\frac{8}{12}$.

Review/Test – Page No. 312

Constructed Response

Question 28.
Ela is knitting a scarf from a pattern. The pattern calls for 4 $\frac{2}{12}$ yards of yarn. She has only 2 $\frac{11}{12}$ yards of yarn. How much more yarn does Ela need to finish knitting the scarf? Explain how you found your answer.
_____ $\frac{□}{□}$ yards

Answer: 1 $\frac{3}{12}$ yards.

Explanation:
Ela’s pattern calls for 4 $\frac{2}{12}$ yards of yarn and Ela has 2 $\frac{11}{12}$ yards of yarn only, so she needs
4 $\frac{2}{12}$– 2 $\frac{11}{12}$
= $\frac{50}{12}$ – $\frac{35}{12}$
= $\frac{15}{12}$
= 1 $\frac{3}{12}$ yards more.

Performance Task

Question 29.
Miguel’s class went to the state fair. The fairground is divided into sections. Rides are in $\frac{6}{10}$ of the fairground. Games are in $\frac{2}{10}$ of the fairground. Farm exhibits are in $\frac{1}{10}$ of the fairground.
A. How much greater is the fraction of the fairground with rides than the fraction with farm exhibits? Draw a model to prove your answer is correct.
$\frac{□}{□}$

Answer: $\frac{5}{10}$.

Explanation:
As the fairground is divided into sections, rides are in $\frac{6}{10}$ of the fairground, games are in $\frac{2}{10}$ of the fairground and Farm exhibits are in $\frac{1}{10}$ of the fairground. So the fraction of the fairground with rides than the fraction with farm exhibits is $\frac{6}{10}$– $\frac{1}{10}$
= $\frac{5}{10}$ greater than farm exhibits.

Question 29.
B. What fraction of the fairground has games and farm exhibits?
Write an equation to show your answer.

Answer: $\frac{3}{10}$.

Explanation:
The fraction of the fairground has games and farm exhibits is $\frac{2}{10}$+$\frac{1}{10}$
= $\frac{3}{10}$.

Question 29.
C. The rest of the fairground is refreshment booths. What fraction of the fairground is refreshment booths? Describe the steps you follow to solve the problem.

Answer: 9 $\frac{1}{10}$.

Explanation:
As the fairground is divided into sections, rides are in $\frac{6}{10}$ of the fairground, games are in $\frac{2}{10}$ of the fairground and Farm exhibits are in $\frac{1}{10}$ of the fairground. So the fraction of the fairground is refreshment booths $\frac{6}{10}$+$\frac{2}{10}$+$\frac{1}{10}$
= $\frac{9}{10}$.
To find a fraction of the fairground is refreshment booths we will subtract $\frac{9}{10}$ with 10, so
10- $\frac{9}{10}$
= $\frac{100-9}{10}$
= $\frac{91}{10}$
= 9 $\frac{1}{10}$.

Conclusion:

Hoping the data gave above on Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review/Test has benefited you a lot. For solving your doubts and need more questions related to the Ch 7 Add and Subtract Fraction refer to Go Math Grade 4 Solution Key & apply them in the real world.

Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test

April 7, 2022March 28, 2022 by Go Math Answer Key

Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test includes all the topics in Chapter 3. 3rd Grade Go Math Solutions Key covers different questions and provides a detailed explanation to all of them. You can test your preparation standard and understand the areas you are lagging and improvise on them.

Enhance your Subject Knowledge by taking the help of the Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test. Get to know the Topics existing in Go Math Ch 3 Understand Multiplication through the quick links present. To help you understand the concepts better we have mentioned detailed solutions for all the Problems in Chapter Test, Performance Test, Cumulative Practice, etc.

Chapter 3: Understand Multiplication Assessment Test

Test – Page 1 – Page No. 31
Test – Page 2 – Page No. 32
Test – Page 3 – Page No. 33
Test – Page 4 – Page No. 34
Test – Page 5 – Page No. 35
Test – Page 6 – Page No. 36

Test – Page 1 – Page No. 31

Question 1.
There are 4 flower beds in Max’s yard. Three rose bushes grow in each flower bed. How many rosebushes are there? Draw circles to model the problem and explain
how to solve it.
_______ rosebushes

Answer: 12 rosebushes

Explanation:

Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test

In the above figure, each big circle represents a flower bed and three small circles represent rosebushes. By using this model students can count the number of circles or add 3 + 3+ 3+ 3 = 12 or multiply 4 (flower beds) × 3 (rosebushes) = 12 rosebushes

Question 2.
Greta put 6 coins into each of 3 stacks. She wrote this number sentence to represent the total number of coins.
3 × 6 = 18
What is a related number sentence that also represents the total number of coins she has?
Options:
a. 6 × 3 = ■
b. 6 + 3 = ■
c. 3 + 3 + 3 = ■
d 6 × 6 = ■

Answer: a.

Explanation: For the written number sentence by 3 × 6 = 18 Greeta, only option a. 6 × 3 = 18 matches. The remaining options don’t give an answer as option a.

Question 3.
Cecile went fishing for three days at a lake. The first jump on the number line shows how many fish she caught the first day. She caught the same number of fish the next two days.
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 1 img 1$
Write the multiplication sentence that the number line shows.
_____ × _____ = _____

Answer: 3 × 3 = 9

Explanation:
Cecile made 3 jumps, for every jump she caught 3 fishes
Therefore 3 × 3 = 9.

Test – Page 2 – Page No. 32

Question 4.
Ben drew an array to show the number of video games he has.
Write a multiplication sentence for the array.
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 2 img 2$
_____ video games

Answer: 8 × 2 = 16.

Explanation:
In the given array each row contains 8 video games, total it has 2 rows
Therefore multiplication sentence for the array = 8 × 2 = 16.

Question 5.
Julissa makes 4 bracelets. She uses 9 charms on each bracelet.
For numbers 5a–5d, tell if the number sentence could be used to find the number of charms Julissa uses.
a. 4 + 9 = ■
i. yes
ii. no

Answer: No

Explanation: He cannot use 4 + 9 in this sentence as it gives result = 13 which not correct.

Question 5.
b. 3 + 3 + 3 + 3 = ■
i. yes
ii. no

Answer: No

Explanation: He cannot use 3 + 3 + 3 + 3 this sentence as it gives result = 13 which not correct.

Question 5.
c. 9 + 9 + 9 + 9 = ■
i. yes
ii. no

Answer: Yes

Explanation: He can use 9 + 9 + 9 + 9 = 36, which gives no of charms used on 4 bracelets.

Question 5.
d. 4 × 9 = ■
i. yes
ii. no

Answer: Yes

Explanation: He can use 4 × 9 = 36, which gives no of charms used on 4 bracelets.

Question 6.
Edith sorts buttons into 4 groups for her art project. Each group contains 6 buttons. How many buttons does Edith sort? Make a bar model to solve the problem.
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 2 img 3$
_____ buttons

Answer: 24 buttons.

Explanation: Given that Edith sorts buttons into 4 groups, where each group contains 6 buttons.

Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test

From the given info, we drew the above diagram, from the above model total no of buttons = 6+6+6+6 = 24 buttons

Question 7.
Select the number sentences that show the Commutative Property of Multiplication. Mark all that apply.
Options:
a. 5 × 2 = 5 + 5
b. 6 × 0 = 6
c. 7 × 5 = 5 × 7
d. 8 × 1 = 1 × 8
e. 9 × 1 = 9

Answer: c,d.

Explanation:
Commutative Property of Multiplication means a × b = b × a.
Therefore options b and c, 7 × 5 = 5 × 7 and 8 × 1 = 1 × 8 shows the property.

Test – Page 3 – Page No. 33

Question 8.
There are 5 tables in the library. Four students are sitting at each table. How many students are sitting in the library?
_____ students

Answer: 5 × 4 = 20 students

Explanation:
Given that there 5 tables in the library, 4 students are sitting on each table
Therefore total no of students = 5 × 4 = 20 students.

Question 9.
Keisha needs 3 equal lengths of rope for a Field Day activity. The jump on the number line shows the length of one rope in yards. How many yards of rope does Keisha need?
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 3 img 4$
_____ yards

Answer: 15 yards.

Explanation:
Given that there are 3 equal length rope
From the number line length of the one rope = 5 yards
Since he is having 3 ropes, the total length of all the 3 ropes = 5 × 3 = 15 yards.

Question 10.
Anna’s mom makes 3 sandwiches every school day. Each sandwich gets 3 slices of cheese. How many slices of cheese will Anna’s mom need for all the sandwiches she makes on 2 school days?
_____ slices of cheese

Answer: 18 slices of cheese.

Explanation: No of Sandwiches Anna’s mom make = 3
Each sandwich having 3 slices of cheese, no of cheese in 3 sandwiches = 3 × 3 = 9
Therefore to make 3 sandwiches for 2 days, the number of cheese slices needed = (3 ×3) × 2 = 18.

Question 11.
Angelo stacked 30 cans of soup collected during a food drive.
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 3 img 5$
Select other ways Angelo could arrange the same number of cans. Mark all that apply.
Options:
a. 1 row of 30
b. 5 rows of 6
c. 6 rows of 6
d. 8 rows of 4
e. 10 rows of 3

Answer: a, b, e.

Explanation: Total no of soup cans = 30, therefore only by arranging as given in options a, b, e, gives us 30 cans.

Test – Page 4 – Page No. 34

Question 12.
Choose the number that makes the sentence true.
The product of any number and $Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 4 img 6$ is zero.
_____

Answer: Product of any number and zero is zero

Explanation:

The product of any number and Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test is zero.

Question 13.
Ellen made this array to show that 2 × 9 = 18.
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 4 img 7$
Part A
Ellen says that 9 × 2 = 18. Is Ellen correct? Draw an array to explain your answer.
i. yes
ii. no

Answer: Yes

Explanation: Yes, Ellen is correct. 9 × 2 = 18

Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test

Question 13.
Part B
Which number property supports your answer? Explain.
________

Answer: Commutative Property of Multiplication.

Explanation: The given array shows 2 × 9 = 18 and 9 × 2 = 18, which is a Commutative Property of Multiplication, so Ellen is correct.

Question 14.
Abdul has a collection of stamps. He puts the stamps in 2 equal groups. There are 7 stamps in each group. How many stamps does Abdul have? Use the number line to show your work.
$Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test Test - Page 4 img 8$
_____ stamps

Answer: 14 stamps.

Explanation:
Given that Abdul has 2 equal groups of stamps
Each group contains 7 stamps in it, so total stamps in both groups = 7 × 2 = 14 stamps.

Test – Page 5 – Page No. 35

Question 15.
Hudson and Asher each collect comic books.
Part A
Hudson sorts his comic books into 3 piles. Each group has 7 comic books. How many comic books does he have?
_____ comic books

Answer: 21 comic books

Explanation:
Given that Hudson sorted his books into 3 piles
Each group has 7 comic books
Total no of comic books in 3 piles = 3 × 7 = 21.

Question 15.
Part B
Asher sorts his comic books into 4 piles. Each pile has 2 comic books in it. Write a multiplication sentence to show how many comic books Asher has.
Then find how many comic books Hudson and Asher have.

Answer: 2 × 4 = 8; 21 + 8 = 29 comic books

Explanation:
Given that Asher sorted his comic books into 4 piles
Each group has 2 comic books
Total no of comic books in 3 piles = 2 × 4 = 8
Total no of comic books both Hudson and Asher have = 21 + 8 = 29.

Question 16.
Aiden sees 4 lifeguard towers at the beach. Each tower has 1 lifeguard. Write a multiplication sentence to show the number of lifeguards Aiden sees.
_____ × _____ = _____ lifeguard towers

Answer: 4 lifeguards.

Explanation: 4 × 1 = 4 lifeguards.

Question 17.
Jorge spends 7 minutes completing each of 4 puzzles. He can use 7 × 4 to find the total amount of time he spends on the puzzles.
For numbers 17a–17d, choose Yes or No to show which expressions are equal to 7 × 4 .
a. 7 + 4
i. yes
ii. no

Answer: No

Explanation: No, 7 × 4 = 28, where in 7 + 4 = 11.

Question 17.
b. 7 + 7 + 7 + 7
i. yes
ii. no

Answer: Yes

Explanation: Yes, 7 × 4 = 28, where in 7 + 7 + 7 + 7 = 28.

Question 17.
c. 4 + 4 + 4 + 4 + 4 + 4 + 4
i. yes
ii. no

Answer: Yes

Explanation: Yes, 7 × 4 = 28, where in 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28.

Question 17.
d. 7 + 7 + 7 + 7 + 7 + 7 + 7
i. yes
ii. no

Answer: No

Explanation: No, 7 × 4 = 28, where in 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49.

Test – Page 6 – Page No. 36

Question 18.
Maya buys 3 bags of dried pears. Each bag contains 6 dried pears.
Select the number sentences that show all the dried pears Maya buys. Mark all that apply.
Options:
a. 3 + 3 + 3 = 9
b. 3 + 3 + 3 + 3 + 3 + 3 = 18
c. 6 + 3 = 9
d. 6 + 6 + 6 = 18
e. 3 × 6 = 18
f. 9 + 9 = 18

Answer: b, d, and e

Explanation:
Given that Maya buys 3 bags of dried pears
Each bag contains 6 dried pears = 3 × 6 = 18
Therefore options b, d, and e match the dried pears Maya buys.

Question 19.
Javier is making 6 smoothies. He puts 4 strawberries and 1 banana in each smoothie.
Part A
Write the total number of strawberries and bananas he uses. Write a multiplication sentence for each
______ strawberries ______ bananas

Answer: 6 × 4 = 24 strawberries, 6 × 1 = 6 bananas.

Explanation:
Given that Javier is making 6 smoothies, uses 4 strawberries and 1 banana in each smoothie
Therefore to make 6 smoothies no of strawberries needed = 6 × 4 = 24 strawberries,
And the number of bananas needed to make 6 smoothies = 6 × 1 = 6 bananas.

Question 19.
Part B
After making 6 smoothies, Javier has 9 strawberries and 4 bananas left. What is the greatest number of smoothies he can make with that fruit if he uses the same recipe for all the smoothies? Draw models and use them to explain.

Answer: At most, he can make 2 more smoothies.

Explanation:

Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Assessment Test

He can make 4 smoothies with 1 banana each, but only 2 smoothies with 4 strawberries each, so the greatest number of smoothies he can make is 2. There will be 2 bananas and 1 strawberry left.

Summary

We believe the knowledge shed regarding the Go Math Grade 3 Chapter 3 Assessment Test has helped you in your way of preparation. If you need any assistance check out the Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication and resolve your doubts at the moment.

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test

April 7, 2022March 28, 2022 by Go Math Answer Key

Enhance your skills using the Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test. Score better grades in the exam by practicing using the 3rd Grade Go Math Answer Key Ch 9 Compare Fractions Assessment Test. We have listed all the topics of Chapter 9 in our Assessment Test and even provided Solutions to all the problems given.

Students can check how much they understood the topics by solving the Questions in Grade 3 Go Math Chapter 9 Compare Fractions Assessment Test. Get acquainted with the areas you are lagging and improvise on them accordingly.

Chapter 9: Compare Fractions Assessment Test

Test – Page 1 – Page No. 91
Test – Page 2 – Page No. 92
Test – Page 3 – Page No. 93
Test – Page 4 – Page No. 94
Test – Page 5 – Page No. 95
Test – Page 6 – Page No. 96

Test – Page 1 – Page No. 91

Question 1.
Frank and Dwayne weed their gardens that are the same size. Frank’s garden is divided into 6 equal sections. Dwayne’s garden is divided into 4 equal sections. Each boy has weeded 2 sections of his garden.
Write a fraction to describe what part of his garden each boy has weeded. Then tell who weeded a larger area. Explain
_________

Answer: Dwayne’s part 2/4 > Frank’s part 2/6.

Explanation:
Frank and Dwayne has the same size of gardens
Frank’s garden is divided into 6 equal sections
Dwayne’s garden is divided into 4 equal sections
Since each has weeded 2 sections of their gardens, Frank’s part would be = 2/6,
Dwayne’s part would be = 2/4.
Therefore Dwayne’s part 2/4 > Frank’s part 2/6,
Since the garden with a greater number of sections will have a smaller area per section.

Question 2.
Eli, Beth, and Cory are reading the same book for class. Eli read $\frac{3}{4}$ of his book. Beth read $\frac{3}{8}$ of her book and Cory read $\frac{3}{6}$ of his book. For 2a–2d, choose Yes or No to indicate whether the comparisons are correct.
a. $\frac{3}{4}$ > $\frac{3}{8}$
i. yes
ii. no

Answer: Yes.

Explanation: 3/4 > 3/8. Since both are reading the same book and book with a greater number of sections will have a lesser value.

Question 2.
b. $\frac{3}{6}$ < $\frac{3}{8}$
i. yes
ii. no

Answer: No, 3/6 < 3/8.

Explanation: It’s not true, Since both are reading the same book, and books with a greater number of sections will have a lesser value. Therefore 3/6 > 3/8).

Question 2.
c. $\frac{3}{8}$ = $\frac{3}{6}$
i. yes
ii. no

Answer: No

Explanation: 3/8 = 3/6. Both are not equal, since the same book has been divided into different no of parts. Therefore both are not equal.

Question 2.
d. $\frac{3}{6}$ < $\frac{3}{4}$
i. yes
ii. no

Answer: Yes.

Explanation: 3/6 < 3/4. Since both are reading the same book and book with a greater number of sections will have a lesser value.

Question 3.
Mark and Lisa are on the swim team. Mark swims $\frac{3}{8}$ mile each day. Lisa swims $\frac{5}{8}$ mile each day. Which statement is correct? Mark all that apply.
Options:
a. Mark swims farther than Lisa each day.
b. Lisa swims the same distance as Mark each day.
c. Lisa swims less than 1 mile each day.
d. Lisa swims farther than Mark each day.

Answer: Both c and d are correct.

Explanation: Lisa swims less than 1 mile while 5/8 mile each day and She swims farther than Mark each day. i.e. 5/8 > 3/8.

Test – Page 2 – Page No. 92

Question 4.
MacKenzie and Cassie used fabric to make costumes for a play. MacKenzie used $\frac{3}{4}$ yard of fabric and Cassie used $\frac{5}{6}$ yard. Who used more fabric? Explain the strategy you used to solve the problem.
_________

Answer:
MacKenzie divided fabric into 4 equal parts and used 3/4 of it. So, 1/4 of it is left. Cassie divided the same yard of fabric into 6 equal parts and used 5/6 of it. Here 1/6 part of it is left, by comparing leftover pieces we can conclude 1/4 > 1/6. Since the larger piece was left with MacKenzie, Cassie has used more fabric.

Question 5.
The soccer team practices passing for $\frac{3}{4}$ hour and shooting for $\frac{4}{5}$ hour. On which drill does the team spend less time? Explain how you can use the model to find the answer.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 2 img 1$

Answer: From the model, we can understand that team has spent less time on Passing. Since the model for 3/4 is shorter than the model for 4/5.

Question 6.
Andrew bought $\frac{7}{8}$ pound of mixed nuts. Margaret bought $\frac{5}{8}$ pound of mixed nuts. Use the fractions and symbols to show which amount is greater.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 2 img 2$

Answer: 5/8 < 7/8 or 7/8 > 5/8

Explanation:

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test

Test – Page 3 – Page No. 93

Question 7.
Mr. Worth opened new jars of 4 different colors of paint for an art project. All of the jars were the same size.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 3 img 3$
Part A Draw lines to show how Mr. Worth could divide one jar of paint into halves, one into thirds, one into fourths, and one into sixths.
Part B Students in his class used an equivalent amount of two paint colors. Use the models to show the amount of paints used. Write two pairs of equivalent fractions to represent the models.

Answer: The below figure represents halves, one-third, one into fourth, one into sixths.

Explanation:

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test
Representing Halves one-third one into fourth one into sixths
Therefore from the above figure, two pairs of equivalent fractions representing the models are 1/2 = 2/4, 1/3 = 2/6.

Question 8.
Dalton rode his skateboard for $\frac{3}{4}$ mile. Amelia rode her skateboard for an equal distance. What is an equivalent fraction that describes how far Amelia rode? Use the models to show your work.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 3 img 4$
$\frac{3}{4}$ = $\frac{□}{□}$

Answer: $\frac{3}{4}$ = $\frac{6}{8}$.

Explanation: Below two pictures give Dalton and Amelia distance covered while riding a skateboard. Though they both rode the same distance to represent them in similar different fractions. We can divide Dalton’s covered as in the 1^st circle and Amelia’s in 2^nd Circle. From the pictures, equivalent fractions will be 3/4 for Dalton and 6/8 for Amelia.

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test

Question 9.
Mr. Barrows opens 2 packs of paper. He puts $\frac{2}{5}$ of a pack in one pile and $\frac{3}{5}$ of a pack in another pile. Which pile has more paper? Show your work.
$\frac{□}{□}$ of a pack

Answer: 3/5 of a pack has more papers.

Explanation: The pile with 3/5 of a pack has more papers. Since 2/5 is there in another pack.

Test – Page 4 – Page No. 94

Question 10.
Treyvon watched $\frac{2}{8}$ a movie. Juan watched $\frac{2}{6}$ of the same movie. Use >, =, or < to compare the parts that they watched.
$\frac{2}{8}$ _____ $\frac{2}{6}$

Answer: $\frac{2}{8}$ < $\frac{2}{6}$ or $\frac{2}{6}$ > $\frac{2}{8}$.

Question 11.
Alison used $\frac{7}{8}$ quart of orange juice and $\frac{3}{8}$ quart of cranberry juice to make some punch.
For 11a–11d, select True or False for each comparison.
a. $\frac{7}{8}$ < $\frac{3}{8}$
i. True
ii. False

Answer: False.

Explanation: 7/8 is greater than 3/8.

Question 11.
b. $\frac{7}{8}$ > $\frac{3}{8}$
i. True
ii. False

Answer: True.

Explanation: Since both have the same denominators, we can compare their numerators directly. Here 7 is greater than 3, therefore 7/8 is greater than 3/8.

Question 11.
c. $\frac{3}{8}$ < $\frac{7}{8}$
i. True
ii. False

Answer: True.

Explanation: $\frac{3}{8}$ < $\frac{7}{8}$

Question 11.
d. $\frac{3}{8}$ = $\frac{7}{8}$
i. True
ii. False

Answer: False.

Explanation: Both are not equal.

Question 12.
Will, Ann, and Jim are working on their science fair projects. Will has finished $\frac{1}{4}$ of his project. Ann has finished $\frac{3}{4}$ of her project, and Jim has finished $\frac{2}{3}$ of his project.
Part A
Who has finished less of their project, Will or Ann?
Explain how you know.
__________

Answer: Will has finished less compared to Ann.

Explanation: Given that will has finished 1/4 of his project wherein Ann has finished 3/4 of her project. Since 1/4 and 3/4 have the same denominator, so we can compare the numerator directly. Since 1 is less than 3, we can say 1/4 is less than 3/4. Thus Will has finished less part of his project compared to Ann.

Question 12.
Part B
Who has finished less of their project, Ann or Jim?
Explain how you know.
__________

Answer: 2/3 is less than 3/4. Therefore, Jim has finished less part of his project compared to Ann.

Explanation: Given that Jim has finished 2/3 of his project were in Ann has finished 3/4 of her project. Since denominators are not the same to compare first we shall make the same. Therefore multiply Jim’s work (2/3) with (4/4) which gives = 8/12 and Ann’s work (3/4) with (3/3) which gives = 9/12. Now by comparing numerators 8/12 is less than 9/12, which means Jim has finished less part of his project compared to Ann.

Test – Page 5 – Page No. 95

Question 13.
Sarah needs $\frac{4}{6}$ yard of ribbon to wrap a gift. She has 6 pieces of ribbon with the following lengths. She can cut the piece if it is too long. Mark all of the pieces of ribbon that Sarah could use.
Options:
a. $\frac{1}{2}$ yard
b. $\frac{6}{6}$ yard
c. $\frac{3}{8}$ yard
d. $\frac{4}{4}$ yard
e. $\frac{1}{3}$ yard
f. $\frac{5}{6}$ yard

Answer: Sarah could use 6/6 yard, 4/4 yard and 5/6 yard of ribbons to wrap gift.

Explanation:
Given that Sarah needs a 4/6 yard of ribbon to wrap a gift.
Lengths of available ribbons are 1/2, 6/6, 3/8, 4/4,1/3, and 5/6.
Comparing all the lengths with 4/6 – 6/6 and 5/6 are having the same denominators. So we compare only their numerators, both 6 and 5 are greater than 4. So these two ribbons are more than enough for her gift wrapping. With ribbon length, 4/4 yard – since complete ribbons all the parts of the ribbon are available thus this length also enough to wrap the gift. Remaining 1/2, 3/8, and 1/3 – we shall make their denominators equal to 4/6 to compare
multiply (1/2) with (3/3) = 3/6, 3 is less than 4 in 4/6. So this is not having enough length
multiply (1/3) with (2/2) = 2/6, 2 is also less than 4. So this also not having enough length.
multiply (3/8) with (6/6) = 18/48 and (4/6) with (8/8) = 32/48. Since 18 is less than 32, this ribbon length also won’t be enough to wrap gifts. Thus Sarah could use only 6/6 yard, 4/4 yard, and 5/6 yard of ribbons to wrap the gift.

Question 14.
There are 8 people having breakfast. Each person wants $\frac{1}{2}$ of an omelet. How many whole omelets are needed? Use the models to show your answer.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 5 img 5$
_____ omelets

Answer: Total they need 4 omelets.

Explanation:
Total no of having omelets are = 8
Each person need 1/2 of omelette, so for 8 persons = (1/2) * 8 = 4.

Question 15.
Michele mixed $\frac{3}{4}$ cup of flour with $\frac{1}{2}$ cup of water to make paste for an art project. Compare the fractions. Choose the symbol that makes the statement true.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 5 img 6$
$\frac{3}{4}$ _____ $\frac{1}{2}$

Answer: $\frac{3}{4}$ > $\frac{1}{2}$.

Explanation:

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test
Let’s make 3/4 and 1/2 denominators the same (1/2) * (2/2) = 2/4.
Since 3 is greater than 2, 3/4 > 1/2.

Question 16.
Jeff has three boxes that weigh $\frac{5}{8}$, $\frac{1}{8}$, and $\frac{3}{8}$ pound. Write the weights in order from least to greatest.

Answer: $\frac{1}{8}$, $\frac{3}{8}$, $\frac{5}{8}$.

Explanation: Weights in the least to greatest form 1/8, 3/8, 5/8.

Test – Page 6 – Page No. 96

Question 17.
Ben measures the lengths of three insects. Draw a line to match each length on the left to the word on the right that describes its place in the order of lengths.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 6 img 7$

Answer:

Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test

Question 18.
Kerri drew a model to show equivalent fractions.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 6 img 8$
Use the model to complete the number sentence.
$\frac{2}{3}$ = $\frac{□}{□}$

Answer: $\frac{2}{3}$ = $\frac{4}{6}$.

Explanation: Here from the model four parts are shaded out of 6, which also equal to $\frac{2}{3}$ by value.

Question 19.
Elaine brought $\frac{3}{4}$ pound of potato salad to a picnic. Jake brought $\frac{2}{3}$ pound of macaroni salad. Who brought more salad? Explain the strategy you used to solve the problem.

Answer: Elaine has brought more Salad compared to Jake.

Explanation:
Elaine has brought $\frac{3}{4}$ pound of potato salad
Jake brought $\frac{2}{3}$ pound of macaroni salad
Lets compare both parts by making their denominators same.Therefore multiply (3/4) * (3/3) = (9/12) and (2/3) * (4/4) = (8/12)
Since 8 is less than 9,$\frac{8}{12}$ < $\frac{9}{12}$.
Which means $\frac{2}{3}$ < $\frac{3}{4}$. Thus Elaine has brought more Salad compared to Jake.

Question 20.
It took Mike $\frac{2}{6}$ hour to clean his room.
$Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test Test - Page 6 img 9$
What fraction is equivalent to $\frac{2}{6}$ ?
$\frac{2}{6}$ = $\frac{□}{□}$

Answer: $\frac{2}{6}$ = $\frac{1}{3}$.

Final Words

Hope the knowledge shared regarding the Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Assessment Test. To know more such info feel free to reach us via comment box and we will get back to you. Check out Go Math Grade 3 Answer Key Chapter 9 Compare Fractions to know more related topics.

Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test

April 7, 2022March 28, 2022 by Go Math Answer Key

Test your level of understanding by taking the help of the Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test. Assess your strengths and weaknesses and allot time accordingly using the 3rd Grade Go Math Assessment Test Answer Key. With consistent practice, you can score better grades in your exam.

Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test contains all the topics of chapter 6. Enhance your subject knowledge using the 3rd Grade Go Math Solutions Key Chapter 6 Assessment Test. Teachers can use these 3rd Grade Go Math Answer Key Ch 6 Understand Division Assessment Test to test students on how much they understand topics. Detailed Solutions are provided for all the concepts and you can refer them to clear your queries.

Chapter 6: Understand Division Assessment Test

Test – Page 1 – Page No. 61
Test – Page 2 – Page No. 62
Test – Page 3 – Page No. 63
Test – Page 4 – Page No. 64
Test – Page 5 – Page No. 65
Test – Page 6 – Page No. 66

Test – Page 1 – Page No. 61

Question 1.
For numbers 1a–1d, select True or False for each equation.
a. 5 ÷ 1 = 5
i. True
ii. False

Answer: True.

Explanation: 5 ÷ 1 = 5, so answer is true.

Question 1.
b. 3 ÷ 3 = 1
i. True
ii. False

Answer: True.

Explanation: 3 ÷ 3 = 1, so the answer is true.

Question 1.
c. 4 ÷ 1 = 1
i. True
ii. False

Answer: False.

Explanation: 4 ÷ 1 = 4, not 1. So the answer is False.

Question 1.
d. 0 ÷ 1 = 0
i. True
ii. False

Answer: True.

Explanation: 0 ÷ 1 = 0, so the answer is true.

Question 2.
Elian is making 36 ounces of punch. He pours the same amount into each of 6 cups. How many ounces of punch does he pour into each cup?
Circle the amount to complete the sentence.
Elian pours $Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 1 img 1$ ounces of punch into each cup.
_____

Answer: 6 each cup.

Explanation:

Elian pours Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test ounces of punch into each cup.

Question 3.
Gina arranges her 21 puzzles in 7 equal stacks. How many puzzles does Gina put in each stack?
Shade squares to make an array to model the problem.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 1 img 2$

Answer: 3 puzzles.

Explanation:

Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test

Test – Page 2 – Page No. 62

Question 4.
Philip has 30 pennies that he exchanges for nickels. He exchanges 5 pennies for each nickel. How many nickels does Philip get?
Make equal groups to model the problem.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 2 img 3$
_____ nickels

Answer: 6 nickels.

Explanation: As Philips has 30 pennies and he exchanges 5 pennies for each nickel, so Philips get 30÷5= 6 nickels.

Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test

Question 5.
A book has 54 pages divided into 6 equal chapters.
How many pages are in each chapter?
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 2 img 4$
_____ pages

Answer: 9 pages.

Explanation: 54÷6= 9 pages.

Question 6.
Select the equations that the array represents.
Mark all that apply.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 2 img 5$
Options:
a. 2 × 4 = 8
b. 3 × 2 = 6
c. 6 ÷ 3 = 2
d. 2 × 3 = 6
e. 6 ÷ 2 = 3
f. 8 ÷ 2 = 4

Answer: b,c,d,e.

Explanation:
3 × 2 = 6
6 ÷ 3 = 2
2 × 3 = 6
6 ÷ 2 = 3

Test – Page 3 – Page No. 63

Question 7.
The 16 players at tennis camp are divided into 4 equal groups. How many players are in each group?
Part A
Draw jumps on the number line to model the problem.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 3 img 6$
Type below:
___________

Answer:

Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test

Question 7.
Part B
Write a division equation to represent the model.
_____ ÷ _____ = _____

Answer: 4

Explanation: 16÷4= 4

Question 8.
Max writes a total of 45 lines in his journal. Each journal entry is 9 lines long. How many journal entries does Max make?
Choose a number from the box to complete the sentence.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 3 img 7$
Max makes _____ journal entries.
_____

Answer: 5

Explanation: Max writes a total of 45 lines in his journal and each journal entry is 9 lines long, so 45÷9= 5 journal entries does Max makes.

Question 9.
A farmer sells baskets that hold 6 peaches each. Etta buys a total of 18 peaches. How many baskets of peaches does Etta buy?
Complete each equation to represent the problem.
6 × _____ = 18; 18 ÷ 6 = _____ ; _____ baskets

Answer: 3 baskets.

Explanation: As the farmer sells baskets that hold 6 peaches each and Etta buys a total of 18 peaches, the number of baskets of peaches does Etty bought is 18÷6= 3 baskets.
6 × 3 = 18;
18 ÷ 6 = 3

Question 10.
Penn has 12 eggs to use in some recipes. Select a way that he could divide all of the eggs equally among the recipes. Mark all that apply.
Options:
a. 6 eggs in each of 2 recipes
b. 5 eggs in each of 3 recipes
c. 3 eggs in each of 4 recipes
d. 4 eggs in each of 4 recipes
e. 2 eggs in each of 6 recipes
f. 4 eggs in each of 3 recipes

Answer: a,c,e,f.

Explanation:
6×2= 12
3×4= 12
2×6= 12
4×3= 12

Test – Page 4 – Page No. 64

Question 11.
Nancy made this array to model a division equation. Which equation could Nancy have modeled? Mark all that apply.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 4 img 8$
Options:
a. 63 ÷ 7 = 9
b. 54 ÷ 6 = 9
c. 72 ÷ 9 = 8
d. 63 ÷ 9 = 7

Answer: a,d.

Explanation:
63 ÷ 7 = 9
63 ÷ 9 = 7

Question 12.
Rico went for a bike ride around a 3-mile loop. He rode a total of 12 miles. How many times did Rico ride his bike around the loop?
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 4 img 9$
_____ times

Answer: 4 times.

Explanation: As Rico went for a bike ride around a 3-mile loop and rode a total of 12 miles, so 12÷3= 4 times Rico ride his bike around the loop.

Question 13.
Write the letter for each problem in the box next to its quotient.
Options:
A. 5 ÷ 5 _____ 0
B. 0 ÷ 5 _____ 5
C. 5 ÷ 1 _____ 1

Answer:
5 ÷ 5= 1
0 ÷ 5= 0
5 ÷ 1= 5.

Question 14.
Karson earns $6 each hour babysitting. Last week she earned a total of $48 babysitting. How many hours did Karson babysit last week?
Choose a number from the box.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 4 img 10$
______ hours

Answer: 8 hours.

Explanation: As Karson earns $6 each hour babysitting and in last week she earned a total of $48 babysitting, so $48÷$6= 8 hours did Karson earn in babysit last week.

Test – Page 5 – Page No. 65

Question 15.
Write the division equation to represent the repeated subtraction.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 5 img 11$
_____ ÷ _____ = _____

Answer: 3.

Explanation:
15÷5= 3

Question 16.
Write the related facts for the array.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 5 img 12$

Answer:
5×5= 25
25÷5= 5

Explain why there are not more related facts for the array.

Answer: There are only two equations, as both factors are the same.

Question 17.
Sierra separates 14 animal cards into equal piles with none left over.
Draw a picture to show how Sierra divides the cards and complete the sentence.
Sierra made ______ piles of cards.

Answer: 2 piles of cards.

Explanation: Here we must know how 14 can be divided. So 14 can be divided into two ways, 7×2= 14 and 2×7= 14. So Sierra made 2 piles of cards.

Could Sierra have separated the cards into 4 equal piles with none left over? Explain why or why not.

Answer: No.

Explanation: Sierra cannot separate into 4 equal piles, as 14 cannot be divided into 4 groups of equal size.

Test – Page 6 – Page No. 66

Question 18.
Circle numbers to complete the related facts.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 6 img 13$ × 6 = 42 42 ÷ $Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 6 img 14$ = 6
_____ _____

Answer: 7,6.

Explanation:
7×6= 42
42÷7= 6

Question 19.
Use numbers from the box to write related multiplication and division facts.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 6 img 15$
_____ × _____ = _____
_____ × _____ = _____
_____ ÷ _____ = _____
_____ ÷ _____ = _____

Answer:
8×4= 32
4×8= 32
32÷4= 8
32÷8= 4

Question 20.
Angela plants 24 rosebushes in flowerbeds in her yard. She plants the same number of rosebushes in each of 6 flowerbeds.
How many rosebushes does Angela plant in each flowerbed? Show your work.
$Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test Test - Page 6 img 16$
______ rosebushes

Answer: 4 rosebushes.

Explanation: As Angela plants 24 rosebushes in flowerbeds in her yard and she plants the same number of rosebushes in each of 6 flowerbeds, so 24÷6= 4 rosebushes.

Go Math Grade 3 Answer Key Chapter 6 Understand Division Assessment Test

Conclusion

Test your Math Skills using the Go Math Grade 3 Chapter 6 Understand Division Assessment Test. Hope, the information shared has shed some light on you. If you have any queries feel free to reach us via comment box and we will resolve them at the earliest. To know more such questions and clear your doubts on the Grade 3 Chapter 6 access Go Math Grade 3 Answer Key Chapter 6 Understand Division and make the most out of them.

Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns

April 7, 2022March 28, 2022 by Go Math Answer Key

$go-math-grade-4-chapter-5-factors-multiples-and-patterns-answer-key$

Go Math Grade 4 Answer Key Chapter 5 includes topics like Factors, Common factors, Divisibilities and Review tests, etc. that aid students to solve the homework and assessment tests. Also, it is the best and ultimate guide for exam preparation. You will find every question was explained in a simplistic way so that you are able to understand the concepts easily. Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns pdf links are available here for each and every lesson. So, kickstart your preparation and score good grades in the exams.

Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns

Improve your Problem-Solving Skills utilizing the Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns. Start practicing the question covered in the Go Math 4th grade Solution Key and Cross Check the Solutions of Chapter 5 Factors, Multiples, and Patterns from here. So that you can easily rectify your mistakes and fill up the knowledge gap. Take the help from the direct links available below and solve the problems covered in Go Math Grade 4 Answer Key.

Common Core – Model Factors – Page No. 283

Model Factors

Use tiles to find all the factors of the product.

Record the arrays on grid paper and write the factors shown.

Question 1.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Model Factors img 1$

Question 2.
Write the factors of: 30

Answer:
The Factors Of 30 are: 1,2,3,5,6,10,15,30.

Explanation:
Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 30 when multiplied together.So the factors of 30 are 1,2,3.5,6,10,15,30.

1×30=30
2×15=30
3×10=30
5×6=30
6×5=30
10×3=30
15×2=30
30×1=30

Question 3.
Write the factors of: 45

Answer: The Factors Of 45 are:1,3,5,9,15,45.

Explanation:
Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 45 when multiplied together.So the factors of 45 are:1,3,5,9,15,45.

1×45=45
3×15=45
5×9=45
9×5=45
15×3=45
45×1=45

Question 4.
Write the factors of: 19

Answer: The Factors Of 19 are:1,19.

Explanation:
Since 19 is a Prime number that means it is divisible by 1 and itself. So the factors of 19 are 1,19.

1×19=19
19×1=19.

Question 5.
Write the factors of: 40

Answer: The Factors Of 40 are:1,2,4,5,8,10,20,40.

Explanation:Factors are the numbers which divides the original number completely. The Factors Of 40 are:1,2,4,5,8,10,20,40.

1×40=40
2×20=40
4×10=40
5×8=40
8×5=40
10×4=40
20×2=40
40×1=40

Question 6.
Write the factors of: 36

Answer: The Factors Of 36 are:1,2,3,4,6,9,12,18,36.

Explanation:
Factors are the numbers which divides the original number completely. The factors of 36 are:1,2,3,4,6,9,12,18,36.

1×36=36
2×18=36
3×12=36
4×9=36
6×6=36
9×4=36
12×3=36
18×3=36
36×1=36.

Question 7.
Write the factors of: 22

Answer: The Factors Of 22 are:1,2,11,22.

Explanation:
Factors are the numbers which divides the original number completely. The factors of 22 are:1,2,11,22.

1×22=22
2×11=22
11×2=22
22×1=22.

Question 8.
Write the factors of: 4

Answer: The Factors Of 4 are:1,2,4.

Explanation:
Factors are the numbers which divides the original number completely. The Factors Of 4 are:1,2,4.

1×4=4
2×2=4
4×1=4.

Question 9.
Write the factors of: 26

Answer: The Factors Of 26 are:1,2,13,26.

Explanation:
Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 26 when multiplied together.So the factors of 26 are:1,2,13,26.

1×26=26
2×13=26
13×2=26
26×1=26.

Question 10.
Write the factors of: 49

Answer: The Factors Of 49 are:1,7,49.

Explanation:
Factors are the numbers which divides the original number completely. The Factors Of 49 are:1,7,49.

1×49=49
7×7=49
49×1=49.

Question 11.
Write the factors of: 32

Answer: The Factors Of 32 are:1,2,4,8,16,32.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 32 when multiplied together.So the factors of 32 are:1,2,4,8,16,32.

1×32=32
2×16=32
4×8=32
8×4=32
16×2=32
32×1=32.

Question 12.
Write the factors of 23

Answer: The Factors Of 23 are:1,23.

Explanation:
Since 23 is a Prime number that means it is divisible by 1 and itself. So the factors of 23 are 1,23.

1×23=23
23×1=23.

Question 13.
Brooke has to set up 70 chairs in equal rows for the class talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?

Answer:
Answer is 2,5,7,10,14.

Explanation:
Let the possible no.of rows be X, As there is no room for more than 20 rows so there should not be more than 20 rows.X should be less than or equal to 20(X<=20). As Brooke has 70 chairs to set up in equal rows we will find the factors of 70 and in that we must pick up the numbers which are less than equal to 20.Therefore the factors of 70 are 2,5,7,10,14.

Question 14.
Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?

Answer: 16

Explanation: If find factors for 1 to 20 we don’t get exactly 5 factors for any number except 16. So the answer is 16.

Common Core – Factors – Page No. 284

Lesson Check

Question 1.
Which of the following lists all the factors of 24?
Options:
a. 1, 4, 6, 24
b. 1, 3, 8, 24
c. 3, 4, 6, 8
d. 1, 2, 3, 4, 6, 8, 12, 24

Answer: d(1, 2, 3, 4, 6, 8, 12, 24)

Explanation:Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 24 when multiplied together.So the factors of 24 are:1, 2, 3, 4, 6, 8, 12, 24.

1×24=24
2×12=24
3×8=24
4×6=24
6×4=4
8×3=24
12×2=24
24×1=24

Question 2.
Natalia has 48 tiles. Which of the following shows a factor pair for the number 48?
Options:
a. 4 and 8
b. 6 and 8
c. 2 and 12
d. 3 and 24

Answer: b(6 and 8)

Explanation: 6 and 8 are factor pair for 48 because 6×8=48.

Spiral Review

Question 3.
The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days?
Options:
a. 210 pounds
b. 2,100 pounds
c. 14,000 pounds
d. 21,000 pounds

Answer: d

Explanation: Let’s round off 2750 pounds to 3000 pounds. In one day 3000 pounds pumpkins were sold out, and in
7 days?? —- 3000×7= 21,000 pounds.

Question 4.
What is the remainder in the division problem modeled below?
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Factors img 2$
Options:
a. 2
b. 3
c. 5
d. 17

Answer: a

Explanation: We can see in the above figure 3 circles with 5 sub circles inside it and a pair of sub circles. Here total sub circles are (3×5)+2=17. If we divide 17 with 3 then we will get reminder as 2. So answer is 2.

Question 5.
Which number sentence is represented by the following array?
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Factors img 3$
Options:
a. 4 × 5 = 20
b. 4 × 4 = 16
c. 5 × 2 = 10
d. 5 × 5 = 25

Answer: a

Explanation: As we can see 4 rows and 5 squares, So 4 × 5 = 20.

Question 6.
Channing jogs 10 miles a week. How many miles will she jog in 52 weeks?
Options:
a. 30 miles
b. 120 miles
c. 200 miles
d. 520 miles

Answer: d

Explanation: No.of weeks = 52. So 1 week = 10 miles, then 52 weeks =?????
52×10=520 miles.

Page No. 287

Question 1.
Is 4 a factor of 28? Draw a model to help.
Think: Can you make a rectangle with 28 squares in 4 equal rows?
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 4$
4 ______ a factor of 28.
Type below:
__________

Is 5 a factor of the number? Write yes or no.

Question 2.
27
Answer: No.

Explanation: Factors of 27 are 1,3,9,27. So the answer is No.

Question 3.
30
Answer : Yes.

Explanation: As the last digit is 0 which is divisible 5.

Question 4.
36
Answer: No

Explanation: 36 is not divisible by 5, So the answer is no

Question 5.
53
Answer: No

Explanation: Factors of 53 are 1, 53. So the answer is No.

Is 9 a factor of the number? Write yes or no.

Question 6.
54
Answer: Yes.

Explanation: As 54 is divisible by 9.

Question 7.
63
Answer: Yes.

Explanation: 63 is divisible by 9, So the answer is Yes

Question 8.
67
Answer: No.

Explanation: 67 is a prime number that means it is divisible by 1 and itself. So the answer is No.

Question 9.
93
Answer: No.

Explanation: The factors of 93 are 1,3,31 and 93. So the answer is No.

List all the factor pairs in the table.

Question 10.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 5$
Answer:
1×24=24 1,24
2×12=24 2,12
3×8=24 3,8
4×6=24 4,6

Explanation: Factors of 24.

Question 11.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 6$
Answer:
1×39=39 1,39
3×13=39. 3,13

Explanation: Factors of 39.

Practice: Copy and Solve List all the factor pairs for the number. Make a table to help.

Question 12.
56
Answer:
1×56=56 1,56
2×23=56 2,23
4×14=56 4,14
7×8=56 7,8
8×7=56 8,7

Explanation: Factors of 56.

Question 13.
64
Answer:
1×64=64 1,64
2×32=64 2,32
4×16=64 4,16
8×8=64 8,8

Explanation: Factors of 64 and factor pair for 64 is 8,8.

Page No. 288

Use the table to solve 14–15.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 7$

Question 14.
Dirk bought a set of stamps. The number of stamps in the set he bought is divisible by 2, 3, 5, 6, and 9. Which set is it?
Answer: 90

Explanation: 90 is divisible by all numbers 2,3,5,6, and 9. So the answer is 90.

Question 15.
Geri wants to put 6 stamps on some pages in her stamp book and 9 stamps on other pages. Explain how she could do this with the stamp set for Sweden.

Answer: 10 pages with 6 stamps and 2 pages with 9 stamps.

Explanation: Geri could break 78 into 60+18, As 60 is divisible by 6, and 18 is divisible by 9. Then she could make 10 pages with 6 stamps as 60÷6=10 and 2 pages with 9 stamps as 18÷9=2.

Question 16.
Use Counterexamples George said if 2 and 4 are factors of a number, then 8 is a factor of the number. Is he correct? Explain.

Answer: No

Explanation: Because if we 12 as an example, 2 and 4 are factors of 12 but not 8.

Question 17.
Classify the numbers. Some numbers may belong in more than one box.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 8$
Answer:
Divisible by 5 and 9 — 45
Divisible by 3 and 9 — 27,45,54,72,81
Divisible by 2 and 6 — 54,72,84.

Common Core – Factors and Divisibility – Page No. 289

Is 6 a factor of the number? Write yes or no.

Question 1.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Factors and Divisibility img 9$

Question 2.
56
Answer: No

Explanation: 56 is not divisible by 6. So the answer is No.

Question 3.
42

Answer: Yes

Explanation: Since 42 is divisible by 6.

Question 4.
66
Answer: Yes

Explanation: 66 is divisible by 6.

Is 5 a factor of the number? Write yes or no.

Question 5.
38
Answer: No

Explanation: If the end is 0 or 5 then the number is divisible by 5. As the number is 38 the answer is No

Question 6.
45

Answer: Yes

Explanation: 45 is divisible by 5. So the answer is Yes

Question 7.
60
Answer: Yes

Explanation: 60 is a factor of 5 because 60 is divisible by 5.

Question 8.
39
Answer: No

Explanation: As 39 is not divisible by 5. So the answer is No.

List all the factor pairs

Question 9.
Factors of 12

Answer:
1 × 12 = 12; ( 1 , 12 )
2 × 6 = 12; ( 2, 6 )
3 × 4 = 12; ( 3 , 4 )

Question 10.
Factors of 25

Answer:
1 ×25 = 25; ( 1 , 25 )
5 × 5 = 25; ( 5 , 5 )

Question 11.
List all the factor pairs for 48.

Answer: Factor pairs of 48 are (1,48),(2,24),(3,16),(4,12),(6,8),(12,2),(6,3),(24,2),(48,1).

Explanation: Factor pairs are the pairs when we multiplied both numbers will get the result. Here factor pairs for 48 are
1×48=48 (1,48)
2×24=48 (2,24)
3×16=48 (3,16)
4×12=48 (4,12)
6×8 =48 (6,8)

Problem Solving

Question 12.

Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six storage containers and not have any left over?

Answer: No

Explanation: 64 is not divisible by 6, So he cannot distribute them equally into six storage containers.

Question 13.
Lori wants to distribute 35 peaches equally into baskets. She will use more than 1 but fewer than 10 baskets. How many baskets does Lori need?

Answer: 5 or 7.

Explanation: First we need to know the factors of 35. The factors of 35 are 1,5,7,35. As Lori uses more than 1 but fewer than 10, the answer is 5 or 7. Lori can distribute 35 peaches equally in 5 or 7 baskets.

Common Core – Factors – Page No. 290

Lesson Check

Question 1.
Which of the following numbers has 9 as a factor?
Options:
a. 28
b. 30
c. 39
d. 45

Answer: d

Explanation: 45 is divisible 9. So the answer is 45.

Question 2.
Which of the following numbers does NOT have 5 as a factor?
Options:
a. 15
b. 28
c. 30
d. 45

Answer: 28

Explanation: 28 is not divisible by 5. So 28 is not a factor of 5.

Spiral Review

Question 3.
Which of the following shows a strategy to use to find 4 × 275?
Options:
a. (4 × 300) + (4 × 25)
b. (4 × 300) – (4 × 25)
c. (4 × 275) – 100
d. (4 × 200) + 75

Answer: b

Explanation: First we must replace 300-25 in the place of 275 then it becomes 4×(300-25), Now we must use the distributive property of multiplication then (4×300)-(4×25). So the answer is b.

Question 4.
Jack broke apart 5 × 216 as (5 × 200) + (5 × 16) to multiply mentally. What strategy did Jack use?
Options:
a. the Commutative Property
b. the Associative Property
c. halving and doubling
d. the Distributive Property

Answer: d

Explanation: Distributive property means if we multiply a sum by a number is same as multiplying each addend by the number and adding the products. This is the strategy Jack used.

Question 5.
Jordan has $55. She earns $67 by doing chores. How much money does Jordan have now?
Options:
a. $122
b. $130
c. $112
d. $12

Answer: a

Explanation: Jordan has $55, she earns by doing chores is $67. So total money is $55+$67=$122.

Question 6.
Trina has 72 collector’s stamps. She puts 43 of the stamps into a stamp book. How many stamps are left?
Options:
a. 29
b. 31
c. 39
d. 115

Answer: a

Explanation: Stamps left are 72-43=29.

Page No. 293

Question 1.
Lucy has 40 bean plants, 32 tomato plants, and 16 pepper plants. She wants to put the plants in rows with only one type of plant in each row. All rows will have the same number of plants. How many plants can Lucy put in each row?
First, read the problem and think about what you need to find. What information will you use? How will you use the information?

Answer: We will find common factors for 40,32 and 16.

Question 1.
Next, make a list. Find the factors for each number in the problem.

Answer:
Factors of 40 are — 1,2,4,5,8,10,20,40
Factors of 32 are — 1,2,4,8,16,32
Factors of 16 are — 1,2,4,8,16

Question 1.
Finally, use the list. Circle the common factors.
So, Lucy can put ___ , ___ , ___ , or ___ plants in each row.

Answer: 1,2,4,8

Explanation: Because 1,2,4,8, are common factors in 40,32,16.

Question 2.
What if Lucy has 64 bean plants instead of 40 bean plants? How many plants can Lucy put in each row?

Answer: 1,2,4,8,16

Explanation: Here we need to find the factors of 64,32 and 16. We get common factors as 1,2,4,8,16.

Question 3.
One common factor of two numbers is 40. Another common factor is 10. If both numbers are less than 100, what are the two numbers?
______ and ______

Answer: 40 and 80.

Explanation: As the next multiple of 40 is 80. So both 40 and 80 are less than 100 and has a common factor as 10.

Question 4.
The sum of two numbers is 136. One number is 51. What is the other number? What are the common factors of these two numbers?

Answer: 85.
Common Factors are 1,17.

Explanation: As 136-51= 85
Factors of 51 are 1,3,17,51
Factors of 85 are 1,5,17,85.

Page No. 294

Question 5.
Analyze A number is called a perfect number if it equals the sum of all of its factors except itself. For instance, 6 is a perfect number because its factors are 1, 2, 3, and 6, and 1 + 2 + 3 = 6. What is the next greater perfect number?

Answer: 28

Explanation: The factors of 28 are 1,2,4,7,14 and 28. If we add 1+2+4+7+14 we will get 28. So 28 is a perfect number.

Question 6.
Sona knits 10 squares a day for 7 days. Can she sew together the squares to make 5 equal-sized blankets? Explain.

Answer: Yes

Explanation: As 10×7= 70 which is a factor of 5.

Question 7.
Julianne earned $296 working at a grocery store last week. She earns $8 per hour. How many hours did Julianne work?
Answer: 37 hours

Explanation: Julianne earned $296 in last week. Per hour she earns $8, So total no.of hours did she worked is
296÷8= 37 hours.

Question 8.
There are 266 students watching a play in the auditorium. There are 10 rows with 20 students in each row and 5 rows with 8 students in each row. How many students are sitting in each of the 2 remaining rows if each of those rows has an equal number of students?

Answer: 13 Students

Explanation: Total number of students is 266. In which 10 rows were filled with 20 students that means 10×20=200 students, and 5 rows were filled with 8 students which means 5×8= 40 students. The total students filled are 240. And to know how many students filled in the remaining 2 rows we need to subtract 266-240=26, As students are filled in 2 rows 26÷2= 13.

Question 9.
Ben is planting a garden with 36 zinnias, 18 marigolds, and 24 petunias. Each row will have only one type of plant. Ben says he can put 9 plants in each row. He listed the common factors of 36, 18 and 24 below to support his reasoning.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
18: 1, 2, 3, 6, 8, 9, 18
24: 1, 2, 3, 4, 6, 8, 9, 12, 24
Is he correct? Explain your answer. If his reasoning is incorrect, explain how he should have found the answer.

Answer: No

Explanation: The factors of 18 and 24 are incorrect which he listed. And the common factors for 36,24 and 18 are 1,2,3 and 6. So he can put 1,2,3 and 6 plants in a row.

Common Core – Common Factors – Page No. 295

Problem Solving Common Factors

Solve each problem.

Question 1.
Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag?
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Common Factors img 10$

Question 2.
Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?

Answer:1,2,3,4,6 or 12 items Simon puts on each wreath.

Explanation: First we will find the common factors of 36,48,60
factors of 36 are: 1,2,3,4,6,9,12,18,36.
factors of 48 are: 1,2,3,4,6,8,12,16,24,48
factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30,60.
The common factors of 36,48,60 are 1,2,3,4,6,12. So Simon can put 1,2,3,4,6 or 12 items on each wreath.

Question 3.
Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes them into groups with the same number of items in each group. All the items in a group will be the same type. How many items can he put in each group?

Answer: Justin can put 1 or 5 items in each group.

Explanation: We will find common factors of 20,25,40.
factors of 20 are: 1,2,4,5,10,20.
factors of 25 are: 1,5,25.
factors of 40 are: 1,2,4,5,8,10,20,40
So common factors are 1 and 5.

Question 4.
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water. The volunteers will put the items into boxes. Each box will have the same number of food items and all the items in the box will be the same type. How many items can they put in each box?

Answer: 1,2,5, or 10.

Explanation: 1,2,5 or 10 are the common factors of 30,50 and 100.
factors for 30 are: 1,2,3,5,6,10,15,30
factors for 50 are: 1,2,5,10,25,50
factors of 100 are: 1,2,4,5,10,20,25,50,100
So answer is 1,2,5,10.

Question 5.
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team?

Answer: 3

Explanation: Lets find the common factors of 12,15,18
factors of 12 are: 1,2,3,4,6,12
factors of 15 are: 1,3,5,15
factors of 18 are: 1,2,3,6,9,18
3 is the common factor for 12,15,18

Common Core – Common Factors – Page No. 296

Lesson Check

Question 1.
What are all the common factors of 24, 64, and 88?
Options:
a. 1 and 4
b. 1, 4, and 8
c. 1, 4, 8, and 12
d. 1, 4, 8, and 44

Answer: b

Explanation:
factors of 24 are: 1,2,3,4,8,12,24
factors of 64 are: 1,2,4,8,16,32,64
factors of 88 are: 1,2,4,8,11,22,44,88

Question 2.
Which number is NOT a common factor of 15, 45, and 90?
Options:
a. 3
b. 5
c. 10
d. 15

Answer: c

Explanation: As 15 and 45 are not divisible by 10.

Spiral Review

Question 3.
Dan puts $11 of his allowance in his savings account every week. How much money will he have after 15 weeks?
Options:
a. $165
b. $132
c. $110
d. $26

Answer: a

Explanation: Dan puts $11 in his savings account every week, So after 15 weeks it will be 15×11=165.
The total money he will have after 15 weeks is $165.

Question 4.
James is reading a book that is 1,400 pages. He will read the same number of pages each day. If he reads the book in 7 days, how many pages will he read each day?
Options:
a. 20
b. 50
c. 140
d. 200

Answer: d

Explanation: Total no.of.pages is 1400, no.of pages James read each day is 1400÷7= 200

Question 5.
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks. Which is the best estimate of the number of hours she volunteered each week?
Options:
a. 10 hours
b. 20 hours
c. 120 hours
d. 714 hours

Answer: b

Explanation: Total hours Emma volunteered is 119 hours over 6 weeks, how much she volunteered each week is
119÷6= 19.833 i.e 20 hours. We must round off to the nearest one i.e 20 hours.

Question 6.
Which strategy can be used to multiply 6 × 198 mentally?
Options:
a. 6 × 198 = (6 × 19) + (6 × 8)
b. 6 × 198 = (6 × 200) + (6 × 2)
c. 6 × 198 = (6 × 200) – (6 × 2)
d. 6 × 198 = (6 + 200) × (6 + 2)

Answer: c

Explanation: By Distributive property of multiplication 6×198 can be written as (6 × 200) – (6 × 2).

Page No. 297

Choose the best term from the box.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 11$

Question 1.
A number that is multiplied by another number to find a product is called a

Answer: Factor.

Question 2.
A number is _________ by another number if the quotient is a counting number and the remainder is zero.
Answer: Divisible.

List all the factors from least to greatest.

Question 3.
8
Answer: 1,2,4,8

Question 4.
14
Answer: 1,2,7,14

Is 6 a factor of the number? Write yes or no.

Question 5.
81
Answer: No

Explanation: 81 is not divisible by 6

Question 6.
45
Answer: No

Explanation: 45 is not divisible by 6

Question 7.
42
Answer: Yes

Explanation: 42 is divisible by 6

Question 8.
56

Answer: No.

Explanation: 56 is not divisible by 6

List all the factor pairs in the table.

Question 9.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 12$

Answer:
1×64=64 1,64
2×32=64 2,32
4×16=64 4,16
8×8=64 8,8

Explanation: Factors of 64

Question 10.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 13$

Answer:
1×44=44 1,44
2×22=44 2,22
11×4=44 11,4

List the common factors of the numbers.

Question 11.
9 and 18

Answer: 1,3,9

Explanation:
Factors of 9 are: 1,3,9
Factors of 18 are: 1,2,3,9,18

Question 12.
20 and 50

Answer: 1,2,5,10

Explanation:
Factors of 20 are: 1,2,4,5,10,20
Factors of 50 are: 1,2,5,10,25,50

Page No. 298

Question 13.
Sean places 28 tomato plants in rows. All rows contain the same number of plants. There are between 5 and 12 plants in each row. How many plants are in each row?

Answer: 7 plants.

Explanation: There are 28 tomato plants in a row. To find out how many plants in a row we will find the factors of 28 i.e 1,2,4,7,14,28. As there are between 5 and 12 plants 7 is the only number between 5 and 12. So 7 plants are planted in each row.

Question 14.
Ella bought some key chains and spent a total of $24. Each key chain costs the same whole-dollar amount. She bought between 7 and 11 key chains. How many key chains did Ella buy?

Answer: 8

Explanation: Ella spent a total of $24. To find how many key chains first we will find the factors of 24. Factors of 24 are
1,2,3,4,6,8,12,24. As Ella bought between 7 and 11 key chains 8 is the only number between 7 and 11. So 8 key chains Ella bought.

Question 15.
Sandy has 16 roses, 8 daisies, and 32 tulips. She wants to arrange all the flowers in the bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?

Answer: 2 roses, 1 daisy, and 4 tulips in 8 bouquets.

Explanation: First we must add all the flowers i.e 16+8+32= 56, Now we can divide 56 flowers equally in each bouquet. Like 2 roses, 1 daisy and 4 tulips in 8 bouquets or 8 roses in 2 bouquets, 8 daisies in 1 bouquet and 8 tulips in 4 bouquets.

Question 16.
Amir arranged 9 photos on a bulletin board. He put the photos in rows. Each row contains the same number of photos. How many photos could be in each row?

Answer: 9 photos in a row and 3 photos in 3 rows or 9 photos in 1 row.

Explanation: Factors of 9 are 1,3,9. So Amir can arrange 9 photos in a row and 3 photos in 3 rows or 9 photos in 1 row.

Page No. 301

Question 1.
Multiply to list the next five multiples of 4.
4 , _____ , _____ , _____ , _____ , _____
1 × 4
4 , _____ , _____ , _____ , _____ , _____

Answer:
4 1×4
8 2×4
12 3×4
16 4×4
20 4×5

Explanation: Multiplies of 4

Is the number a factor of 6? Write yes or no.

Question 2.
2

Answer: Yes

Explanation: 6 is divisible by 2. So 2 is the factor of 6.

Question 3.
6

Answer: Yes

Explanation: 6 is divisible by 6.

Question 4.
16

Answer: No

Explanation: 16 is not divisible by 6

Question 5.
18

Answer: Yes

Explanation: 18 is divisible by 6

Is the number a multiple of 6? Write yes or no.

Question 6.
3

Answer: No

Explanation: Multiples of 6 are 6,12,18,24,30, etc.

Question 7.
6

Answer: Yes

Explanation: 1×6= 6. So 6 is multiple of 6.

Question 8.
16

Answer: No

Explanation: Multiples of 6 are 6,12,18,24,30, etc.

Question 9.
18

Answer: Yes

Explanation: Multiples of 6 are 6,12,18,24,30, etc.

Is the number a multiple of 3? Write yes or no.

Question 10.
4

Answer: No

Explanation: Multiples of 3 are 3,6,9,12,15,etc.

Question 11.
8

Answer: No

Explanation: Multiples of 3 are 3,6,9,12,15,etc.

Question 12.
24

Answer: Yes

Explanation: Multiples of 3 are 3,6,9,12,15,etc.

Question 13.
38

Answer: No

Explanation: Multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36,39,42,etc.

Question 14.
List the next nine multiples of each number. Find the common multiples.
Multiples of 2: 2, _________________
Multiples of 8: 8, _________________
Common multiples: _________________

Answer: 8,16.

Explanation:
Multiples of 2: 2,4,6,8,10,12,14,16,18,20.
Multiples of 8: 8,16,24,32,40,48,56,64,72,80.
So common multiples are: 8,16

Generalize Algebra Find the unknown number.

Question 15.
12, 24, 36, _____

Answer: 48

Explanation:
12×1= 12
12×2= 24
12×3= 36
12×4= 28

Question 16.
25, 50, 75, 100, ______

Answer: 125

Explanation:
25×1= 25
25×2= 50
25×3= 75
25×4= 100
25×5= 125

Tell whether 20 is a factor or multiple of the number.

Write factor, multiple, or neither.

Question 17.
10

Answer: Multiple

Explanation: 2×10= 20.

Question 18.
20

Answer: Factor and multiple

Explanation:
1×20= 20
20÷1= 20.

Question 19.
30

Answer: Neither

Explanation:
Factors of 30 are: 1,2,3,5,6,10,15,and 30.
Multiples of 30 are: 30,60,90,etc.

Write true or false. Explain.

Question 20.
Every whole number is a multiple of 1.

Answer: True.

Explanation: For every whole number which is multiplied with 1, the result will be that number.

Question 21.
Every whole number is a factor of 1.

Answer: False

Explanation: Not every whole number is a factor of 1.

Question 22.
Julio wears a blue shirt every 3 days. Larry wears a blue shirt every 4 days. On April 12, both Julio and Larry wore a blue shirt. What is the next date that they will both wear a blue shirt?
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 14$

Answer: April 24

Explanation:
As Julio wears a blue shirt every 3 days and another shirt in the remaining 4 days, So 4×3 days= 12
Larry wears a blue shirt every 4 days and another shirt in the remaining 3 days, So 3×4 days= 12
12+12= 24. So the next date will be April 24.

Page No. 302

Complete the Venn diagram. Then use it to solve 23–25.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 15$

Question 23.
What multiples of 4 are not factors of 48?

Answer: 20,28,32,36,40,44.

Explanation:
Multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48.
Not a factors of 48 are 20,28,32,36,40,44.

Question 24.
What factors of 48 are multiples of 4?

Answer: 4,8,12,16,24,48.

Explanation:
Multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,48.
Factors of 48 are: 1,2,4,8,12,16,24,48.

Question 25.
Pose a Problem Look back at Problem 24. Write a similar problem by changing the numbers. Then solve.

Answer: Let’s take factors of 64 are multiples of 8?
8,16,32,64.

Explanation:
Multiples of 8 are: 8,16,24,32,40,48,56,64,72,80
Factors of 64 are: 1,2,4,8,16,32,64

Question 26.
Kia paid $10 for two charms. The price of each charm was a multiple of $2. What are the possible prices of the charms?

Answer: $2,$8 and $4,$6.

Explanation: Since the price was multiple of 2 and Kia paid $10 for two charms, So possible prices are $2+$8=$10
and $4+$6=$10.

Question 27.
Look for Structure The answer is 9, 18, 27, 36, 45. What is the question?

Answer: Write the multiples of 9

Question 28.
How do you know whether a number is a multiple of another number?

Answer: When the number is divisible by the number then that number is multiple of another number.

Explanation: For example, if we take a number i.e 8 which is divisible by 2 and 8 is a multiple of 2.

Question 29.
For numbers 29a–29e, select True or False for each statement.
a. The number 45 is a multiple of 9.
i. True
ii. False

Answer: True

Explanation: As 9×5= 45, So 45 is multiple of 9.

Question 29.
b. The number 4 is a multiple of 16.
i. True
ii. False

Answer: False.

Explanation: As 16 is divisible by 4 and not a multiple of 16.
Multiple of 16 are : 16,32,48,64,80.

Question 29.
c. The number 28 is a multiple of 4.
i. True
ii. False

Answer: True.

Explanation: 4×7=28.

Question 29.
d. The number 4 is a factor of 28.
i. True
ii. False

Answer: True.

Explanation:
Factors of 28 are: 1,2,4,7,14,28.

Question 29.
e. The number 32 is a factor of 8.
i. True
ii. False

Answer:

Explanation:

Common Core – Factors and Multiples – Page No. 303

Factors and Multiples
Is the number a multiple of 8? Write yes or no.

Question 1.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Factors and Multiples img 16$

Question 2.
8
Answer: Yes

Explanation: Since 8×1=8, it is a multiple of 8

Question 3.
20
Answer: No

Explanation: 20 is not a multiple of 8

Question 4.
40
Answer: Yes

Explanation: 8×5=40, So 40 is multiple of 8

List the next nine multiples of each number. Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 7:
Common multiples:

Answer:

Explanation:
Multiples of 4: 4,8,12,16,20,24,28,32,36,40.
Multiples of 7: 7,14,21,28,35,42,49,56,63,70.
Common Multiples: 28,

Question 6.
Multiples of 3:
Multiples of 9:
Common multiples:

Answer: 9,18,45,54,63, etc.

Explanation:
Multiples of 3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63.
Multiples of 9: 9,18,27,36,45,54,63,72,81,90.
Common multiples: 9,18,45,54,63, etc.

Question 7.
Multiples of 6:
Multiples of 8:
Common multiples:

Answer: 24,48,72.

Explanation:
Multiples of 6: 6,12,18,24,30,36,42,48,54,60,66,72,78.
Multiples of 8: 8,16,24,32,40,48,56,64,72,80.
Common multiples: 24,48,72.

Tell whether 24 is a factor or multiple of the number. Write factor, multiple, or neither.

Question 8.
6

Answer: Multiple

Explanation: 6×4=24

Question 9.
36

Answer: Neither

Explanation: 36 is not a factor or multiple of 24.

Question 10.
48

Answer: Factor

Explanation: 24×2= 48, So 48 is a factor of 24

Problem Solving

Question 11.
Ken paid $12 for two magazines. The cost of each magazine was a multiple of $3. What are the possible prices of the magazines?

Answer: $3+$9=$12.

Explanation: As each magazine cost was multiple of $3, The possible price for 2 magazines are $3+$9=$12, which is a multiple of 3

Question 12.
Jodie bought some shirts for $6 each. Marge bought some shirts for $8 each. The girls spent the same amount of money on shirts. What is the least amount they could have spent?

Answer: $24

Explanation: As they spent the same amount of money which means the number should be multiple of $6 and $8, So multiples of 6 are: 6,12,18,24,30,36,42 and
multiples of 8 are: 8,16,24,32,40. The least amount they could spend is 24. As 24 is the least common multiple.

Common Core – Factors and Multiples – Page No. 304

Lesson Check

Question 1.
Which list shows numbers that are all multiples of 4?
Options:
a. 2, 4, 6, 8
b. 3, 7, 11, 15, 19
c. 4, 14, 24, 34
d. 4, 8, 12, 16

Answer: d

Explanation: Multiples of 4 are 4,8,12,16.

Question 2.
Which of the following numbers is a common multiple of 5 and 9?
Options:
a. 9
b. 14
c. 36
d. 45

Answer: 45

Explanation: 5×9= 45

Spiral Review

Question 3.
Jenny has 50 square tiles. She arranges the tiles into a rectangular array of 4 rows. How many tiles will be left over?
Options:
a. 0
b. 1
c. 2
d. 4

Answer: 2

Explanation: As Jenny arranges in 4 rows, each row contains 12 tiles. So 12×4= 48. The tiles left are 50-48=2.

Question 4.
Jerome added two numbers. The sum was 83. One of the numbers was 45. What was the other number?
Options:
a. 38
b. 48
c. 42
d. 128

Answer: a

Explanation: The sum of two numbers is 83, in that one number is 45. To find another number we will do subtraction,
i.e 83-45=38.

Question 5.
There are 18 rows of seats in the auditorium. There are 24 seats in each row. How many seats are in the auditorium in all?
Options:
a. 42
b. 108
c. 412
d. 432

Answer: d

Explanation:
No.of rows= 18, each row has 24 seats. So total no.of seats are 18×24= 432.

Question 6.
The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735?
Options:
a. 7
b. 700
c. 735
d. 7,000

Answer: b

Explanation: In 6,735 the 7 is in the Hundreds Place. So the answer is 7.

Page No. 307

Question 1.
Use the grid to model the factors of 18. Tell whether 18 is prime or composite.

Factors of 18: ____ , ____ , ____ , ____ , ____ , ____
Think: 18 has more than two factors.
So, 18 is _________ .

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 18 are: 1,2,3,6,9,18.

Tell whether the number is prime or composite.

Question 2.
11
Think: Does 11 have other factors besides 1 and itself?

Answer: Prime number.

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 3.
73

Answer: Prime number

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 4.
69

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 69 are: 1,3,23,69.

Question 5.
42

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 42 are: 1,2,3,6,7,21,42.

Tell whether the number is prime or composite.

Question 6.
18

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 18 are: 1,2,3,6,9,18.

Question 7.
49

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 49 are 1,7,49.

Question 8.
29

Answer: Prime number.

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 9.
64

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 64 are: 1,2,4,8,32,64.

Question 10.
33

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 33 are: 1,3,11,33.

Question 11.
89

Answer: Prime number.

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 12.
52

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 52 are: 1,2,4,13,26,52.

Question 13.
76

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 76 are: 1,2,4,19,38,76.

Write true or false for each statement. Explain or give an example to support your answer.

Question 14.
Only odd numbers are prime numbers.

Answer: False.

Explanation: Not all odd numbers are prime numbers. For example. 39 is an odd number but not a prime number because it is divisible by 3 and 13.

Question 15.
A composite number cannot have three factors.

Answer: False

Explanation: A Composite number is a number that has more than two factors.
For example. 21 is a composite number and the factors of 21 are 1,3,7,21.

Question 16.
I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number. What number am I?

Answer: 97

Explanation:
Prime numbers between 60 to 100 are 61,67,71,73,79,83,89,97. 97 is the number which ones digit is two less than tens digit.

Question 17.
Name a 2-digit odd number that is prime. Name a 2-digit odd number that is composite.

Answer:
2 digit Prime odd numbers are 11,13,17 etc.
2 digit Composite odd numbers are 15,21,39

Explanation: A Prime number is a number that is divisible 1 and itself.
The number which has more than two factors is called composite numbers.

Question 18.
Choose the words that correctly complete the sentence.
The number 9 is img 18 because it has img 19 two factors.
Type below:
__________

Page No. 308

The Sieve of Eratosthenes
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 20$
Eratosthenes was a Greek mathematician who lived more than 2,200 years ago. He invented a method of finding prime numbers, which is now called the Sieve of Eratosthenes.

Question 19.
Follow the steps below to circle all prime numbers less than 100. Then list the prime numbers.
STEP 1
Cross out 1, since 1 is not prime.
STEP 2
Circle 2, since it is prime. Cross out all other multiples of 2.
STEP 3
Circle the next number that is not crossed out. This number is prime. Cross out all the multiples of this number.
STEP 4
Repeat Step 3 until every number is either circled or crossed out.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 21$
So, the prime numbers less than 100 are

Answer: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 20.
Explain why the multiples of any number other than 1 are not prime numbers.

Answer:

Common Core – Prime and Composite Numbers – Page No. 309

Prime and Composite Numbers

Tell whether the number is prime or composite

Question 1.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Prime and Composite Numbers img 22$

Question 2.
68

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 68 are: 1,2,4,17,34,69.

Question 3.
52

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 52 are: 1,2,4,13,26,52.

Question 4.
63

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 63 are: 1,2,3,7,9,21,63.

Question 5.
75

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 75 are: 1,3,5,15,25,75

Question 6.
31

Answer: Prime number.

Explanation: 31 is a prime number that means it is divisible by 1 and itself.

Question 7.
77

Answer: Composite number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 77 are: 1,7,11,77.

Question 8.
59

Answer: Prime number

Explanation: 59 is a prime number that means it is divisible by 1 and itself.

Question 9.
87

Answer: Composite Number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 87 are: 1,3,29,87.

Question 10.
72

Answer: Composite Number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Question 11.
49

Answer: Composite Number.

Explanation: The number which has more than two factors is called composite numbers.
Factors of 49 are 1,7,49.

Question 12.
73

Answer: Prime number.

Explanation: A Prime number is a number that is divisible 1 and itself.

Problem Solving

Question 13.
Kai wrote the number 85 on the board. Is 85 prime or composite?

Answer: Composite number

Explanation: The number which has more than two factors is called composite numbers.
Factors of 85 are 1,5,17,85

Question 14.
Lisa says that 43 is a 2-digit odd number that is composite. Is she correct?

Answer: No

Explanation: 43 is a prime number. A Prime number is a number that is divisible 1 and itself.

Common Core – Prime and Composite Numbers – Page No. 310

Lesson Check

Question 1.
The number 5 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Answer: Prime number.

Explanation: A Prime number is a number that is divisible 1 and itself.

Question 2.
The number 1 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Answer: d

Explanation: A Prime number is a number that is divisible 1 and itself. So prime number should have two divisors but 1 has only one divisor. The number which has more than two factors is called composite numbers. So 1 doesn’t have more than two factors. So 1 is neither Prime nor Composite.

Spiral Review

Question 3.
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
Options:
a. 134 calories
b. 150 calories
c. 154 calories
d. 231 calories

Answer: c

Explanation: Total no.of calories are 924, which serves 6 people. To find each serving we will perform division
924÷6= 154 calories.

Question 4.
A store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts. What is the fewest boxes the clerk will need to pack all the shirts?
Options:
a. 9
b. 8
c. 7
d. 6

Answer: b

Explanation: As the box holds only 6 shirts, 42 shirts are packed in 7 boxes, and the remaining 3 shirts will be packed in another box. So the total number of boxes is 8.

Question 5.
Which number rounds to 200,000?
Options:
a. 289,005
b. 251,659
c. 152,909
d. 149,889

Answer: c

Explanation: 152,909 is nearest to 200,000.

Question 6.
What is the word form of the number 602,107?
Options:
a. six hundred twenty thousand,seventeen
b. six hundred two thousand, one hundred seven
c. six hundred twenty-one thousand, seventeen
d. six hundred two thousand, one hundred seventy

Answer: b

Page No. 313

Use the rule to write the numbers in the pattern.

Question 1.
Rule: Subtract 10. First term: 100
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 23$

Answer: 100,90,80,70,60,..

Explanation:
100
100-10= 90
90-10= 80
80-10= 70
70-10= 60

Use the rule to write the numbers in the pattern.
Describe another pattern in the numbers.

Question 2.
Rule: Multiply by 2. First term: 4
4 , _____ , _____ , _____ , _____ , …….

Answer: 4,8,16,32,64,…

Explanation:
4
4×2= 8
8×2= 16
16×2= 32
32×2= 64

Question 3.
Rule: Skip-count by 6. First term: 12
12 , _____ , _____ , _____ , _____ , …….

Answer: 12,18,24,30,36,…

Explanation:
12
12+6= 18
18+6= 24
24+6= 30
30+6= 36

Use the rule to write the first twelve numbers in the pattern. Describe another pattern in the numbers.

Question 4.
Rule: Add 7. First term: 3

Answer:
3
3+7= 10
10+7= 17
17+7= 34
34+7= 41
41+7= 48
48+7= 55
55+7= 62
62+7= 69
69+7= 76
76+7= 83
83+7= 90.

Explanation: Added 7 to the given term.

Question 5.
5. Rule: Add 2, add 1. First term: 12

Answer: 12,14,15,17,19,21,22,24,25,27,28,30,31.

Explanation:
12
12+2= 14
14+1= 15
15+2= 17
17+1= 19
19+2= 21
21+1= 22
22+2= 24
24+1= 25
25+2= 27
27+1= 28
28+2= 30
30+1= 31

Question 6.
Use Patterns Marcie likes to collect stickers, but she also likes to give them away. Currently, Marcie has 87 stickers in her collection. If Marcie collects 5 new stickers each week and gives away 3 stickers each week, how many stickers will Marcie have in her collection after 5 weeks?
_______ stickers

Answer: 97 stickers

Explanation: Marcie has 87 stickers, in 1st week she collects 5 stickers and gives away 3 stickers, that means
87+5-3= 89
2nd week 89+5-3= 91
3rd week 91+5-3= 93
4th week 93+5-3= 95
5th week 95+5-3= 97.

Page No. 314

Question 7.
John is saving for his trip to see the Alamo. He started with $24 in his savings account. Every week he earns $15 for baby-sitting. Out of that, he spends $8 and saves the rest. John uses the rule add 7 to find out how much money he has at the end of each week. What are the first 8 numbers in the pattern?

Answer: $24, $31, $38, $45, $52, $59, $66, $73.

Explanation:
24
24+7= 31
31+7= 38
38+7= 45
45+7= 52
52+7= 59
59+7= 66
66+7= 73.

Question 8.
Draw a check under the column that describes the number.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 24$

Pose a Problem

Question 9.
An activity at the Math Fair shows two charts.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 25$
Use at least two of the numbers and an operation from the charts to write a pattern problem. Include the first five terms of your pattern in the solution to your problem.
Pose a problem. Solve your problem.
Describe other patterns in the terms you wrote.

Answer:
2+3= 5 Addition.
10-6= 4 Subtraction.
5×2= 10 Multiplication.

Common Core – Number Patterns – Page No. 315

Number Patterns

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 1.
Rule: Add 8. First term: 5
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Common Core Number Patterns img 26$

Question 2.
Rule: Subtract 7. First term: 95

Answer: 95,88,81,74,67,60,53,46,39,32,25,118,11.

Explanation: 95
95-7= 88
88-7= 81
81-7= 74
74-7= 67
67-7= 60
60-7= 53
53-7= 46
46-7= 39
39-7= 32
32-7= 25
25-7= 18
18-7= 11

Question 3.
Rule: Add 15, subtract 10. First term: 4

Answer: 4,19,9,24,14,29,19,34,24,39,29,44,34.

Explanation: 4
4+15= 19
19-10= 9
9+15= 24
24-10= 14
14+15= 29
29-10= 19
19+15= 34
34-10= 24
24+15= 39
39-10=29
29+15=44
44-10=34

Question 4.
Rule: Add 1, multiply by 2. First term: 2

Answer: 2,4,5,10,11,22,23,46,47,94,95,190.

Explanation: 2
2+1= 2
2×2= 4
4+1= 5
5×2= 10
10+1= 11
11×2= 22
22+1= 23
23×2= 46
46+1= 47
47×2= 94
94+1= 95
95×2= 190.

Problem Solving

Question 5.
Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is the rule for the pattern?

Answer:

Explanation: 1
1+4= 5
5+4= 9
9+4= 13
13+4= 17
17+4= 21
21+4= 25
25+4=29

Question 6.
An artist is arranging tiles in rows to decorate a wall. Each new row has 2 fewer tiles than the row below it. If the first row has 23 tiles, how many tiles will be in the seventh row?

Answer: 11 tiles.

Explanation: 23
23-2= 21
21-2= 19
19-2= 17
17-2= 15
15-2= 13
13-2= 11

Common Core – Number Patterns – Page No. 316

Lesson Check

Question 1.
The rule for a pattern is add 6. The first term is 5. Which of the following numbers is a term in the pattern?
Options:
a. 6
b. 12
c. 17
d. 22

Answer: c

Explanation: 5
5+6= 11
11+6= 17

Question 2.
What are the next two terms in the pattern 3, 6, 5, 10, 9, 18, 17, . . .?
Options:
a. 16, 15
b. 30, 31
c. 33, 34
d. 34, 33

Answer: d

Explanation: 3
3×2= 6
6-1= 5
5×2= 10
10-1= 9
9×2= 18
18-1= 17
17×2= 34
34-1= 33

Spiral Review

Question 3.
To win a game, Roger needs to score 2,000 points. So far, he has scored 837 points. How many more points does Roger need to score?
Options:
a. 1,163 points
b. 1,173 points
c. 1,237 points
d. 2,837 points

Answer: a

Explanation: Roger has scored 837 points, He needs to score 2000 points to win, So to know how much more points do Roger needs we need to subtract i.e 2,000-837= 1,163.

Question 4.
Sue wants to use mental math to find 7 × 53. Which expression could she use?
Options:
a. (7 × 5) + 3
b. (7 × 5) + (7 × 3)
c. (7 × 50) + 3
d. (7 × 50) + (7 × 3)

Answer: d

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.

Question 5.
Pat listed numbers that all have 15 as a multiple. Which of the following could be Pat’s list?
Options:
a. 1, 3, 5, 15
b. 1, 5, 10, 15
c. 1, 15, 30, 45
d. 15, 115, 215

Answer: a

Explanation:
1×15= 15
3×5= 15
5×3= 15
15×1= 15

Question 6.
Which is a true statement about 7 and 14?
Options:
a. 7 is a multiple of 14.
b. 14 is a factor of 7.
c. 14 is a common multiple of 7 and 14.
d. 21 is a common multiple of 7 and 14.

Answer: c

Explanation:
7×2=14
14×1=14

Review/Test – Page No. 317

Question 1.
List all the factors of the number.
14: ______ , ______ , ______ , ______

Answer: 1,2,7,14

Explanation: Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 14 when multiplied together. So the factors of 14 are 1,2,7,14.

Question 2.
Select the numbers that have a factor of 5. Mark all that apply.
Options:
a. 15
b. 3
c. 45
d. 5
e. 50
f. 31

Answer: a,c,d,e.

Explanation: Factors are the numbers that divide the original number completely.

Question 3.
Jackson was making a poster for his room. He arranged 50 trading cards in the shape of a rectangle on the poster.
For 3a–3e, choose Yes or No to tell whether a possible arrangement of cards is shown.
a. 5 rows of 10 cards
i. yes
ii. no

Answer: Yes

Explanation: 5 rows of 10 cards that means 5×10= 50. So the answer is Yes.

Question 3.
b. 7 rows of 8 cards
i. yes
ii. no

Answer: No

Explanation: 7×8= 56, There will be extra cards. So the answer is No.

Question 3.
c. 25 rows of 2 cards
i. yes
ii. no

Answer: Yes.

Explanation: 25×2=50. So the answer is Yes

Question 3.
d. 50 rows of 1 card
i. yes
ii. no

Answer: Yes

Explanation: 50×1=50. So the answer is Yes.

Question 3.
e. 45 rows of 5 cards
i. yes
ii. no

Answer: No

Explanation: 45×5= 225. Which is not equal to 50. So the answer No.

Question 4.
List all the factor pairs in the table.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 27$

Answer:
1×48= 48 1,48
2×24= 48 2,24
3×16= 48 3,16
4×12= 48 4,12
6×8= 48 6,8

Explanation: Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 30 when multiplied together.

Review/Test – Page No. 318

Question 5.
Classify the numbers. Some numbers may belong in more than one box.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 28$

Answer:
Divisible by 5 and 9: 90
Divisible by 6 and 9: 54,72,90
Divisible by 2 and 6: 54,72,84,90,96

Question 6.
James works in a flower shop. He will put 36 tulips in vases for a wedding. He must use the same number of tulips in each vase. The number of tulips in each vase must be greater than 1 and less than 10. How many tulips could be in each vase?

Answer: 2, 3, 4, 6, 9.

Explanation:

Question 7.
Brady has a card collection with 64 basketball cards, 32 football cards, and 24 baseball cards. He wants to arrange the cards in equal piles, with only one type of card in each pile. How many cards can he put in each pile? Mark all that apply.
Options:
a. 1
b. 2
c. 3
d. 4
e. 8
f. 32

Answer: a,b,d,e

Explanation:
Factors of 64 are 1,2,4,8,16,32,64.
Factors of 32 are 1,2,4,8,16,32.
Factors of 24 are 1,2,3,4,6,8,12,24.
Common factors are 1,2,4,8.

Question 8.
The Garden Club is designing a garden with 24 cosmos, 32 pansies, and 36 marigolds. Each row will have only one type of plant in each row. Ben says he can put 6 plants in each row. He listed the common factors of 24, 32, and 36 below to support his reasoning.
24: 1, 2, 3, 4, 6, 8, 12, 24
32: 1, 2, 4, 6, 9, 16, 32
36: 1, 2, 3, 4, 6, 8, 12, 18, 36
Is he correct? Explain your answer. If his reasoning is incorrect, explain how he should have found the answer.

Answer: No. He can put 1,2,4 plants in each row

Explanation: The factors of 32 are incorrect. He listed as 6 and 9 are factors of 32 which is wrong and 8 is not a factor of 36.
Factors of 32 are 1,2,4,8,16,32.
Factors of 36 are 1,2,3,4,6,9,18,36.
Common factors of 24,32 and 36 are 1,2,4. So he can put 1,2,4 plants in each row.

Review/Test – Page No. 319

Question 9.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 29$
Part A
The museum is hosting a show for July that features the oil paintings by different artists. All artists show the same number of paintings and each will show more than 1 painting. How many artists could be featured in the show?

Answer: 2,3,5,6,10,15

Explanation:
Factors of 30 are 1,2,3,5,6,10,15,30.

Question 9.
Part B
The museum wants to display all the art pieces in rows. Each row has the same number of pieces and the same type of pieces. How many pieces could be in each row? Explain how you found your answer.

Answer: 1,3.

Explanation:
Factors of 30 are 1,2,3,5,6,10,15,30.
Factors of 24 are 1,2,3,4,6,8,12,24
Factors of 21 are 1,3,7,21
Common Factors are 1,3

Question 10.
Charles was skip counting at the Math Club meeting. He started to count by 8s. He said 8, 16, 24, 32, 40, and 48. What number will he say next?

Answer: 56

Explanation: Multiples of 8
8×1= 8
8×2= 16
8×3= 24
8×4= 32
8×5= 40
8×6= 48
8×7= 56.

Question 11.
Jill wrote the number 40. If her rule is add 7, what is the fourth number in Jill’s pattern? How can you check your answer?

Answer: 61

Explanation:
40
40+7= 47
47+7= 54
54+7= 61, And the fourth number is 61

Review/Test – Page No. 320

Question 12.
For numbers 12a–12e, select True or False for each statement.
a. The number 36 is a multiple of 9.
i. True
ii. False

Answer: True

Explanation: 9×4= 36.

Question 12.
b. The number 3 is a multiple of 9.
i. True
ii. False

Answer: False

Explanation: Multiples of 9 are 9,18,27,36,45,54,63, etc.

Question 12.
c. The number 54 is a multiple of 9.
i. True
ii. False

Answer: True

Explanation: 9×6= 54

Question 12.
d. The number 3 is a factor of 9.
i. True
ii. False

Answer: True

Explanation: Factors of 9 are 1,3,9.

Question 12.
e. The number 27 is a factor of 9.
i. True
ii. False

Answer: True

Explanation: Factors of 27 are 1,3,9,27

Question 13.
What multiple of 7 is also a factor of 7?

Answer: 7

Explanation: 7 is both multiple and a factor of 7.

Question 14.
Manny makes dinner using 1 box of pasta and 1 jar of sauce. If pasta is sold in packages of 6 boxes and sauce is sold in packages of 3 jars, what is the least number of dinners that Manny can make without any supplies leftover?

Answer: 6

Manny has 1 box of pasta and 1 jar of sauce and he sold in a package of 6 boxes of pasta and 3 jars of sauce. Let the packages of pasta be 6P and jars of sauce be 3s.
As Manny sold without any leftover 3S=6P,
If we take 1 package of pasta then P=1,
And 3S=6×1, where S= 6/3 which is equal to 2,
So for every package of pasta, we need 2 packages of sauce,
So the minimum purchase is 2 packages of sauce and 1 package of pasta. Since pasta packages are 6 boxes the minimum number of meals is 6.

Question 15.
Serena has several packages of raisins. Each package contains 3 boxes of raisins. Which could be the number of boxes of raisins Serena has? Mark all that apply.
Options:
a. 9
b. 18
c. 23
d. 27
e. 32

Answer: a,b,d

Explanation: Factors of 3.

Question 16.
Choose the words that make the sentence true.
The number 7 is $Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 30$ because it has $Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 31$ two factors.
The number 7 is _________ because it has
_________ two factors.

Answer: The number 7 is a prime number because it has exactly two factors.

Explanation: A Prime number is a number that is divisible 1 and itself.

Review/Test – Page No. 321

Question 17.
Winnie wrote the following riddle: I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number.
Part A
What number does Winnie’s riddle describe? Explain.

Answer: 97

Explanation: 97 is the number which ones digit is two less than tens digit.

Question 17.
Part B
Winnie’s friend Marco guessed that her riddle was about the number 79. Why can’t 79 be the answer to Winnie’s riddle?
Explain.

Answer: It’s wrong because in Winnie’s riddle ones digit is two less than tens digit. But in 79 ones digit is two greater than tens digit.

Explanation: In 79 ones digit is two greater than tens digit. So Marco guess was incorrect.

Question 18.
Classify the numbers as prime or composite.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 32$

Answer: Prime numbers are 37, 71
Composite numbers are 65, 82

Explanation:
A Composite number is a number that has more than two factors.
A Prime number is a number that is divisible 1 and itself.

Question 19.
Erica knits 18 squares on Monday. She knits 7 more squares each day from Tuesday through Thursday. How many squares does Erica knit on Friday?

Answer: 46 squares.

Explanation: 18
18+7= 25
25+7= 32
32+7= 39
39+7= 46.

Question 20.
Use the rule to write the first five terms of the pattern.
Rule: Add 10, subtract 5
First term: 11 ______ ______ ______ ______

Answer: 11,21,16,26,21.

Explanation: 11
11+10= 21
21-5= 16
16+10= 26
26-5= 21

Review/Test – Page No. 322

Question 21.
Elina had 10 tiles to arrange in a rectangular design. She drew a model of the rectangles she could make with the ten tiles.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns Review/Test img 33$
Part A
How does Elina’s drawing show that the number 10 is a composite number?

Answer: 10 is a composite number because it has more than two factors.

Explanation: The number which has more than two factors is called composite numbers.

Question 21.
Part B
Suppose Elina used 15 tiles to make the rectangular design. How many different rectangles could she make with the 15 tiles? Write a list or draw a picture to show the number and dimensions of the rectangles she could make.

Answer: 2

Explanation: one by 15 tiles and second by 3tiles in a row.

Question 21.
Part Cs
Elina’s friend Luke said that he could make more rectangles with 24 tiles than with Elina’s 10 tiles. Do you agree with Luke? Explain.

Answer: Yes

Explanation: As 24 has more factors than 10.

Page No. 329

Use the model to write an equivalent fraction.

Question 1.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 34$
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 35$
$\frac{1}{5}$ = $\frac{□}{□}$

Answer: 1/5= 2/10

Explanation: From the above figure we can see that there are 5 equal parts and in that 1 part is shaded. So the fraction of the shaded part is 1/5.

Question 2.
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 36$
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 37$
$\frac{2}{3}$ = $\frac{□}{□}$

Answer: 2/3= 6/9

Explanation: From the above figure we can see that there are 3 equal parts and in that 2 part is shaded. So the fraction of the shaded part is 2/3.

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

Question 3.
$\frac{1}{6}$ _____ $\frac{2}{12}$

Answer: 1/6=2/12

Explanation: The denominator and numerators are equal for both the fractions. So 1/6=2/12 are equal.

Question 4.
$\frac{2}{5}$ _____ $\frac{6}{10}$

Answer: 2/5≠ 6/10

Explanation: The denominator and numerators are not equal for both the fractions.

Question 5.
$\frac{4}{12}$ _____ $\frac{1}{3}$

Answer: 4/12=1/3

Explanation: The denominator and numerators are equal for both the fractions.

Question 6.
$\frac{5}{8}$ _____ $\frac{2}{4}$

Answer: 5/8≠2/4

Explanation: The denominator and numerators are not equal for both the fractions.

Question 7.
$\frac{5}{6}$ _____ $\frac{10}{12}$

Answer: 5/6=10/12

Explanation: The denominator and numerators are equal for both the fractions.

Question 8.
$\frac{1}{2}$ _____ $\frac{5}{10}$

Answer: 1/2=5/10

Explanation: The denominator and numerators are equal for both the fractions.

Question 9.
Manny used 8 tenth-size parts to model $\frac{8}{10}$. Ana used fewer parts to model an equivalent fraction. How does the size of a part in Ana’s model compare to the size of a tenth-size part? What size part did Ana use?

Answer: Larger than a tenth-size part. And she used the fifth-size part.

Explanation: A part of Ana’s model is larger than a tenth-size part. And she used the fifth-size part.

Question 10.
Use a Concrete Model How many eighth-size parts do you need to model $\frac{3}{4}$? Explain.

Answer: 6

Explanation: Let the parts be X, then 1/8×X=3/4. By calculation, we will get X as 6.
So we need 6 parts.

Page No. 330

Question 11.
Ben brought two pizzas to a party. He says that since 14_ of each pizza is left, the same amount of each pizza is left. What is his error?
$Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns img 38$

Answer: As the size of pizzas is not the same, So 1/4 of leftover pizza is not equal to another.

Question 12.
For numbers 12a–12d, tell whether the fractions are equivalent by selecting the correct symbol.
a. $\frac{3}{15}$ _____ $\frac{1}{6}$

Answer: 3/5≠1/6

Question 12.
b. $\frac{3}{4}$ _____ $\frac{16}{20}$

Answer: 3/4≠16/20

Question 12.
c. $\frac{2}{3}$ _____ $\frac{8}{12}$

Answer: 2/3=8/12

Question 12.
d. $\frac{4}{5}$ _____ $\frac{8}{10}$

Answer: 4/5=8/10.

Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review/Test

April 7, 2022March 27, 2022 by Go Math Answer Key

$go-math-grade-4-chapter-2-multiply-by-1-digit-numbers-review-test-answer-key$

Get the Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review/Test from this page and test your preparation standards. By downloading the 4th grade Go Math Chapter 2 Solution Key pdf you can make use of this guide whenever you need. So, start preparing with the HMH Go Math Grade 4 Review/Test Answer Key and score good marks in the exam.

Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review/Test

Improve your conceptual learning through the Go Math Grade 4 Answer Key Homework FL Review/Test. This guide is very helpful to tally your answers & correct the mistakes by providing various methods to solve the questions. Learn the concepts properly and approach different techniques to solve problems in Chapter 2 Multiply by 1-Digit Numbers.

Chapter 2: Review/Test

Review/Test – Page No. 95
Review/Test – Page No. 96
Review/Test – Page No. 97
Review/Test – Page No. 98

Review/Test – Page No. 95

Vocabulary

Choose the best term from the box.

Question 1.
To find the product of a 3-digit number and a 1-digit number, you can multiply the ones, multiply the tens, multiply the hundreds, and find the sum of each.
_________

Question 1.
$Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review Test img 1$

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:
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.

Concepts and Skills

Estimate. Then find the product.

Question 3.
5 5
× 2
———-
Estimate: _________
Product: _________

Answer:
Estimate: 150
Product: 110

Explanation:
5 5
× 2
———-
110

Question 4.
$2 5
× 3
———-
Estimate: $ _________
Product: $ _________

Answer:
Estimate: $ 100
Product: $ 75

Explanation:
$2 5
× 3
———-
$ 75

Question 5.
3 0 6
× 8
———-
Estimate: _________
Product: _________

Answer:
Estimate: 2,500.
Product: 2,448.

Explanation:
3 0 6
× 8
———-
2,448

Question 6.
$9 2 4
× 5
———-
Estimate: $ _________
Product: $ _________

Answer:
Estimate: $ 5,000
Product: $ 4,620.

Explanation:
$9 2 4
× 5
———-
4,620

Question 7.
3, 563
× 9
———-
Estimate: _________
Product: _________

Answer:
Estimate: 30,000.
Product: 32,067

Explanation:
3, 563
× 9
———-
32,067

Question 8.
7, 048
× 7
———-
Estimate: _________
Product: _________

Answer:
Estimate: 50,000
Product: 49,336

Explanation:
7, 048
× 7
———-
49,336

Question 9.
6, 203
× 3
————
Estimate: _________
Product: _________

Answer:
Estimate: 19,000
Product: 18,609

Explanation:
6, 203
× 3
————
18,609

Question 10.
8, 798
× 6
————
Estimate: _________
Product: _________

Answer:
Estimate: 53,000
Product: 52,788

Explanation:
8, 798
× 6
————
52,788

Review/Test – Page No. 96

Fill in the bubble completely to show your answer.

Question 11.
Which number sentence shows the Distributive Property?
Options:
a. 2 × 3 = 3 × 2
b. 5 × 0 = 0
c. 3 × (5 + 2) = (3 × 5) + (3 × 2)
d. (3 × 7) × 4 = 3 × (7 × 4)

Answer: c

Explanation:
The distributive property means solving the expression in the form of a×(b+c). So the correct option is 3 × (5 + 2) = (3 × 5) + (3 × 2).

Question 12.
Look at the pattern below. What is the missing number?
$Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review Test img 2$
Options:
a. 8,000
b. 6,000
c. 600
d. 60

Answer: b

Explanation:
5×6,000= 30,000.

Question 13.
Which comparison sentence represents the equation?
45 = 5 × 9
a. 9 more than 5 is 45
b. 9 is 5 times as many as 45
c. 5 is 4 times as many as 45
d. 45 is 5 times as many as 9

Answer: d

Explanation:
45 is 5 times as many as 9.

Question 14.
There are 4 times as many alligators as crocodiles. If the total number of alligators and crocodiles is 40, how many alligators are there?
Options:
a. 40
b. 32
c. 24
d. 8

Answer: b

Explanation:
As there are 4 times as many alligators as crocodiles and if the total number of alligators and crocodiles is 40. To find how many alligators are there, we will put them in a group of 5 as there are 4 alligators and 1 crocodile, so 40÷5= 8 groups, in which 32 are alligators and 8 are crocodiles.

Review/Test – Page No. 97

Fill in the bubble completely to show your answer.

Question 15.
Gardeners at Seed Stop are planting seeds in 12-row seed trays. They plant 8 seeds in each row. How many plants will there be in each tray if all of the seeds germinate, or grow?
Options:
a. 84
b. 86
c. 96
d. 104

Answer: c

Explanation:
As gardeners at Seed Stop are planting seeds in 12-row seed trays, and they plant 8 seeds in each row. So the number of plants will there be in each tray are 12×8= 96.

Question 16.
Which shows the product of 4 × 15 × 25?
Options:
a. 150
b. 1,200
c. 1,500
d. 1,600

Answer: c

Explanation:
The product of 4×15×25= 1,500.

Question 17.
A Broadway musical group will have 9 performances. The theater can seat 2,518 people. If all of the seats at each performance are taken, how many people will see the show?
Options:
a. 18,592
b. 22,652
c. 22,662
d. 31,622

Answer: c

Explanation:
As a broadway musical group will have 9 performances and the theater can seat 2,518 people, so number of people will see the show are 9×2,518= 22,662.

Question 18.
The table below shows the type of film sold and the number of rolls in one pack at a local gift shop.
$Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review Test img 3$
Hannah buys 3 packs of 36 exposure film and 2 packs of 24 exposure film. She uses 8 rolls of film. How many rolls does she have left?
Options:
a. 8
b. 12
c. 20
d. 24

Answer: b

Explanation:
Hannah buys 3 packs of 36 exposure film and 2 packs of 24 exposure film, so the total number of films are 3×4= 12, 2×4= 8 which is 12+8= 20. And she uses 8 rolls, then the number of rolls left are 20-8= 12.

Review/Test – Page No. 98

Constructed Response

Question 19.
John’s grade has 3 classrooms. Each classroom has 14 tables. Two students sit at each table. About how many students are there in all? Use pictures, words, or numbers to show how you know.
About ______ students

Answer: 84 students.

Explanation:
As John’s grade has 3 classrooms, and each classroom has 14 tables and two students sit at each other, so total number of students are 14×2= 28 as John has 3 classrooms, so 28×3= 84 students.

Performance Task

Justin has $450 to buy supplies for the school computer lab. He buys 8 boxes of printer paper that cost $49 each.
$Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review Test img 4$

Question 20.
A. About how much money does Justin spend on the printer paper? Describe how you made your estimate.
About $ ______

Answer: $400.

Explanation:
As each printer paper costs $49 and Justin buys 8 boxes, so total costs $49×8= $392. And the estimated cost is $400.

Question 20.
B. Find the actual amount of money Justin spends on the printer paper. Explain whether your estimate is close to the actual price.
Actual price $ ______

Answer: $392.

Explanation:
The actual amount of money Justin spends on the printer paper is $49×8= $392. Yes, the estimation is close to the actual price.

Question 20.
C. Will Justin have enough money left over to buy 3 packages of blank DVDs that cost $17 each? Explain your answer.

Answer: Yes, Justin will have enough money left.

Explanation:
As Justin left some money which is $450-$392= $51, after he bought printer paper for $392, so he can buy 3 packages of blank DVDs that cost $17 each which costs $17×3= $51.

Conclusion:

Our math experts wishing that you collect the Go Math Grade 4 Answer Key Homework FL Chapter 2 Multiply by 1-Digit Numbers Review/Test effective. If you want to grasp more concepts of chapter 2, access the Go Math Grade 4 Chapter 2 Multiply by 1-Digit Numbers homework practice FL Answer Key and seek help whenever you need it.

Go Math Grade 4 Answer Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review/Test

April 7, 2022March 27, 2022 by Go Math Answer Key

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

Improve your subject knowledge and problem-solving skills with the help of Go Math Grade 4 Answer Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review/Test Pdf. All the questions and answers covered in this HMH Go Math Grade 4 Review/Test Answer Key are prepared by math experts and support students to score good marks in the exam.

Go Math Grade 4 Answer Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review/Test

Students who are searching for the best review/test guide can refer to this helpful Go Math Grade 4 Solution Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review/Test. As it includes all the concepts in Chapter 6 Fraction Equivalence and Comparison. So, students can discover the methods to solve the problems easily and can explore the knowledge by giving the question from Review/Test. Click on the respective link and download it for better practice.

Chapter 6: Review/Test

Review/Test – Page No. 261
Review/Test – Page No. 262
Review/Test – Page No. 263
Review/Test – Page No. 264

Review/Test – Page No. 261

Choose the best term from the box.
$Go Math Grade 4 Answer Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review Test img 1$

Question 1.
A ________________ is a common multiple of two or more denominators.
________

Answer:
A common denominator is a common multiple of two or more denominators..

Question 2.
A fraction is in _________________ when the numerator and denominator have only 1 as a common factor
________

Answer:
A fraction is in simplest form when the numerator and denominator have only 1 as a common factor.

Question 3.
A ________________ is a known size or amount that helps you understand another size or amount.
________

Answer:
A benchmark is a known size or amount that helps you understand another size or amount.

Write two equivalent fractions.

Question 4.
$\frac{4}{6}$

Answer: $\frac{6}{9}$ and $\frac{8}{12}$.

Explanation:
To find equivalent fractions we will multiply its numerator and denominator by the same number. Firstly we will calculate GCF for the given fraction i.e $\frac{4}{6}$, the GCF for (4,6) is 2. As GCF is not equal to 1, we will divide the numerator and denominator by 2. By dividing with 2 we will get the fraction as $\frac{2}{3}$. Now we will multiply the numerator and denominator with 3,
So the fraction will be 3($\frac{2}{3}$)
= $\frac{6}{9}$. For the second equivalent fraction, we will multiply numerator and denominator with 4,
So the fraction will be 4($\frac{2}{3}$)
= $\frac{8}{12}$.
So, the two equivalent fractions of $\frac{4}{6}$ are $\frac{6}{9}$ and $\frac{8}{12}$.

Question 5.
$\frac{6}{10}$

Answer: $\frac{9}{15}$ and $\frac{12}{20}$.

Explanation:
To find equivalent fractions we will multiply its numerator and denominator by the same number. Firstly we will calculate GCF for the given fraction i.e $\frac{6}{10}$, the GCF for (6,10) is 2. As GCF is not equal to 1, we will divide the numerator and denominator by 2. By dividing with 2 we will get the fraction as $\frac{3}{5}$. Now we will multiply the numerator and denominator with 3,
So the fraction will be 3($\frac{3}{5}$)
= $\frac{9}{15}$. For the second equivalent fraction, we will multiply numerator and denominator with 4,
So the fraction will be 4($\frac{3}{5}$)
= $\frac{12}{20}$.
So, the two equivalent fractions of $\frac{3}{5}$ are $\frac{9}{15}$ and $\frac{12}{20}$.

Question 6.
$\frac{2}{8}$

Answer: $\frac{3}{12}$ and $\frac{4}{16}$.

Explanation:
To find equivalent fractions we will multiply its numerator and denominator by the same number. Firstly we will calculate GCF for the given fraction i.e $\frac{2}{8}$, the GCF for (2,8) is 2. As GCF is not equal to 1, we will divide the numerator and denominator by 2. By dividing with 2 we will get the fraction as $\frac{1}{4}$. Now we will multiply the numerator and denominator with 3,
So the fraction will be 3($\frac{1}{4}$)
= $\frac{3}{12}$. For the second equivalent fraction, we will multiply numerator and denominator with 4,
So the fraction will be 4($\frac{1}{4}$)
= $\frac{4}{16}$.
So, the two equivalent fractions of $\frac{2}{8}$ are $\frac{3}{12}$ and $\frac{4}{16}$.

Write each pair of fractions as a pair of fractions with a common denominator.

Question 7.
$\frac{3}{4} \text { and } \frac{7}{8}$

Answer: $\frac{6}{8}$ , $\frac{7}{8}$.

Explanation:
To get the common denominators we will multiply $\frac{3}{4}$ with 2, so that the fraction will be $\frac{6}{8}$. As the other fraction is $\frac{7}{8}$. So the denominators are the same.

Question 8.
$\frac{2}{3} \text { and } \frac{1}{4}$

Answer: $\frac{8}{12}$ and $\frac{3}{12}$.

Explanation:
To get the common denominators we will multiply $\frac{2}{3}$ with 4 and $\frac{1}{4}$ with 3, so that the fractions will be $\frac{8}{12}$ and $\frac{3}{12}$. So the denominators are same.

Question 9.
$\frac{7}{10} \text { and } \frac{4}{5}$

Answer: $\frac{7}{10}$ and $\frac{8}{10}$.

Explanation:
To get the common denominators we will multiply $\frac{4}{5}$ with 2, so that the fraction will be $\frac{8}{10}$. As the other fraction is $\frac{7}{10}$. And the denominators are same.

Compare. Write <, >, or 5.

Question 10.
$\frac{5}{8}$ _____ $\frac{5}{12}$

Answer: $\frac{5}{8}$ > $\frac{5}{12}$.

Explanation:
To compare $\frac{5}{8}$ and $\frac{5}{12}$ first we will find LCM of 8 and 12.
And the LCM of (8,12) is 24. Now we will multiply $\frac{5}{8}$ with 3 and $\frac{5}{12}$ with 2, so the fraction will be $\frac{15}{24}$ and the other fraction is $\frac{10}{24}$.
So $\frac{15}{24}$ is greater than $\frac{10}{24}$.

Question 11.
$\frac{10}{12}$ _____ $\frac{5}{6}$

Answer: $\frac{10}{12}$ = $\frac{5}{6}$.

Explanation:
To compare $\frac{10}{12}$ and $\frac{5}{6}$,first we will find LCM of 12 and 6.
And the LCM of (12,6) is 12. Now we will multiply $\frac{5}{6}$ with 2, so the fraction will be $\frac{10}{12}$ and the other fraction is $\frac{10}{12}$.
So $\frac{10}{12}$ is equal to $\frac{10}{12}$.

Question 12.
$\frac{1}{2}$ _____ $\frac{3}{10}$

Answer: $\frac{1}{2}$ > $\frac{3}{10}$.

Explanation:
To compare $\frac{1}{2}$ and $\frac{3}{10}$ first we will find LCM of 2 and 10.
And the LCM of (2,10) is 10. Now we will multiply $\frac{1}{2}$ with 5, so the fraction will be $\frac{5}{10}$ and the other fraction is $\frac{3}{10}$.
So $\frac{5}{10}$ is greater than $\frac{3}{10}$.

Question 13.
$\frac{1}{4}$ _____ $\frac{1}{3}$

Answer: $\frac{1}{4}$ < $\frac{1}{3}$.

Explanation:
To compare $\frac{1}{4}$ and $\frac{1}{3}$ first we will find LCM of 4 and 3.
And the LCM of (4,3) is 12. Now we will multiply $\frac{1}{4}$ with 3 and $\frac{1}{3}$ with 4, so the fraction will be $\frac{3}{12}$ and the other fraction is $\frac{4}{12}$.
So $\frac{3}{12}$ is less than $\frac{4}{12}$.

Write the fractions in order from least to greatest.

Question 14.
$\frac{2}{3}, \frac{3}{4}, \frac{1}{6}$

Answer: $\frac{1}{6}$ < $\frac{2}{3}$< $\frac{3}{4}$.

Explanation:
To write the fraction from least to greatest we will find LCM of 3,4,6. And the LCM of (3,4,6) is 12. Now we will multiply
$\frac{2}{3}$ with 4 and $\frac{3}{4}$ with 3 and $\frac{1}{6}$ with 2, so the fraction will be
$\frac{8}{12}$ and $\frac{9}{12}$, $\frac{2}{12}$
So $\frac{2}{12}$ is less than $\frac{8}{12}$ is less than $\frac{9}{12}$.

Question 15.
$\frac{7}{10}, \frac{4}{5}, \frac{1}{2}, \frac{4}{12}$

Answer: $\frac{4}{12}$ < $\frac{1}{2}$< $\frac{7}{10}$< $\frac{4}{5}$.

Explanation:
To write the fraction from least to greatest we will find LCM of 10,5,2,12. And the LCM of (10,5,2,12) is 60. Now we will multiply
$\frac{7}{10}$ with 6 and $\frac{4}{5}$ with 12 and $\frac{1}{2}$ with 30 and $\frac{4}{12}$ with 5 , so the fraction will be
$\frac{42}{60}$ and $\frac{48}{60}$, $\frac{30}{60}$, $\frac{20}{60}$
So $\frac{20}{60}$ is less than $\frac{30}{60}$ is less than $\frac{42}{60}$ is less than
$\frac{48}{60}$.

Review/Test – Page No. 262

Fill in the bubble completely to show your answer.

Question 16.
Paco needs at least $\frac{3}{8}$ yard of twine to build a model ship. How much twine could he buy?
Options:
a. $\frac{3}{10}$ yard
b. $\frac{1}{4}$ yard
c. $\frac{3}{5}$ yard
d. $\frac{1}{8}$ yard

Answer: c.

Explanation:

a) 3/10 yard. As we know that for two rational numbers with the same numerator but with different denominators the number whose denominator is smaller is a greater quantity.
Hence 3/10 < 3/8. And option a is incorrect.

b) 1/4 yard. As to compare to rational numbers we have to either make the numerator equal or their denominator equal. Hence here we multiply and divide 1/4 by 2 to get 8 in the denominator. As 2/8 < 3/8
since the denominator is the same and the number with the same denominator but with different numerators are compared as whose numerator is greater is a greater quantity. And the option b is incorrect.

c) 3/4 yard. As both the numbers have the same numerator but different denominator and we know that for two rational numbers with the same numerator but with different denominators the number whose denominator is smaller is a greater quantity. As 3/8 < 3/4, so option c is correct.

d) 1/8 yard. As both the numbers have the same denominator and we know that for two rational numbers with the same denominator but with the different numerators, the number whose numerator is smaller is a smaller quantity. So 1/8 < 3/8 and the option d is incorrect.

Question 17.
Rachel, Nancy, and Diego were in a fishing competition. Rachel’s fish was $\frac{7}{8}$ foot long, Nancy’s fish was $\frac{1}{4}$ foot long, and Diego’s fish was $\frac{1}{2}$ foot long. What are the lengths of the fish in order from least to greatest?
Options:
a. $\frac{7}{8}$ foot, $\frac{1}{2}$ foot, $\frac{1}{4}$ foot
b. $\frac{1}{2}$ foot, $\frac{7}{8}$ foot, $\frac{1}{4}$ foot
c. $\frac{7}{8}$ foot, $\frac{1}{4}$ foot, $\frac{1}{2}$ foot
d. $\frac{1}{4}$ foot, $\frac{1}{2}$ foot, $\frac{7}{8}$ foot

Answer: d

Explanation:
As Rachel’s fish was $\frac{7}{8}$ foot long, Nancy’s fish was $\frac{1}{4}$ foot long, Diego’s fish was $\frac{1}{2}$ foot long, so to find the lengths of the fish in order from least to greatest we will find the LCM of (8,4,2), so the LCM of (8,4,2) is 8 and we will multiply $\frac{1}{4}$ with 2 and $\frac{1}{2}$ with 4, so the fraction will be $\frac{2}{8}$ and $\frac{4}{8}$. The lengths of the fish in order from least to greatest are $\frac{2}{8}$, latex]\frac{4}{8}[/latex], latex]\frac{7}{8}[/latex]

Question 18.
Amy needs $\frac{6}{8}$ gallon of fruit juice to make punch. She needs an equal amount of sparkling water. How much sparkling water does she need?
Options:
a. $\frac{2}{8}$ gallon
b. $\frac{1}{2}$ gallon
c. $\frac{2}{3}$ gallon
d. $\frac{3}{4}$ gallon

Answer: d

Explanation:
Amy needs $\frac{6}{8}$ gallon of fruit juice to make punch and she needs an equal amount of sparkling water, so Amy needs $\frac{6}{8}$ or $\frac{3}{4}$ gallon.

Question 19.
Gavin is building a model of a kitchen. In the model, $\frac{2}{5}$ of the floor tiles are white, $\frac{1}{2}$ of the floor tiles are yellow, and $\frac{1}{10}$ of the floor tiles are brown. How many floor tiles could be in the model?
Options:
a. 2
b. 5
c. 10
d. 17

Answer: c

Explanation:
As Gavin is building a model of a kitchen and $\frac{2}{5}$ of the floor tiles are white, $\frac{1}{2}$ of the floor tiles are yellow, and $\frac{1}{10}$ of the floor tiles are brown. To find the total number of tiles we will add up all color tiles. For that, we will multiply $\frac{1}{2}$ with 5 and $\frac{2}{5}$ with 2 to set the denominators equal. Then the fractions will be $\frac{5}{10}$ and $\frac{4}{10}$. Now add all three
$\frac{5}{10}$+$\frac{4}{10}$+$\frac{1}{10}$
= 10.
So the number of floor tiles modeled is 10

Review/Test – Page No. 263

Fill in the bubble completely to show your answer.

Question 20.
Bill has enough money to buy no more than $\frac{1}{2}$ pound of cheese. How much cheese could he buy?
Options:
a. $\frac{1}{3}$ pound
b. $\frac{4}{6}$ pound
c. $\frac{5}{8}$ pound
d. $\frac{3}{4}$ pound

Answer: a

Explanation:
As Bill has enough money to buy no more than $\frac{1}{2}$ pound of cheese, so he needs to buy $\frac{1}{3}$ pounds.

Question 21.
Students planted 6 equal-size gardens on Earth Day. They divided each garden into 3 equal sections and planted herbs in 2 of the 3 sections. What fraction of the gardens did the students plant with herbs?
Options:
a. $\frac{3}{6}$
b. $\frac{2}{6}$
c. $\frac{6}{18}$
d. $\frac{12}{18}$

Answer: d

Explanation:
As students planted 6 equal-size gardens on Earth Day, and they divided each garden into 3 equal sections and planted herbs in 2 of the 3 sections, so the fraction of the gardens did the students plant with herbs are we need to multiply 6×3 and will get 18 sections in all gardens, then we need to multiply 2×6 and get 12 sections are herbs. So, 12 out of 18 are herbs i.e $\frac{12}{18}$.

Question 22.
Noah and Leslie live the same distance from school. Which could be the distances they live from school?
Options:
a. $\frac{7}{100}$ kilometer and $\frac{7}{10}$ kilometer
b. $\frac{5}{10}$ kilometer and $\frac{1}{5}$ kilometer
c. $\frac{80}{100}$ kilometer and $\frac{8}{10}$ kilometer
d. $\frac{6}{10}$ kilometer and $\frac{2}{5}$ kilometer

Answer: c.

Explanation:
The option c is correct, as $\frac{80}{100}$ km is equal to $\frac{8}{10}$ when it is reduced.

Question 23.
Keiko needs $\frac{8}{12}$ yard of fabric to finish her quilt. What is $\frac{8}{12}$ written in simplest form?
Options:
a. $\frac{4}{6}$
b. $\frac{2}{3}$
c. $\frac{3}{4}$
d. $\frac{1}{2}$

Answer: b

Explanation:
As Keiko needs $\frac{8}{12}$ yard of fabric to finish her quilt and the simplest form of $\frac{8}{12}$ is $\frac{2}{3}$.

Review/Test – Page No. 264

Question 24.
Sam needs $\frac{4}{6}$ cup of laundry detergent for his laundry. The cap on top of the laundry detergent holds $\frac{1}{3}$ cup. He has 1 capful of detergent. Does he have enough? Explain.

Answer: Sam does not have enough.

Explanation:
As Sam needs $\frac{4}{6}$ cup of laundry detergent for his laundry and the cap holds only $\frac{1}{3}$ and Sam has 1 capful of detergent, and Sam needs 2 cups instead of 1 cup because $\frac{4}{6}$ is equivalent to $\frac{2}{3}$ and Sam only has $\frac{1}{3}$ cup, so he needs 2 cups.

Question 25.
The table shows the distances of some places in town from the school.
$Go Math Grade 4 Answer Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review Test img 2$
A. Are any of the places shown in the table closer than $\frac{1}{2}$ mile to school? Explain how you know.

Answer: Library $\frac{3}{5}$ mile.

Explanation:
To find which place is closer, we will find the LCM of the denominators i.e (5,2,4,10). And the LCM of (5,2,4,10) is 20, so we will divide $\frac{3}{5}$ with 4, $\frac{1}{2}$ with 10, $\frac{3}{4}$ with 5 and $\frac{8}{10}$ with 2. So that the fractions will have same denominators and we can find easily which place is closer. And the fractions after multiplying are $\frac{12}{20}$, $\frac{10}{20}$, $\frac{15}{20}$ and $\frac{16}{20}$. So the places closer than $\frac{1}{2}$ mile to school are post office which is $\frac{10}{20}$ mile and next place is library which is $\frac{12}{20}$ mile.

Question 25.
B. Are any of the places shown in the table the same distance from school? Explain how you know.

Answer: Yes.

Question 25.
C. Which place is farthest from school? Explain.

Answer: Townhall.

Explanation:
Townhall is the farthest from the school as it’s distance is $\frac{8}{10}$ mile.

Conclusion:

Ace up your preparation with this Go Math Grade 4 Answer Key Chapter 6 Homework FL in pdf download. Hence, you can practice effectively and score good grades in the exam. Here, we have curated a detailed explanation of questions from ch 6 and provided Go Math Grade 4 Answer Key Homework FL Chapter 6 Fraction Equivalence and Comparison Review/Test. So, We advise students to understand the topics and apply them in the real world.

Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million

April 7, 2022March 27, 2022 by Go Math Answer Key

$go-math-grade-4-chapter-1-place-value-addition-and-subtraction-to-one-million-answer-key$

Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million pdf formatted download links are provided here for all concepts. Students of Grade 4 can take help from Go Math solutions for better preparation and score high marks in the exams. Want to help the students in offering immense knowledge? this is the best resource for them. So, Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million is helpful and understandable by students. It includes each and every question with step by step explanation in a simple way.

Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million

Chapter 1 of Go Math 4th Grade Answer Keys includes topis like Place value relationships, Read and write numbers, Compare and Order numbers, Round numbers, Rename numbers, etc. All these topics are illustrated explicitly which addresses the toppers to learn quickly. Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million Questions & Solutions are provided in a fundamental way that makes students not find any difficulty in learning & solving.

Chapter 1-Lesson 1:

Common Core – Model Place Value Relationships (Page 5)
Common Core – Model Place Value Relationships (Page 6)
Common Core – Model Place Value Relationships (Page 7)
Common Core – Model Place Value Relationships (Page 8)
Common Core – Model Place Value Relationships (Page 9)
Common Core – Model Place Value Relationships (Page 10)

Chapter 1-Lesson 2:

Common Core – Read and Write Numbers (Page 11)
Common Core – Read and Write Numbers (Page 12)
Common Core – Read and Write Numbers (Page 13)
Common Core – Read and Write Numbers (Page 14)
Common Core – Read and Write Numbers (Page 15)
Common Core – Read and Write Numbers (Page 16)

Chapter 1-Lesson 3:

Common Core – Compare and Order Numbers (Page 18)
Common Core – Compare and Order Numbers (Page 20)
Common Core – Compare and Order Numbers (Page 21)
Common Core – Compare and Order Numbers (Page 22)

Chapter 1-Lesson 4:

Common Core – Round Numbers (Page 24)
Common Core – Round Numbers (Page 25)
Common Core – Round Numbers (Page 26)
Common Core – Round Numbers (Page 27)
Common Core – Round Numbers (Page 28)

Chapter 1-Lesson 5:

Common Core – Chapter 1 -Mid-Chapter Checkpoint (Page 29)
Common Core – Chapter 1 -Mid-Chapter Checkpoint (Page 30)

Chapter 1-Lesson 6:

Common Core – Investigate • Rename Numbers (Page 32)
Common Core – Investigate • Rename Numbers (Page 33)
Common Core – Investigate • Rename Numbers (Page 34)
Common Core – Investigate • Rename Numbers (Page 35)
Common Core – Investigate • Rename Numbers (Page 36)

Chapter 1-Lesson 7:

Common Core – Add Whole Numbers (Page 39)
Common Core – Add Whole Numbers (Page 40)
Common Core – Add Whole Numbers (Page 41)
Common Core – Add Whole Numbers (Page 42)

Chapter 1-Lesson 8:

Common Core – Subtract Whole Numbers (Page 44)
Common Core – Subtract Whole Numbers (Page 45)
Common Core – Subtract Whole Numbers (Page 46)
Common Core – Subtract Whole Numbers (Page 47)
Common Core – Subtract Whole Numbers (Page 48)

Chapter 1-Lesson 9:

Problem Solving • Comparison Problems with Addition and Subtraction (Page 50)
Problem Solving • Comparison Problems with Addition and Subtraction (Page 51)
Problem Solving • Comparison Problems with Addition and Subtraction (Page 52)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 53)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 54)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 55)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 56)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 57)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 58)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 59)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 60)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 65)
Problem Solving • Comparasion Problems with Addition and Substraction (Page 66)

Common Core – Model Place Value Relationships (Page 5)

$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million$

Question 1.
Describe the pattern in the shapes of the models. What will be the shape of the model for 10,000?

Answer: The pattern shows cube, long, flat, cube. So the shape of the model for 10,000 will be long.

Question 2.
Describe the pattern you see in the sizes of the models. How will the size of the model for 100,000 compare to the size of the model for 10,000?

Answer: Each model is 10 times the previous model, so the model for 100,000 will be 10 times the size of the model for 10,000.

Common Core – Model Place Value Relationships (Page 6)

Value of a Digit

The value of a digit depends on its place-value position in the number. A place-value chart can help you understand the value of each digit in a number. The value of each place is 10 times the value of the place to the right.

$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 2$

Question 1.
The value of the digit 9 is 9 ten thousands, or:

Answer: The place value of the digit 9 in 894,613 is 90,000.

Compare the values of the underlined digits.
2,304 16,135

Answer: The value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Explanation: Every digit in a number has a place value and the place value can be defined as the value represented by a digit in a number on the basis of its position in the number. So the place value of the digit 3 in 2,304 is 300. And the place value of the digit 3 in 16,135 is 30. As each hundred is 10 times as many as 10, so 3 hundreds are ten times as many as 3 tens. So, the value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Question 2.
STEP 1 Find the value of 3 in 2,304.
Show 2,304 in a place-value chart.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 3$

Answer: The value of 3 in 2,304 is 300

Explanation:

Question 2.
STEP 2 Find the value of 3 in 16,135.

Show 16,135 in a place-value chart.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 4$
So, the value of 3 in 2,304 is ___________ times the value of 3 in 16,135.

Answer: The value of 3 in 16,135 is 30. So, the value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Explanation:
Each hundred is 10 times as many as 10, so 3 hundreds are ten times as many as 3 tens. So, the value of 3 in 16,135 is 30. So, the value of 3 in 2,304 is 10 times the value of 3 in 16,135.

Common Core – Model Place Value Relationships (Page 7)

Question 1.
Complete the table below.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 5$

Answer:

Explanation:

Find the value of the underlined digit.

Question 2.
703,890

Answer: The value of the digit 7 in 703,890 is 700,000.

Question 3.
63,540

Answer: The value of the digit 4 in 63,540 is 40.

Question 4.
182,034

Answer: The value of the digit 8 in 182,034 is 80,000.

Question 5.
345,890

Answer: The value of the digit 5 in 345,890 is 5,000.

Compare the values of the underlined digits.

Question 6.
2,000 and 200

The value of 2 in 2,000 is ___________ times the value of 2 in 200

Answer: 10 times.

Explanation: The value of 2 in 2000 is 10 times the value of 2 in 200.

Question 7.
40 and 400

The value of 4 in 400 is ___________ times the value of 4 in 40

Answer: 10 times.

Explanation: The value of 4 in 400 is 10 times the value of 4 in 40.

Find the value of the underlined digit.

Question 8.
230,001

Answer: The place value of the digit 3 in 230,001 is 30,000.

Question 9.
803,040

Answer: The place value of the digit 3 in 230,001 is 30,000.

Question 10.
46,842

Answer: The place value of the digit 2 in 46,842 is 2.

Question 11.
980,650

Answer: The place value of the digit 9 in 980,650 is 900,000.

Compare the values of the underlined digits.

Question 12.
67,908 and 76,908

Answer: The value of 7 in 76,908 is 10 times the value of 7 in 67,908.

Explanation: As the value of 7 in 76,908 is 70,000 and the value of 7 in 67,908 is 7,000. So the value of 7 in 76,908 is 10 times the value of 7 in 67,908.

Question 13.
546,300 and 3,456

Answer: The value of 3 in 3,456 is 10 times the value of 3 in 546,300.

Explanation: As the value of 3 in 3,456 is 3,000 and the value of 3 in 546,300 is 300. So the value of 3 in 3,456 is 10 times the value of 3 in 546,300.

Question 14.
Greg has collected 4,385 pennies and Hannah has collected 3,899 pennies. How many times as great as the value of 3 in 4,385 is the value of 3 in 3,899?

Answer: The value of the digit 3 in 3,899 is 10 times more than the value of the digit 3 in 4,385.

Explanation:
The value of the digit 3 is 4,385 is 300 and the value of 3 in 3,899 is 3000. So the value of the digit 3 in 3,899 is 10 times more than the value of the digit 3 in 4,385.

Question 15.
Shawn wants to model the number 13,450 using base-ten blocks. How many large cubes, flats, and longs does he need to model the number?

Answer: Shawn needs 13 large cubes, 4 flats, and 5 longs.

Explanation: Each large cube represents 1000, so 13 large cubes will represent 13×1000= 13,000, and each flat represent 100 so each 4 flats represent 4×100= 400, and each long represents 10 so 5 longs represent 5×10= 50.
So 13,000+400+50= 13,450.

Common Core – Model Place Value Relationships (Page 8)

$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 6$

Question 14.
What is the value of the digit 7 in the population of Memphis?

Answer: The value of digit 7 in 676,640 is 70,000.

Explanation: The population of Memphis is 676,640, so the value of digit 7 in 676,640 is 70,000.

Question 14.
What is the value of the digit 1 in the population of Denver?

Answer: The value of the digit 1in 610,345 is 10,000.

Explanation: The population of Denver is 610,345, so the value of the digit 1in 610,345 is 10,000.

Question 14.
How many times as great as the value of the digit 1 in the population of Cleveland is this value?

Answer: The value of digit 1 in 431,369 is 1000.

Explanation: The population of Cleveland is 431,369, so the value of digit 1 in 431,369 is 1000.

Question 14.
Which city’s population has a 4 in the hundred thousands place?

Answer: Cleveland is the city with 4 in the hundred thousands place.

Explanation: Cleveland is the city with 4 in the hundred thousands place. As the population of Cleveland is 431,369 and the value of 4 in 431,369 is 400,000.

Question 15.
How many models of 100 do you need to model 3,200? Explain.

Answer: 32 hundreds.

Explanation: As 3 thousands are the same as 30 hundreds, so 30 hundreds+ 2 hundreds= 32 hundreds.

Question 16.
Sid wrote 541,309 on his paper. Using numbers and words, explain how the number would change if he switched the digits in the hundred thousands and tens places.

Answer: The number is 41,359.

Explanation: The number would be 041,359, but since zeros are not recorded when they are in the left-most place value position. So the number now is 41,359.

Question 17.
There are 686,147 books at the Greenville Library. What is the value of the digit 8 in this number?
(a) 80
(b) 8,000
(c) 80,000
(d) 800.000

Answer: The value of the digit 8 in 686,147 is 80,000.

Explanation: As there are 686,147 books in the library, so the value of the digit 8 in 686,147 is 80,000.

Question 18.
The value of 7 in 375,081 is 7,000.
(a) True
(b) False

Answer: False.

Explanation: As the digit 7 is in thousands place, so the value of 7 in 375,081 is 70,000.

Question 18.
The value of 6 in 269,480 is 600,000.
(a) True
(b) False

Answer: False.

Explanation: As the digit 6 is in thousands place, so the value of 6 in 269,480 is 60,000.

Question 18.
The value of 5 in 427,593 is 500.
(a) True
(b) False

Answer: True.

Explanation: As the digit 5 is in hundreds place, so the value of 5 in 427,593 is 500.

Question 18.
The value of 1 in 375,081 is 10.
(a) True
(b) False

Answer: False.

Explanation: As the digit 1 is in ones place, so the value of 1 in 375,081 is 1.

Question 18.
The value of 4 in 943,268 is 40,000.
(a) True
(b) False

Answer: True.

Explanation: As the digit 4 is in thousands place, so the value of 4 in 943,268 is 40,000.

Common Core – Model Place Value Relationships (Page 9)

Model Place Value Relationships

Find the value of the underlined digit.

Question 1.
6,035
30

Question 2.
43,782

Answer: The value of 7 in 43,782 is 700

Explanation: As the digit 7 is in hundreds place so the value of 7 in 43,782 is 700.

Question 3.
506,087

Answer: The value of 7 in 506,087 is 7.

Explanation: As the digit 7 is in ones place so the value of 7 in 506,087 is 7.

Question 4.
49,254

Answer: The value of 9 in 49,254 is 9,000.

Explanation: As the digit 9 is in thousands place so the value of 9 in 49,254 is 9,000.

Question 5.
136,422

Answer: The value of 3 in 136,422 is 30,000.

Explanation: As the digit 3 is in thousands place so the value of 3 in 136,422 is 30,000.

Question 6.
673,512

Answer: The value of 5 in 673,512 is 500.

Explanation: As the digit 5 is in hundreds place so the value of 5 in 673,512 is 500.

Question 7.
814,295

Answer: The value of 8 in 814,295 is 800,000.

Explanation: As the digit 8 is in hundred thousands place so the value of 8 in 814,295 is 800,000.

Question 8.
736,144

Answer: The value of 6 in 736,144 is 6,000.

Explanation: As the digit 6 is in thousands place so the value of 6 in 736,144 is 6,000.

Compare the values of the underlined digits.

Question 9.
6,300 and 530

The value of 3 in ___________ is ___________ times the value of 3 in ___________ .

Answer: The value of 3 in 6,300 is 10 times the value of 3 in 530.

Explanation:
The value of 3 in 6300 is 300 and the value of 3 in 530 is 30.
So the value of 3 in 6,300 is 10 times the value of 3 in 530.

Question 10.
2,783 and 7,283

The value of 2 in ___________ is ___________ times the value of 2 in ___________ .

Answer: The value of 2 in 2,738 is 10 times the value of 2 in 7,238.

Explanation:
The value of 2 in 2,738 is 2,000 and the value of 2 in 7,238 is 200.
So the value of 2 in 2,738 is 10 times the value of 2 in 7,238.

Question 11.
34,258 and 47,163

The value of 4 in ___________ is ___________ times the value of 4 in ___________.

Answer: The value of 4 in 47,163 is 10 times the value of 4 in 34,258.

Explanation:
The value of 4 in 47,163 is 40,000 and the value of 4 in 34,258 is 4000.
So the value of 4 in 47,163 is 10 times the value of 4 in 34,258.

Question 12.
503,497 and 26,475

The value of 7 in ___________ is ___________ times the value of 7 in ___________ .

Answer: The value of 7 in 26,475 is 10 times the value of 7 in 503,497.

Explanation:
The value of 7 in 26,475 is 70 and the value of 7 in 503,497 is 7.
So the value of 7 in 26,475 is 10 times the value of 7 in 503,497.

Problem Solving

Use the table for 13–14.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 7$

Question 13.
What is the value of the digit 9 in the attendance at the Redskins vs. Titans game?

The value of 9 is ___________ .

Answer: The value of 9 is 9,000.

Explanation: As the digit 9 is in thousands place, so the value of the digit 9 in 69,143 is 9,000.

Question 14.
The attendance at which game has a 7 in the ten thousands place?

Answer: Ravens vs. Panthers attendance is 73,021

Explanation: The attendance at Ravens vs. Panthers game has a 7 in the ten thousands place.

Common Core – Model Place Value Relationships (Page 10)

Lesson Check

Question 1.
During one season, a total of 453,193 people attended a baseball team’s games. What is the value of the digit 5 in the number of people?
(a) 500
(b) 5,000
(c) 50,000
(d) 500,000

Answer: c.

Explanation: The total number of people attended for baseball game are 453,193 and the value of the digit 5 in 453,193 is 5 ten thousands which is 50,000.

Question 2.
Hal forgot the number of people at the basketball game. He does remember that the number had a 3 in the tens place. Which number could Hal be thinking of?
(a) 7,321
(b) 3,172
(c) 2,713
(d) 1,237

Answer: d.

Explanation: The number which has 3 in tens place is 1,237.

Spiral Review

Question 3.
Hot dog buns come in packages of 8. For the school picnic, Mr. Spencer bought 30 packages of hot dog buns. How many hot dog buns did he buy?
(a) 24
(b) 38
(c) 110
(d) 240

Answer: d

Explanation: The number of hot dog buns in a package are 8 and Mr. Spencer bought 30 packages, so the total number of hot dog buns he bought is 8×30= 240.

Question 4.
There are 8 students on the minibus. Five of the students are boys. What fraction of the students are boys?
(a) $\frac{3}{8}$
(b) $\frac{5}{8}$
(c) $\frac{5}{5}$
(d) $\frac{8}{8}$

Answer: b.

Explanation: The total number of students are 8 and in that 5 are boys, so the fraction of the students are boys is $\frac{5}{8}$

Question 5.
The clock below shows the time when Amber leaves home for school. At what time does Amber leave home?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 8$
(a) 2:41
(b) 8:02
(c) 8:10
(d) 8:20

Answer: c

Explanation: Amber leaves home for school at 8:10.

Question 6.
Jeremy drew a polygon with four right angles and four sides with the same length.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 9$
What kind of polygon did Jeremy draw?
(a) hexagon
(b) square
(c) trapezoid
(d) triangle

Answer: b

Explanation: Jeremy draws a square, as it’s all sides are equal.

Common Core – Read and Write Numbers (Page 11)

Question 1.
The International Space Station uses 262,400 solar cells to change sunlight to electricity. Write 262,400 in standard form, word form, and expanded form.

Use a place-value chart. Each group of three digits separated by a comma is called a period. Each period has hundreds, tens, and ones. The greatest place-value position in the thousands period is hundred thousands.

Write 262,400 in the place-value chart below.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 10$

Answer:
The word form of 262,400 is two hundred sixty-two thousand, four hundred, and the expanded form of 262,400 is 200,000+60,000+2,000+400.

Explanation:

Use place value to read and write numbers.

Question 2.
Word Form: ninety-two thousand,one hundred seventy
Standard Form: ___________
Expanded Form: 90,000 + 2,000 + ___________ + 70

Answer:
Standard Form: 92,170.
Expanded Form: 90,000+2,000+100+70+0.

Explanation:
A standard form is a way to write large numbers in a short way. So the standard form of ninety-two thousand,one hundred seventy is 92,170.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of ninety-two thousand,one hundred seventy is 90,000+2,000+100+70+0.

Question 2.
Standard Form: 200,007
Word Form: two hundred ___________
Expanded Form: ___________ + 7

Answer:
Word Form: Two hundred thousand, seven.
Expanded Form: 200,000+7

Explanation:
A word form is a way to write the numbers in words. So word form of 200,007 is two hundred thousand seven.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of 200,007 is 200,000+7

Common Core – Read and Write Numbers (Page 12)

Question 1.
How can you use place value and period names to read and write 324,904 in word form?

Read and write the number in two other forms.

Answer:
The word form of 324,904 is three hundred twenty-four thousand nine hundred four.
The expanded form of 324,904 is 300,000+20,000+4,000+900+4.

Explanation:
A word form is a way to write the numbers in words. So word form of 324,904 is three hundred twenty-four thousand nine hundred four.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of 324,904 is 300,000+20,000+4,000+900+4.

Question 2.
four hundred eight thousand, seventeen

Answer:
Standard Form: 408,017.
Expanded Form: 400,000+8,000+10+7.

Explanation:
A standard form is a way to write large numbers in a short way. So the standard form of four hundred eight thousand, seventeen is 408,017.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of four hundred eight thousand, seventeen is 400,000+8,000+10+7.

Question 3.
65,058

Read and write the number in two other forms.

Answer:
The word form of 65,058 is sixty-five thousand, fifty-eight.
The expanded form of 65,058 is 60,000+5,000+50+8.

Explanation:
A word form is a way to write the numbers in words. So word form of 65,058 is sixty-five thousand, fifty-eight.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of 65,058 is 60,000+5,000+50+8.

Question 4.
five hundred eight thousand

Answer:
Standard Form: 508,000.
Expanded Form: 500,000+8,000.

Explanation:
A standard form is a way to write large numbers in a short way. So the standard form of five hundred eight thousand is 508,000.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of five hundred eight thousand is 500,000+8,000.

Question 5.
forty thousand, six hundred nineteen

Answer:
Standard Form: 40,619.
Expanded Form: 40,000+600+10+9.

Explanation:
A standard form is a way to write large numbers in a short way. So the standard form of forty thousand, six hundred nineteen is 40,619.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of forty thousand, six hundred nineteen is 40,000+600+10+9.

Question 6.
570,020

Answer:
The word form of 570,020 is five hundred, seventy thousand, twenty.
The expanded form of 570,020 is 500,000+70,000+20.

Explanation:
A word form is a way to write the numbers in words. So word form of 570,020 is five hundred, seventy thousand, twenty.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of 570,020 is 500,000+70,000+20.

Question 7.
400,000 + 60,000 + 5,000 + 100

Answer:
Standard Form: 465,100.
Word Form: Four hundred, sixty-five thousand, one hundred.

Explanation:
A standard form is a way to write large numbers in a short way. So the standard form of 400,000 + 60,000 + 5,000 + 100 is 465,100.
A word form is a way to write the numbers in words. So word form of 400,000 + 60,000 + 5,000 + 100 is Four hundred, sixty-five thousand, one hundred.

Question 8.
During the week of the county fair, fifteen thousand, six hundred nine entry tickets were sold. Is it correct to write the number as 15,069? Explain.

Answer: No.

Explanation: The standard form of fifteen thousand, six hundred nine is 15,609.

Question 9.
There were 94,172 people at a football game on Saturday. On Monday, 1,000 fewer people were at a football game. In word form, how many people were at the football game on Monday?

Answer: The word form of 93,172 is ninety-three thousand one hundred seventy-two.

Explanation: The total number of people are 94,172 as there are 1000 fewer people on Monday, so the total number of people are
94,172-1,000= 93,172. So the word form of 93,172 is ninety-three thousand one hundred seventy-two.

Question 10.
Richard got 263,148 hits when he did an Internet search. What is the value of the digit 6 in this number? Explain.

Answer: The value of 6 in 263,148 is 60,000.

Explanation: As Richard got 263,148 hits and the digit 6 is in the ten thousands place, so the value of 6 in 263,148 is 60,000.

Common Core – Read and Write Numbers (Page 13)

Question 11.
Yvonne wrote the numbers sixteen thousand, nine hundred eighteen and 64,704 on the board. Which of the numbers has a greater value in the thousands place?

Answer: 16,918 has a greater value in the thousands place.

Explanation: As Yvonne wrote sixteen thousand, nine hundred eighteen in word form, so standard form is 16,918. And 64,704 was written on board, so the number with greater value in thousands place is 16,918 as the digit 6 is in thousands place wherein 64,704 the digit 4 is in thousands place. So 16,918 has greater value in thousands place.

Question 12.
Matthew found the sum of 3 thousands 4 hundreds 3 tens 1 one + 4 thousands 8 hundreds 3 tens 5 ones. Victoria found the sum of 5 thousands 7 hundreds 4 ones + 3 thousands 2 hundreds 3 tens 1 one. Who had the greater sum? What was the greater sum?

Who had the greater sum?
What was the greater sum?

Answer: Victoria had a greater sum and the sum is 8,935.

Explanation: The sum of Matthew is 3 thousands 4 hundreds 3 tens 1 one (3431) + 4 thousands 8 hundreds 3 tens 5 ones (4835)= 8,266 and the sum of Victoria 5 thousands 7 hundreds 4 ones (5704) + 3 thousands 2 hundreds 3 tens 1 one (3231)= 8,935. So Victoria had the greater sum and the sum is 8,935.

Use the table for 13–15.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 11$

Question 13.
Use Graphs Which city has a population of two hundred fifty-five thousand, one hundred twenty-four?

Answer: Greensboro

Explanation: Greensboro has two hundred fifty-five thousand, one hundred twenty-four population and it was represented word form and the standard form of two hundred fifty-five thousand, one hundred twenty-four is 255,124.

Question 14.
Write the population of Raleigh in expanded form and word form.

Answer: The expanded form of 405,612 is 400,000+5,000+600+10+2 and the word form of 405,612 is four hundred five thousand, six hundred twelve.

Explanation: The population of Raleigh city is 405,612 and the expanded form of 405,612 is 400,000+5,000+600+10+2 and the word form of 405,612 is four hundred five thousand, six hundred twelve.

Question 15.
What’s the Error? Sophia said that the expanded form for 605,970 is 600,000 + 50,000 + 900 + 70. Describe Sophia’s error and give the correct answer.

Answer: The error in Sophia’s expanded form is 600,000+5,000+900+70.

Explanation: The error in Sophia’s expanded form is 600,000+5,000+900+70 as digit 5 is in the thousands place.

Common Core – Read and Write Numbers (Page 14)

Question 16.
Mark tossed six balls while playing a number game. Three balls landed in one section, and three balls landed in another section. His score is greater than one hundred thousand. What could his score be?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 12$

a. What do you know?

Answer: Mark’s score will be 300,000+30,000= 330,000.

Explanation: As Mark tossed six balls while playing a number game and that three balls landed in one section, and three balls landed in one section, and three balls landed in another section. Since his score is greater than one hundred thousand, which means that three of the balls landed in the section of 100,000 this will make the score 300,000. If the other three balls, landed in the section of 10,000 this will make the score of three balls to be 30,000. Therefore Mark’s score will be 300,000+30,000= 330,000.

Question 16.
b. How can you use what you know about place value to find what Mark’s score could be?

Answer: To find Mark’s score we will see where the ball will be landed. If the ball is landed in the 100,000 section then the score will be 100,000 and if the ball is landed in the 10,000 section then the score will be 10,000.

Question 16.
c. Draw a diagram to show one way to solve the problem.

Answer:

Question 16.
Complete the sentences.
Three balls could have landed in the ___________ section.
Three balls could have landed in the ___________ section.
Mark’s score could be ___________

Answer:
Three balls could have landed in the 100,000 section.
Three balls could have landed in the 10,000 section.
Mark’s score could be 330,000.

Question 17.
What is another way to write 615,004?
Mark all that apply.
(a) six hundred fifteen thousand, four
(b) six hundred five thousand, fourteen
(c) 60,000 + 10,000 + 5,000 + 4
(d) 600,000 + 10,000 + 5,000 + 4

Answer: a,c.

Explanation: The another way to write 615,004 is six hundred fifteen thousand, four and 600,000 + 10,000 + 5,000 + 4

Common Core – Read and Write Numbers (Page 15)

Read and Write Numbers

Read and write the number in two other forms.

Question 1.
six hundred ninety-two thousand, four
standard form: 692,004;
expanded form: 600,000 + 90,000 + 2,000 + 4

Question 2.
314,207

Answer:
Word Form: Three hundred fourteen, two hundred seven.
Expanded Form: 300,000+10,000+4,000+200+7.

Explanation:
A word form is a way to write the numbers in words. So word form of 314,207 is Three hundred fourteen, two hundred seven.
The expanded form is a way to write numbers by showing the value of each digit. So the expanded form of 314,207 is 300,000+10,000+4,000+200+7.

Question 3.
600,000 + 80,000 + 10

Answer:
Word Form: Six hundred eighty thousand ten.
Standard Form: 680,010.

Explanation:
A word form is a way to write the numbers in words. So word form of 314,207 is Three hundred fourteen, two hundred seven.
A standard form is a way to write large numbers in a short way. So the standard form of 600,000 + 80,000 + 10 is 680,010.

Use the number 913,256.

Question 4.
Write the name of the period that has the digits 913.

Answer: The name of the period that has the digits 913 is Thousand

Explanation: The name of the period that has the digits 913 is Thousand. As we got two periods and 913 are in thousands period and 256 are in units period.

Question 5.
Write the digit in the ten thousands place.

Answer: 1.

Explanation: In 913,256, the digit 1 is in the ten thousands place.

Question 6.
Write the value of the digit 9.

Answer: The value of 9 is nine hundred thousands.

Explanation: In 913,256 the digit 9 is in hundred thousands place, so the value of 9 is nine hundred thousands or 900,000.

Problem Solving

Use the table for 7 and 8.

$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 13$

Question 7.
Which state had a population of eight hundred four thousand, one hundred ninety-four?

Answer: South Dakota

Explanation: The population of eight hundred four thousand, one hundred ninety-four is South Dakota which is 804,194.

Question 8.
What is the value of the digit 8 in Alaska’s population?

Answer: 80,000.

Explanation: The value of the digit 8 in Alaska’s population is 80,000.

Common Core – Read and Write Numbers (Page 16)

Lesson Check

Question 1.
Based on a 2008 study, children 6–11 years old spend sixty-nine thousand, one hundred eight minutes a year watching television. What is this number written in
standard form?
(a) 6,918
(b) 69,108
(c) 69,180
(d) 690,108

Answer: b

Explanation: As 6–11 years old spend sixty-nine thousand, one hundred eight minutes a year watching television, the standard form of sixty-nine thousand, one hundred eight is 69,108

Question 2.
What is the value of the digit 4 in the number 84,230?
(a) 4
(b) 400
(c) 4,000
(d) 40,000

Answer: c

Explanation: The value of the digit 4 in the number 84,230 is 4,000.

Spiral Review

Question 3.
An ant has 6 legs. How many legs do 8 ants have in all?
(a) 14
(b) 40
(c) 45
(d) 48

Answer: d

Explanation: As ant has 6 legs, so for 8 ants 6×8= 48 legs.

Question 4.
Latricia’s vacation is in 4 weeks. There are 7 days in a week. How many days is it until Latricia’s vacation?
(a) 9 days
(b) 11 days
(c) 20 days
(d) 28 days

Answer: d

Explanation: As Latricia’s vacation is in 4 weeks and a week has 7 days, so for 4 weeks it will be 4×7= 28 days.

Question 5.
Marta collected 363 cans. Diego collected 295 cans. How many cans did Marta and Diego collect in all?
(a) 668
(b) 658
(c) 568
(d) 178

Answer: b

Explanation: Marta collected 363 cans and Diego collected 295 cans, so total number of cans both collected are 363+295= 658.

Question 6.
The city Tim lives in has 106,534 people. What is the value of the 6 in 106,534?
(a) 6,000
(b) 600
(c) 60
(d) 6

Answer: a

Explanation: The value of 6 in 106,534 is 6,000.

Common Core – Compare and Order Numbers (Page 18)

Question 1.
Compare 15,327 and 15,341.
Write <, >, or =. Use the number line to help.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 14$
15,327 _______ 15,341

Answer: 15,327 < 15,341

Explanation: The number 15,327 < 15,341 as 327 is less than 341.

Compare. Write <, >, or =.

Question 2.
$631,328 _______ $640,009

Answer: $631,328 < $640,009.

Explanation: The number $631,328 < $640,009.

Question 3.
56,991 _______ 52,880

Answer: 56,991 > 52,880.

Explanation: The number 56,991 > 52,880.

Question 4.
708,561 _______ 629,672

Answer: 708,561 > 629,672.

Explanation: The number 708,561 > 629,672.

Question 5.
143,062 _______ 98,643

Answer: 143,062 > 98,643.

Explanation: The number 143,062 > 98,643.

Order from greatest to least.

Question 6.
20,650; 21,150; 20,890
________ ; ________ ; ________.

Answer: 21,150>20,890>20,650.

Explanation: The numbes from greatest to least are 21,150>20,890>20,650.

Common Core – Read and Write Numbers (Page 19)

Compare. Write <, >, or =.

Question 7.
$2,212 _______ $2,600

Answer: $2,212 < $2,600.

Explanation: The number $2,212 < $2,600.

Question 8.
88,304 _______ 88,304

Answer: 88,304 = 88,304.

Explanation: The number 88,304 = 88,304.

Question 9.
$524,116 _______ $61,090

Answer: $524,116 > $61,090.

Explanation: The number $524,116 > $61,090.

Question 10.
751,272 _______ 851,001

Answer: 751,272 < 851,001.

Explanation: The number 751,272 < 851,001.

Order from least to greatest.

Question 11.
41,090; 41,190; 40,009
_______ ; _______ ; _______

Answer: 40,009<41,090<41,190.

Explanation: The numbers from least to greatest are 40,009<41,090<41,190.

Question 12.
910,763; 912,005; 95,408
_______ ; _______ ; _______

Answer: 95,408<910,763<912,005.

Explanation: The numbers from least to greatest are 95,408<910,763<912,005.

Identify Relationships Algebra Write all of the digits that can replace each

Question 13.
567 < 5 _______ 5 < 582

Answer: 567<575<582.

Explanation: The suitable number to fit the equation is 7, so 567<575<582.

Question 14.
464,545 > 4 _______ 3,535 > 443,550
464,545 > 4 _______ 3,535 > 443,550

Answer:
464,545>453,535>443,550.
464,545>463,535>443,550.

Explanation: The suitable number to fit the equation is 5 or 6. So
464,545>453,535>443,550.
464,545>463,535>443,550.

Question 15.
Leah’s car has 156,261 miles on the odometer. Casey’s car has 165,002 miles on the odometer. Mike’s car has 145,834 miles on the odometer. Whose car has the most miles? Order the number of miles from least to greatest.

Answer: Casey’s car has the most miles and the order of the miles from least to greatest is 145,834<156,261<165,002.

Explanation: As Leah’s car has 156,261 miles and Casey’s car has 165,002 miles and Mike’s car has 145,834 miles. So Casey’s car has the most miles and the order of the miles from least to greatest is 145,834<156,261<165,002.

Question 16.
At Monica’s Used Cars, the sales staff set a goal of $25,500 in sales each week. The sales for three weeks were $28,288; $25,369; and $25,876. Which total did not meet the goal?
(a) $28,288
(b) $25,369
(c) $25,876

Answer: b

Explanation: $25,369 did not meet the goal. As the staff set the goal to $25,500 and $25,369 is less than $25,500.

Question 17.
What’s the Error? Max said that 36,594 is less than 5,980 because 3 is less than 5. Describe Max’s error and give the correct answer.

Answer: 3 is less than 5 but 30,000 is greater than 5,000 that is Max’s error.

Explanation: 3 is less than 5 but the digit 3 in 36,594 is in ten thousands place so the place value of 3 is 30,000 and the digit 5 in 5,980 is in thousands place and the place value of 5 is 5000. This is Max’s error.

Common Core – Compare and Order Numbers (Page 20)

Use the picture graph for 18–20.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 15$

Question 18.
Use Graphs In which month shown did Grand Canyon National Park have about 7,500 tent campers?

Answer: September.

Explanation: We can see from the above figure that september month has 5000+2500= 7500.

Question 19.
How many more campers were there in July and August than in June and September?

Answer: 10,000 more campers in July and August.

Explanation:
The campers in July and August are 15,000+12,500= 27,500
The campers in June and September are 10,000+7,500= 17,500
So 27,500-17,500= 10,000 more campers in July and August.

Question 20.
What if during the month of October, the park had 22,500 tent campers? How many symbols would be placed on the pictograph for October?

Answer: There will be four full symbols and one half symbol.

Explanation: As each symbol represents 5,000 tent campers, for 22,500 tent campers there will be four full symbols and one half symbol which means 5,000+5,000+5,000+5,000+2,500= 22,500.

Question 21.
What’s the Question?

Compare: 643,251; 633,512; and 633,893.
The answer is 633,512.

Answer: What is the least number?

Explanation: As we can see in the given the answer that 633,512 is less than the other two numbers. So the question would be What is the least number?

Question 22.
Zachary’s school set a goal of collecting 12,155 cans of food each day. In the first 3 days the school collected 12,250 cans; 10,505 cans; and 12,434 cans. Write each number in the box that tells whether or not the school met its goal.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 16$
(a) 12,250 cans
(b) 10,505 cans
(c) 12,434 cans

Answer: 12,250 and 12,434 met the daily goal and 10,505 didn’t meet the daily goal.

Explanation: As Zachary’s school set a goal of collecting 12,155 cans of food each day, so 12,250 and 12,434 met the daily goal and 10,505 didn’t meet the daily goal.

Common Core – Compare and Order Numbers (Page 21)

Compare and Order Numbers

Compare. Write < .> or =.

Question 1.
3,273 < 3,279

Question 2.
$1,323 _______ $1,400

Answer: $1,323 < $1,400.

Explanation: The number $1,323 is less than $1,400.

Question 3.
52,692 _______ 52,692

Answer: 52,692 = 52,692.

Explanation: The number 52,692 is equal to 52,692.

Question 4.
$413,005 _______ $62,910

Answer: $413,005 > $62,910

Explanation: The number $413,005 is greater than $62,910

Question 5.
382,144 _______ 382,144

Answer: 382,144= 382,144

Explanation: The number 382,144 is equal to 382,144

Question 6.
157,932 _______ 200,013

Answer: 157,932 < 200,013

Explanation: The number 157,932 is less than 200,013.

Question 7.
401,322 _______ 410,322

Answer: 401,322 < 410,322.

Explanation: The number 401,322 is less than 410,322.

Question 8.
989,063 _______ 980,639

Answer: 989,063 > 980,639

Explanation: The number 989,063 is greater than 980,639.

Question 9.
258,766 _______ 258,596

Answer: 258,766 > 258,596.

Explanation: The number 258,766 is greater than 258,596.

Order from least to greatest.

Question 10.
23,710; 23,751; 23,715
_______< _______ < _______

Answer: 23,710<23,715<23,751

Explanation: The numbers from least to greatest are 23,710<23,715<23,751

Question 11.
52,701; 54,025; 5,206
_______ < _______ < _______

Answer: 5,206<52,701<54,025.

Explanation: The numbers from least to greatest are 5,206<52,701<54,025.

Question 12.
465,321; 456,321; 456,231
_______ < _______ < _______

Answer: 456,231<456,321<465,321.

Explanation: The numbers from least to greatest are 456,231<456,321<465,321.

Question 13.
$330,820; $329,854; $303,962
_______ < _______ < _______

Answer: $329,854<$303,962<$330,820.

Explanation: The numbers from least to greatest $329,854<$303,962<$330,820.

Problem Solving

Question 14.
An online newspaper had 350,080 visitors in October, 350,489 visitors in November, and 305,939 visitors in December. What is the order of the months from greatest to least number of visitors?
1. _______
2. _______
3. _______

Answer: November, October, December.

Explanation: As 350,489 is greater than 305,939. So the order of the months from greatest to the least number of visitors are November, October, and December.

Question 15.
The total land area in square miles of each of three states is shown below.
Colorado: 103,718
New Mexico: 121,356
Arizona: 113,635
What is the order of the states from least to greatest total land area?
1. _______
2. _______
3. _______

Answer: Colorado, Arizona, New Mexico.

Explanation: As 103,718 is less than 113,635 is less than 121,356. So the order of the state from least to greatest is Colorado, Arizona, New Mexico.

Common Core – Compare and Order Numbers (Page 22)

Lesson Check

Question 1.
At the yearly fund-raising drive, the nonprofit company’s goal was to raise $55,500 each day. After three days, it had raised $55,053; $56,482; and $55,593. Which amount was less than the daily goal?
(a) $55,500
(b) $55,053
(c) $55,593
(d) $56,482

Answer: b

Explanation: As the goal is to raise $55,500 each day and $55,053 didn’t reach the goal. As $55,053 is less than $55,550.

Question 2.
Which of the following lists of numbers is in order from greatest to least?
(a) 60,343; 60,433; 63,043
(b) 83,673; 86,733; 86,373
(c) 90,543; 90,048; 93,405
(d) 20,433; 20,343; 20,043

Answer: d

Explanation: The numbers in order from greatest to least is 20,433, 20,343, 20,043.

Spiral Review

Question 3.
Jess is comparing fractions. Which fraction is greater than $\frac{5}{6}$?
(a) $\frac{7}{8}$
(b) $\frac{4}{5}$
(c) $\frac{3}{4}$
(d) $\frac{2}{3}$

Answer: a

Explanation: As $\frac{5}{6}$ in decimals is 0.83 and
$\frac{7}{8}$= 0.875
$\frac{4}{5}$= 0.80
$\frac{3}{4}$= 0.75
$\frac{2}{3}$= 0.67
So, $\frac{7}{8}$ is greater than $\frac{5}{6}$.

Question 4.
What is the perimeter of the rectangle below?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 17$
(a) 14 inches
(b) 26 inches
(c) 28 inches
(d) 48 inches

Answer: c.

Explanation: The perimeter of the rectangle is 2(l+w)
= 2(8+6)
= 2(14)
= 28 inches.

Question 5.
A website had 826,140 hits last month. What is the value of the 8 in 826,140?
(a) 800
(b) 8,000
(c) 80,000
(d) 800,000

Answer:

Explanation: The value of the digit 8 in 826,140 is 800,000.

Question 6.
Which is 680,705 written in expanded form?
(a) 680 + 705
(b) 68,000 + 700 + 5
(c) 600,000 + 8,000 + 700 + 5
(d) 600,000 + 80,000 + 700 + 5

Answer: d

Explanation: The expanded form of 680,705 is 600,000+80,000+700+5

Common Core – Round Numbers (Page 24)

Question 1.
What number is halfway between 100,000 and 200,000?

Answer: 150,000.

Explanation: The number is halfway between 100,000 and 200,000 is 150,000.

Question 2.
How does knowing where the halfway point is help you find which hundred thousand 138,202 is closest to? Explain.

Answer: The location of a number relative to the halfway point help you tell if it is closer to the lesser or the greater rounding number.

Question 3.
What number is halfway between 70,000 and 80,000?

Answer: 75,000.

Explanation: The number is halfway between 70,000 and 80,000 is 75,000.

Question 4.
What is 75,000 rounded to the nearest ten thousand? Explain.

Answer: 80,000.

Explanation: As 75,000 is exactly halfway between 70,000 and 80,000 rounds to the greater number.

Round to the place value of the underlined digit.

Question 5.
64,999

Answer: 60,000.

Explanation: The place value of 6 in 64,999 is 60,000.

Question 5.
850,000

Answer: 800,000.

Explanation: The place value of 8 in 850,000 is 800,000.

Question 5.
301,587

Answer: 1,000.

Explanation: The place value of 1 in 301,587 is 1,000.

Question 5.
10,832

Answer: 0.

Explanation: The place value of 0 in 10,832 is 0 because 0 is in thousands place, so 0×1000= 0.

Common Core – Round Numbers (Page 25)

Question 1.
Suppose 255,113 people live in a city. Is it reasonable to say that about 300,000 people live in the city? Use the number line to help you solve the problem. Explain.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 18$

Answer: Yes, 300,000 is a reasonable estimate.

Explanation: As 255,113 is closer to 300,000 than 200,000. So 300,000 is a reasonable estimate.

Round to the place value of the underlined digit.

Question 2.
934,567

Answer: 935,000.

Explanation: Round off the value means making a number simpler but keeping its value close to what it was. The result is less accurate but easy to use. So round off 934,567 to 935,000.

Question 3.
641,267

Answer: 640,000.

Explanation: Round off the value means making a number simpler but keeping its value close to what it was. The result is less accurate but easy to use. So round off 641,267 to 640,000.

Question 4.
234,890

Answer: 200,000.

Explanation: Round off the value means making a number simpler but keeping its value close to what it was. The result is less accurate but easy to use. So round off 234,890 to 200,000.

Question 5.
347,456

Answer: 350,000.

Explanation: Round off the value means making a number simpler but keeping its value close to what it was. The result is less accurate but easy to use. So round off 347,456 to 350,000.

Question 6.
To the nearest hundred, a factory produced 3,600 jars of applesauce on Thursday and 4,200 jars of apple sauce on Friday. To the nearest thousand, how many jars of apple juice did they produce during the two days?

Answer: 7,800 jars.

Explanation:
The number of jars of apple sauce on Thursday= 3,600 jars
The number of jars of apple sauce on Friday= 4,200 jars.
So the total number of jars they produced during the two days is 3,600+4,200= 7,800 jars.

Question 7.
The number 2,000 is missing a digit. The number rounded to the nearest thousand is 3,000. List all of the possibilities for the missing digit. Explain your answer.

Answer: 5,6,7,8,9.

Explanation: If the digit in the hundreds place 5,6,7,8,9, then the number is closer to 3,000 than 2,000 and if the digit in the hundreds place is 5, the number is exactly halfway between 2,000 and 3,000. So we can round off to the greater number.

Common Core – Round Numbers (Page 26)

Question 8.
A male elephant weighs 6,728 pounds. A female elephant weighs 5,843 pounds. To the nearest hundred, what is the total weight of the two elephants?

Answer: 12,600 pounds.

Explanation:
The weight of a male elephant is 6,728 pounds
The weight of a female elephant is 5,843 pounds
So total weight is 6,728+5,843= 12,571.
Rounding off to the nearest hundred, so the value is 12,600.

Question 9.
About 300,000 people attended a festival. For numbers 9a–9e choose Yes or No to show whether each number could be the exact number of people that attended the festival.

a. 351,213
(a) yes
(b) no

Answer: No

Explanation: By rounding off 351,213 to the nearest thousands place then the value will be 351,000 which is more than 300,000. So the answer is No.

Question 9.
b. 249,899
(a) yes
(b) no

Answer: No.

Explanation: By rounding off 249,899 to the nearest thousands place then the value will be 250,000 which is less than 300,000. So the answer is No.

Question 9.
c. 252,348
(a) yes
(b) no

Answer: No.

Explanation: By rounding off 252,348 to the nearest thousands place then the value will be 252,000 which is less than 300,000. So the answer is No.

Question 9.
d. 389,001
(a) yes
(b) no

Answer: No

Explanation: By rounding off 389,001 we will get the value as 400,000 but not 300,000. So the answer is no.

Question 9.
e. 305,992
(a) yes
(b) no

Answer: Yes.

Explanation: By rounding off 305,992 we will get the value as 300,000 which is equal to 300,000. So the answer is yes.

Common Core – Round Numbers (Page 27)

Round Numbers

Round to the place value of the underlined digit.

Question 1.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 19$
Look at the digit to the right. If the digit to the right is less than 5, the digit in the rounding place stays the same.

Change all the digits to the right of the rounding place to zero.

Question 2.
123,499

Answer: 123,000.

Explanation: The digit to the right to the underlined number is less than 5, so the digit in the rounding place stays the same, and all the digits to the right of the rounding place to zero. So the value will be 123,000.

Question 3.
552,945

Answer: 600,000.

Explanation: The digit to the right to the underlined number is equal to 5, so the underlined digit will be increased by 1 and will round up to the nearest hundred thousands place. So the value is 600,000.

Question 4.
389,422

Answer: 390,000.

Explanation: The digit to the right to the underlined number is greater than 5, so the underlined digit will be increased by 1 and will round up to the nearest hundred thousands place. So the value is 390,000.

Question 5.
209,767

Answer: 200,000.

Question 6.
191,306

Answer: 191,000.

Question 7.
66,098

Answer: 70,000.

Question 8.
73,590

Answer: 74,000.

Question 9.
149,903

Answer: 100,000.

Question 10.
684,303

Answer: 684,000.

Question 11.
499,553

Answer: 500,000.

Problem Solving

Use the table for 12–13.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 20$

Question 12.
Find the height of Mt. Whitney in the table. Round the height to the nearest thousand feet.
_______ feet

Answer: 14,000 feet.

Explanation: The height of Mt. Whitney in the table is 14,494 feet, by rounding off to nearest thousand the height will be 14,000 feet.

Question 13.
What is the height of Mt. Bona rounded to the nearest ten thousand feet?
_______ feet

Answer: 20,000 feet.

Explanation: The height of Mt. Bona is 16,500 feet, by rounding off to the nearest ten thousand the height will be 20,000 feet.

Common Core – Round Numbers (Page 28)

Lesson Check

Question 1.
Which number is 247,039 rounded to the nearest thousand?
(a) 200,000
(b) 250,000
(c) 247,000
(d) 7,000

Answer: c

Explanation: The number rounded to the nearest thousand is 247,000.

Question 2.
To the nearest ten thousand, the population of Vermont was estimated to be about 620,000 in 2008. Which might have been the exact population of Vermont in 2008?
(a) 626,013
(b) 621,270
(c) 614,995
(d) 609,964

Answer: b

Explanation: The exact population of Vermont in 2008 is 621,270. As the estimated population is 620,000 and the number is rounded off to the nearest thousand, so the exact population of Vermont is 621,270.

Spiral Review

Question 3.
Which symbol makes the following number sentence true?
$546,322 Ο $540,997
(a) <
(b) >
(c) =
(d) +

Answer: b

Explanation: The number $546,322 is greater than $540,997.

Question 4.
Pittsburgh International Airport had approximately 714,587 passengers in August 2009. Which number is greater than 714,587?
(a) 714,578
(b) 704,988
(c) 714,601
(d) 714,099

Answer: c

Explanation: 714,601 is greater than 714,587.

Question 5.
June made a design with 6 equal tiles. One tile is yellow, 2 tiles are blue, and 3 tiles are purple. What fraction of the tiles are yellow or purple?
(a) $\frac{1}{6}$
(b) $\frac{2}{6}$
(c) $\frac{3}{6}$
(d) $\frac{4}{6}$

Answer: d

Explanation: Total tiles are 6 tiles and in that one tile is yellow and 3 purple tiles and the total yellow and purple tiles are 4 tiles. So the fraction of the yellow tile and purple tile is $\frac{4}{6}$.

Question 6.
The fourth grade collected 40,583 cans and plastic bottles. Which of the following shows that number in word form?
(a) forty thousand, five hundred eighty
(b) forty thousand, five hundred eighty-three
(c) four thousand, five hundred eighty-three
(d) four hundred thousand, five hundred eighty

Answer: b.

Explanation: The word form of 40,583 is forty thousand, five hundred eighty-three.

Common Core – Chapter 1 -Mid-Chapter Checkpoint (Page 29)

Choose the best term from the box.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 21$

Question 1.
The _______ of 23,850 is 20,000 + 3,000 + 800 + 50.

Answer: Expanded form.

Explanation: The expanded form of 23,850 is 20,000 + 3,000 + 800 + 50.

Question 2.
You can _______ to find about how much or how many.

Answer: Round.

Explanation: You can round to find about how much or how many.

Question 3.
In 192,860 the digits 1, 9, and 2 are in the same _________

Answer: Period.

Explanation: In 192,860 the digits 1, 9, and 2 are in the same period.

Find the value of the underlined digit.

Question 4.
380,671

Answer: 80,000.

Explanation: The place value of the digit 8 in 380,671 is 80,000.

Question 5.
10,698

Answer: 90.

Explanation: The place value of the digit 9 in 10,698 is 90.

Question 6.
650,234

Answer: 600,000

Explanation: The place value of the digit 6 in 650,234 is 600,00.

Write the number in two other forms.

Question 7.
293,805

Answer:
Expanded form: 200,000+90,000+3,000+800+5.
Word form: two hundred ninety three thousand,eight hundred five.

Explanation:
The expanded form of 293,805 is 200,000+90,000+3,000+800+5.
The word form of 293,805 is two hundred ninety three thousand,eight hundred five.

Question 8.
300,000 + 5,000 + 20 + 6

Answer:
Standard form: 305,026.
Word form: three hundred five thousand twenty six.

Explanation:
The standard form of 300,000 + 5,000 + 20 + 6 is 305,026.
The word form of 300,000 + 5,000 + 20 + 6 is three hundred five thousand twenty six.

Compare. Write <, >, or =.

Question 9.
457,380 _______ 458,590

Answer:
457,380 < 458,590

Explanation:
The number 457,380 is less than 458,590.

Question 10.
390,040 _______ 39,040

Answer:
390,040 > 39,040

Explanation:
The number 390,040 is greater than 39,040.

Question 11.
11,809 _______ 11,980

Answer:
11,809 > 11,980

Explanation:
The number 11,809 is greater than 11,980.

Round to the place of the underlined digit.

Question 12.
140,250

Answer: 100,000.

Explanation: The place value of the digit 1 in 140,250 is 100,000.

Question 13.
10,450

Answer: 400.

Explanation: The place value of the digit 4 in 10,450 is 400.

Question 14.
126,234

Answer: 6,000.

Explanation: The place value of the digit 6 in 126,234 is 6,000.

Common Core – Chapter 1 -Mid-Chapter Checkpoint (Page 30)

Question 15.
Last year, three hundred twenty-three thousand people visited the museum. What is this number written in standard form?

Answer: 323,000.

Explanation: The standard form of three hundred twenty-three thousand is 323,000.

Question 16.
Rachael rounded 16,473 to the nearest hundred. Then she rounded her answer to the nearest thousand. What is the final number?

Answer: 17,000.

Explanation: When we round a number to the nearest we check the tens place digit, if the digit is less than 5 then the number is rounded to the previous hundred while if it is 5 or more than 5 then the number is rounded to the next hundred. As tens place digit is 7, so
16,473= 16,500. And when we need to round the number to the nearest thousand and will check the hundred place digit which is 5. So when 16,500 is rounded off to the nearest thousand the value will be 17,000.

Question 17.
What is the highest volcano in the Cascade Range?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 22$

Answer: Mt. Rainier

Explanation: Mt. Rainier is the highest volcano in the Cascade Range with a height of 14,410 ft.

Question 18.
Richard got 263,148 hits when he did an Internet search. What is the value of the digit 6 in this number?

Answer:

Explanation: Richard got 263,148 which is in standard form, so we will convert into expanded form to find the value of the digit 6. The expanded form of 263,148 is 200,000+60,000+3,000+100+40+8. The value of the digit 6 is 60,000.

Common Core – Investigate • Rename Numbers (Page 32)

Question 1.
How is the number of large cubes and flats in the first model related to the number of flats in the second model?

Answer: 10 flats.

Explanation: We need 10 flats to make a large cube, so 1 large cube and 2 flats are the same as 10 flats and 2 flats or 12 flats.

Question 2.
Can you model 1,200 using only longs? Explain.

Answer: Yes.

Explanation: We need 12 flats to model 1,200. Since there are 10 longs in each flat, you need 120 longs.

Question 3.
You renamed 1,200 as hundreds. How can you rename 1,200 as tens? Explain.

Answer: 120 tens.

Explanation: As each long is a ten, and we need 120 longs to model 1,200. So we will rename as 120 tens.

Question 4.
What would the models in Step A and Step B look like for 5,200? How can you rename 5,200 as hundreds?

Answer: We can rename 5,200 as 52 hundred.

Explanation: In Step A, the model would have 5 large cubes and 2 flats to model 5 thousands and 2 hundreds. In step B, the model would have 52 flats. So we can rename 5,200 as 52 hundred.

Common Core – Investigate • Rename Numbers (Page 33)

Rename the number. Draw a quick picture to help.

Question 1.
150
_______ tens

Answer: 15 tens.

Explanation: As each long is a ten, so we need 15 longs to model 150.

Question 2 (request help)
1,400
_______ hundreds

Answer: 14 hundreds.

Explanation: As each box is a hundred, so we need 14 box to model 1,400.

Question 3.
2 thousands 3 hundreds
_______ hundreds

Answer: 23 hundred.

Explanation: As each box is a hundred, so we need 23 box to model 2,300.

Question 4.
13 hundreds
_______ thousand _______ hundreds

Answer: 1 thousand and 3 hundred.

Explanation: The group of 10 boxes are equal to thousand, so for 13 hundreds we need 1 thousand and 3 hundred.

Rename the number. Use the place-value chart to help.

Question 5.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 23$
18 thousands = _______

Answer: 18,000.

Explanation:

Question 6.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 24$
570,000 = 57 _______

Answer: 57 ten thousand.

Explanation:

Rename the number.

Question 7 (request help)
580= _______ tens

Answer: 58 tens.

Question 8.
740,000= _______ten thousands

Answer: 74 ten thousand.

Question 9.
8 hundreds 4 tens = 84 _______

Answer: 84 tens.

Question 10.
29 thousands = _______

Answer: 29,000.

Common Core – Investigate • Rename Numbers (Page 34)

Question 11.
A toy store is ordering 3,000 remote control cars. The store can order the cars in sets of 10. How many sets of 10 does the store need to order?
_______ sets

Answer: 300 sets.

Explanaton: Number of cars ordering by the toy store are 3,000 and the store can order the sets of 10, so number of sets are 3000/10 = 300 sets.

Question 11.
a. What information do you need to use?

Answer: The store is ordering 3,000 remote control cars and the cars come in the set of 10.

Question 11.
b. What do you need to find?

Answer: We need to find how many sets of 10 the store need to order.

Question 11.
c. How can renaming numbers help you solve this problem?

Answer: We can rename 3,000 as tens to find how many sets of 10 make 3,000.

Question 11.
d. Describe a strategy you can use to solve the problem.

Answer: We can use place value chart to see how many tens are in 3,000.

Question 11.
e. How many sets of 10 remote control cars does the store need to buy?
_______ sets

Answer: 300 sets.

Explanation: 300 sets of 10 remote control cars store needs to buy.

Question 12.
Ivan sold 53 boxes of oranges on Friday and 27 boxes on Saturday during a citrus sale. There were 10 oranges in each box. How many oranges did he sell in all?
_______ oranges

Answer:

Explanation: Ivan sold 53 boxes of oranges on Friday and 27 boxes on Saturday, so total number of boxes are 53+27= 80. As each box contains 10 oranges, so total number of oranges he sold is 80×10= 800 oranges.

Question 12.
Use Reasoning A store sold a total of 15,000 boxes of buttons last month, and 12,000 boxes this month. If the store sold 270,000 buttons, how many buttons were in each box?
_______ buttons

Answer: 10 buttons.

Explanation: As store sold a total of 15,000 boxes of buttons last month, and 12,000 boxes this month, so total number of button boxes sold are 15,000+12,000= 27,000 boxes. And the store sold 270,000 buttons, so total number of buttons in each box are
270,000/27,000= 10 buttons.

For numbers 14a–14d, select True or False for each statement.

Question 14.
a. 9 hundreds 3 tens can be renamed as 39 tens.
(a) True
(b) False

Answer: False

Explanation: 9 hundreds 3 tens can rename as 93 tens.

Question 14.
b. 370,000 can be renamed as 37 ten thousands.
(a) True
(b) False

Answer: True.

Explanation: Yes, 370,000 can be renamed as 37 ten thousands.

Question 14.
c. 780 can be renamed as 78 tens.
(a) True
(b) False

Answer: True.

Explanation: Yes, 780 can be renamed as 78 tens.

Question 14.
d. 42,000 can be renamed as 42 thousands.
(a) True
(b) False

Answer: True

Explanation: Yes, 42,000 can be renamed as 42 thousands.

Common Core – Investigate • Rename Numbers (Page 35)

Rename Numbers
Rename the number. Use the place-value chart to help.

Question 1.
760 hundreds = 76,000
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 25$

Question 2.
805 tens = _______

Answer: 8,050.

Explanation:

THOUSANDS			ONES
Hundreds	Tens	Ones	Hundreds	Tens	Ones
		8	0	5	0

Question 3.
24 ten thousands = ________

Answer: 240,000.

Explanation:

THOUSANDS			ONES
Hundreds	Tens	Ones	Hundreds	Tens	Ones
2	4	0	0	0	0

Rename the number.

Question 4.
720 = _______ tens

Answer: 72 tens.

Explanation: The number 720 can be rename as 72 tens.

Question 5.
4 thousands 7 hundreds = 47 _______

Answer: 47 hundred.

Explanation: 4 thousands 7 hundreds can rename as 47 hundred.

Question 6.
25,600 = _______ hundreds

Answer: 256 hundred.

Explanation: 25,600 can rename as 256 hundred.

Question 7.
204 thousands = _______

Answer: 204,000.

Explaantion: 204 thousands can rename as 204,000.

Problem Solving

Question 8.
For the fair, the organizers ordered 32 rolls of tickets. Each roll of tickets has 100 tickets. How many tickets were ordered in all?
_______ tickets

Answer: 3200 tickets.

Explanation: Total number of rolls of tickets ordered by the organizers are 32 rolls and each roll contains 100 tickets. So number of tickets were ordered are 32×100= 3200 tickets.

Question 9.
An apple orchard sells apples in bags of 10. The orchard sold a total of 2,430 apples one day. How many bags of apples was this?
_______ bags

Answer: 243 bags.

Explantion: Total number of apples sold by orchard are 2,430 apples, and the orchard sells apples in a bag of 10, so number of apples are 2,430÷10= 243 bags.

Question 10.
Explain how you can rename 5,400 as hundreds. Include a quick picture or a place-value chart in your explanation.
_______ hundreds

Answer: 54 hundred.

Explanation: In 5,400 there are 2 zeros and also in 100 there are 2 zeros, so 2 zeros equals hundred and 100= 1 hundred, because it has a 1 front of the 2 zeros. So 5,400= 54 hundreds, because it has a 54 in front of the 2 zeros.

Common Core – Investigate • Rename Numbers (Page 36)

Lesson Check

Question 1.
A dime has the same value as 10 pennies. Marley brought 290 pennies to the bank. How many dimes did Marley get?
(a) 29
(b) 290
(c) 2,900
(d) 29,000

Answer: a.

Explanation: As a dime has the same value as 10 pennies, Marley brought 290 pennies. So their will be 290/10= 29 dimes MArley will get.

Question 2.
A citrus grower ships grapefruit in boxes of 10. One season, the grower shipped 20,400 boxes of grapefruit. How many grapefruit were shipped?
(a) 204
(b) 2,040
(c) 20,400
(d) 204,000

Answer: d.

Explanation: Number of boxes are 10 and the grower shipped 20,400 boxes of grapefruit. So number of grapefruits were shipped are 20,400×10= 204,000.

Spiral Review

Question 3.
There were 2,605 people at the basketball game. A reporter rounded this number to the nearest hundred for a newspaper article. What number did the reporter use?
(a) 2,600
(b) 2,610
(c) 2,700
(d) 3,000

Answer: a.

Explanation: Number of people at the basketball game are 2,605 as reporter rounded to nearest hundred, so the number will be 2,600.

Question 4.
To get to Level 3 in a game, a player must score 14,175 points. Ann scores 14,205 points, Ben scores 14,089 points, and Chuck scores 10,463 points. Which score is greater than the Level 3 score?
(a) 14,205
(b) 14,175
(c) 14,089
(d) 10,463

Answer: a.

Explanation: Ann score is greater than the level 3 score and the score is 14,205.

Question 5.
Henry counted 350 lockers in his school. Hayley counted 403 lockers in her school. Which statement is true?
(a) The 3 in 350 is 10 times the value of the 3 in 403.
(b) The 3 in 350 is 100 times the value of the 3 in 403.
(c) The 3 in 403 is 10 times the value of the 3 in 350.
(d) The 3 in 403 is 100 times the value of the 3 in 350.

Answer: b

Explanation: The statement b is correct, as 3 in 350 is 100 times the value of the 3 in 403.

Question 6.
There are 4 muffins on each plate. There are 0 plates of lemon muffins. How many lemon muffins are there?
(a) 4
(b) 2
(c) 1
(d) 0

Answer:d.

Explanation: 0 lemon muffins are there.

Common Core – Add Whole Numbers (Page 39)

Question 1.
Use the grid to find 738,901 + 162,389.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 26$
Use the grid to align the addends by place value.

Answer: 901,290

Explanation:

Estimate. Then find the sum.

Question 2.
72,931 + 18,563
Estimate: _______
Sum: _______

Answer:
Estimate: 90,000.
Sum: 91,494.

Explanation: The sum of 72,931 + 18,563= 91,494.

Question 3.
432,068 + 239,576
Estimate: _______
Sum: _______

Answer:
Estimate: 700,000.
Sum: 671,644.

Explanation: The sum of 432,068 + 239,576= 671,644.

Question 4.
64,505 + 38,972
Estimate: _______
Sum: _______

Answer:
Estimate: 100,000.
Sum: 103,477.

Explanation: The sum of 64,505 + 38,972= 103,477.

Question 5.
839,136 + 120,193
Estimate: _______
Sum: _______

Answer:
Estimate: 960,000.
Sum: 959,329.

Explanation: The sum of 839,136 + 120,193= 959,329.

Question 6.
186,231 + 88,941
Estimate: _______
Sum: _______

Answer:
Estimate: 280,000.
Sum: 275,172.

EXplanation: The sum of 186,231 + 88,941= 275,172.

Question 7.
744,201 + 168,900
Estimate: _______
Sum: _______

Answer:
Estimate: 900,000.
Sum: 913,101.

Explanation: The sum of 744,201 + 168,900= 913,101.

Question 8.
For the first football game of the season, 62,732 fans attended. The number of fans at the second game was 469 more than at the first game. What is the total number of fans that attended the first two games?
_______ fans

Answer: 125,933 fans.

Explanation: The first game had 62,732 fans, the second game was 469 more, so the second game fans attended is 62,732+469= 63,201. The total number of fans attended are 62,732+63,201= 125,933.

Question 9.
Daisy’s Flower Shop sold 135,649 flowers during its first year. The second year, the shop sold 9,754 more flowers than it did its first year. The third year, it sold 1,343 more flowers than it did in the second year. How many flowers did the shop sell during the three years?
_______ flowers

Answer:

Explanation:

Reason Abstractly Algebra Find the missing number and name the property you used to find it. Write Commutative or Associative.

Question 10.
(4,580 + 5,008) + 2,351 = 4,580 + ( _______ +2,351)

Answer: Associative property.

Explanation: (4,580 + 5,008) + 2,351 = 4,580 + ( 5,008 +2,351). The associative property states that when three or more numbers are added or multiplied. The sum or the product is the same regardless of the grouping of the addends.

Question 11.
7,801+ _______ =4,890+7,801

Answer: Commutative property.

Explanation: 7,801+ 4,890 = 4,890+7,801. Commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

Question 12.
2,592 + 3,385 = 3,385+ _______

Answer: Commutative property.

Explanation: 2,592 + 3,385 = 3,385+ 2,592. Commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

Common Core – Add Whole Numbers (Page 40)

Use the table for 13–14.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 27$

Question 13.
What is the combined population of the three major Alaskan cities? Estimate to verify your answer.
Estimate: _______
Sum: _______

Answer:
Estimate: 350,000.
Sum: 352,222.

Explanation: The combined population of the three major Alaskan cities are 352,222.

Question 14.
The digit 5 occurs two times in the population of Fairbanks. What is the value of each 5? Explain your answer.
First 5: _______
Second 5: _______

Answer:
First 5: 5,000.
Second 5: 50.

Explanation: To find the value of the digit 5 we will expand the 35,252, the expanded form of 35,252 is 30,000+5,000+200+50+2. So the value of first digit 5 is 5,000 and the second digit 5 is 50.

Question 15.
Kaylie has 164 stamps in her collection. Her friend Nellie has 229 more stamps than Kaylie. How many stamps do Kaylie and Nellie have?
_______ stamps

Answer: 393 stamps.

Explanation: Number of stamps did Kaylie has are 164 stamps and Nellie has 229 more stamps, so total stamps Kaylie and Nellie has 164+229= 393 stamps.

Question 16.
Alaska’s Glacier Bay National Park had 431,986 visitors one year. The next year, the park had 22,351 more visitors than the year before. How many people visited during the two years? Show your work and explain how you found your answer.
_______ visitors

Answer: 886,503 Visitors.

Explanation: The number of visitors in Alaska’s Glacier Bay is 431,986 in one year and in the next year the number of visitors is 22,351 more. So the number of people visited in the second year is 431,986+22,351= 454,517. And the number of visitors in two years are 431,986+454,517= 886,503.

Common Core – Add Whole Numbers (Page 41)

Add Whole Numbers
Estimate. Then find the sum.

Question 1.
Estimate: 90,000
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 28$

Question 2.
73,404 + 27,865
Estimate: _______
Sum: _______

Answer:
Estimate: 100,000.
Sum: 101,269.

Explanation:
73,404 –> 70,000
+27,865 –>+ 30,000
———– ———–
101,269 100,000

Question 3.
404,446 + 396,755
Estimate: _______
Sum: _______

Answer:
Estimate: 800,000.
Sum: 801,201.

Explanation:
404,446 –> 400,000
+396,755 –>+ 400,000
———– ———–
801,201 800,000

Question 4.
137,638 + 52,091
Estimate: _______
Sum: _______

Answer:
Estimate: 200,000.
Sum: 189,729.

Explanation:
137,638 –> 100,000
+ 52,091 –>+ 100,000
———– ———–
189,729 200,000

Question 5.
200,629 + 28,542
Estimate: _______
Sum: _______

Answer:
Estimate: 250,000.
Sum: 229,171.

Explanation:
200,629 –> 200,000
+ 28,542 –>+ 50,000
———– ———–
229,171 250,000

Question 6.
212,514 + 396,705
Estimate: _______
Sum: _______

Estimate: 600,000.
Sum: 609,219.

Explanation:
212,514 –> 200,000
+ 396,705 –>+ 400,000
———– ———–
609,219 600,000

Question 7.
324,867 + 6,233
Estimate: _______
Sum: _______

Estimate: 331,000
Sum: 331,100

Explanation:
324,867 –> 325,000
+ 6,233 –>+ 6,000
———– ———–
331,100 331,000

Question 8.
462,809 + 256,738
Estimate: _______
Sum: _______

Estimate: 800,000.
Sum: 719,547.

Explanation:
462,809 –> 500,000
+ 256,738 –>+ 300,000
———– ———–
719,547 800,000.

Question 9.
624,836 + 282,189

Estimate: _______
Sum: _______

Estimate: 900,000
Sum: 907,025

Explanation:
624,836 –> 600,000
+ 282,189 –>+ 300,000
———– ———–
907,025 900,000.

Problem Solving

Use the table for 10–12.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 29$

Question 10.
Beth and Cade were on one team. What was their total score?
_______

Answer: The total score is 407,502.

Explanation: Beth scores 251,567 and Cade scores 155,935. So the total score is 251,567+155,935= 407,502.

Question 11.
Dillan and Elaine were on the other team. What was their total score?
_______

Answer: 409,928

Explanation: Dillan score is 188,983 and Elaine score is 220,945. So the total score is 188,983+220,945= 409,928.

Question 12.
Which team scored the most points?
_______

Answer: Second-team scores the most points.

Explanation: Second-team scores the most points which are 409,928 whereas 1st team scores 407,502.

Question 13.
Have students write a story problem that can be solved by finding the sum of 506,211 and 424,809. Have them solve the problem.

Answer: 931,020.

Explanation: Town A has a population of 506,211 and town B has a population of 424,809. What is the total population?
Town A population is 506,211 and the town B population is 424,809. So the total population is 506,211+424,809= 931,020.

Common Core – Add Whole Numbers (Page 42)

Lesson Check

Question 1.
The coastline of the United States is 12,383 miles long. Canada’s coastline is 113,211 miles longer than the coastline of the United States. How long is the coastline of Canada?
(a) 100,828 miles
(b) 115,594 miles
(c) 125,594 miles
(d) 237,041 miles

Answer: 125,594 miles.

Explanation: Coastline of the United States is 12,383 miles long and Canada’s coastline is 113,211 miles longer than the coastline of the United States, so the total length of the coastline of Canada is 12,383+113,211= 125,594.

Question 2.
Germany is the seventh largest European country and is slightly smaller by area than Montana. Germany has a land area of 134,835 square miles and a water area of 3,011 square miles. What is the total area of Germany?
(a) 7,846 square miles
(b) 131,824 square miles
(c) 137,846 square miles
(d) 435,935 square miles

Answer: 137,846 miles.

Explanation: The land area of Germany is 134,835 square miles and the water area is 3,011 square miles, so the total area of Germany is 134,835+3,011= 137,846 miles.

Spiral Review

Question 3.
In an election, about 500,000 people voted in all. Which number could be the exact number of people who voted in the election?
(a) 429,455
(b) 441,689
(c) 533,736
(d) 550,198

Answer: 533,736

Explanation: As 500,000 people are voted so the exact number of people who voted in the election is 533,736.

Question 4.
In 2007, Pennsylvania had approximately 121,580 miles of public roads. What is 121,580 rounded to the nearest thousand?
(a) 100,000
(b) 120,000
(c) 121,000
(d) 122,000

Answer: 122,000.

Explanation: The number 121,580 is rounded to the nearest thousand is 122,000.

Question 5.
Which of the following lists of numbers is in order from greatest to least?
(a) 33,093; 33,903; 33,309
(b) 42,539; 24,995; 43,539
(c) 682,131; 628,000; 682,129
(d) 749,340; 740,999; 740,256

Answer: 749,340; 740,999; 740,256.

Explanation: The numbers in order from greatest to least is 749,340; 740,999; 740,256.

Question 6.
Which symbol makes the following statement true?
$413,115 ________ $431,511
(a) <
(b) >
(c) =
(d) +

Answer: a

Explanation: $413,115 < $431,511.

Common Core – Subtract Whole Numbers (Page 44)

Question 1.
Subtract. Use the grid to record the problem.
637,350 − 43,832
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 30$

Answer: 1,076,182.

Explanation:

Estimate. Then find the difference.

Question 2.
14,659 − 11,584
Estimate: _______
Difference: _______

Estimate: 3,000
Sum: 3,075

Explanation:

14,659 –> 15,000
– 11,584 –> -12,000
———– ———–
3,075 3,000

Question 3.
456,912 − 37,800
Estimate: _______
Difference: _______

Estimate: 420,000.
Sum: 419,112.

Explanation:

456,912 –> 460,000
– 37,800 –> – 40,000
———– ———–
419,112 420,000

Question 4.
407,001 − 184,652
Estimate: _______
Difference: _______

Estimate: 210,000.
Sum: 222,349.

Explanation:

407,001 –> 410,000
– 184,652 –> – 200,000
———– ———–
222,349 210,000

Question 5.
942,385 − 461,803
Estimate: _______
Difference: _______

Estimate: 400,000.
Sum: 480,582.

Explanation:

942,385 –> 900,000
– 461,803 –> -500,000
———– ———–
480,582 400,000

Question 6.
798,300 − 348,659
Estimate: _______
Difference: _______

Estimate: 500,000.
Sum: 449,641.

Explanation:

798,300 –> 800,000
– 348,659 –> -300,000
———– ———–
449,641 500,000

Question 7.
300,980 − 159,000
Estimate: _______
Difference: _______

Estimate: 141,000.
Sum: 141,980.

Explanation:

300,980 –> 301,000
– 159,000 –> -160,000
———– ———–
141,980 141,000

Common Core – Subtract Whole Numbers (Page 45)

Practice: Copy and Solve Subtract. Add to check.

Question 8.
653,809 – 256,034 = _______

Answer: 397,775.

Explanation: 653,809 – 256,034 = 397,775.

Question 9.
258,197 – 64,500 = _______’

Answer: 163,697.

Explanation: 258,197 – 64,500 = 163,697.

Question 10.
496,004 – 398,450 = _______

Answer:

Explanation: 496,004 – 398,450 = 97,554.

Question 11.
500,000 – 145,609 = _______

Answer: 354,391.

Explanation: 500,000 – 145,609= 354,391.

Reason Abstractly Algebra Find the missing digit.

Question 12.
6,532 − 4,1_5 = 2,407

Answer: 2

Explanation: To find the missing digit we will subtract 6,532-2,407= 4,125.

Question 13.
_08,665−659,420 = 149,245

Answer: 8

Explanation: To find the missing digit we will add 149,245+659,420= 808,665.

Question 14.
697,320 − 432,_08 = 264,712

Answer: 6

Explanation: To find the missing digit we will subtract 697,320-264,712= 432,608.

Use the table for 15–16.

Question 15.
Estimate Reasonableness How many more acres were grown in 1996 than in 1986? Estimate to check the reasonableness of your answer.
_______ acres

Answer: 200,000 acres.

Explanation: The number of acres in 1986 is 466,256 and the number of acres in 1996 is 656,598. So the number of acres grown in 1996 is 656,598- 466,256= 190,342. So the estimated answer is 200,000 acres.

Question 16.
What is the difference between the greatest number of acres and the least number of acres used for growing oranges?
_______ acres

Answer: 206,830.

Explanation: The greatest number of acres is 673,086 and the least number of acres is 466,256. So the difference between the greatest number of acres and the least number of acres are 673,086- 466,256= 206,830.

Question 17.
Workers at a paper company count the number of boxes of paper in the warehouse each month. In January, there were 106,341 boxes of paper. In February, there were 32,798 fewer boxes than there were in January. In March, there were 25,762 fewer boxes than there were in February. How many boxes were in the warehouse in March?
_______ boxes

Answer: 106,341-58,560= 47,781 boxes.

Explanation: Total number of boxes is 106,341 in January and in February there were 32,798 boxes and in march, there were 25,762 fewer boxes. Total boxes are 32,798+25,762= 58,560, so the number of boxes were in the warehouse in March is 106,341-58,560= 47,781 boxes.

Question 18.
There are 135,663 kilometers of U.S. coastline that border the Pacific Ocean. There are 111,866 kilometers of U.S. coastline that border the Atlantic Ocean. How many more kilometers of U.S. coastline border the Pacific Ocean than the Atlantic Ocean? Solve the problem and show how to check your answer.
_______ km

Answer: 23,797 km.

Explanation: There are 135,663 kilometers of US coastline in the Pacific Ocean and 111,866 kilometers in the Atlantic ocean. So the number of kilometers of US coastline border the Pacific Ocean than the Atlantic Ocean is 135,663- 111,866= 23,797 km.

Common Core – Subtract Whole Numbers (Page 46)

Question 19.
What’s the Error? Maryland has an area of 12,407 square miles. Texas has an area of 268,601 square miles. How much larger is Texas than Maryland?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 31$

Read how Janice solved the problem.
Find her error.

Texas: 268,601 square miles
Maryland: 12,407 square miles
I can subtract to find the difference.
268,601
–12,407
144,531

Solve the problem and correct her error.

Answer: Texas is 256,194 square miles larger than Maryland.

Explanation:
Texas: 268,601 square miles
Maryland: 12,407 square miles
I can subtract to find the difference.
268,601- 12,407= 256,194.
So Texas is 256,194 square miles larger than Maryland.

Question 20.
Verify Reasoning of Others Describe Janice’s error.

Answer: Janice did not align the digits by place value when subtracted the numbers.

Common Core – Subtract Whole Numbers (Page 47)

Subtract Whole Numbers
Estimate. Then find the difference.

Question 1.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 32$

Question 2.
428,731 – 175,842
Estimate: ______
Difference: ______

Answer:
Estimate: 200,000.
Difference: 252,889.

Explanation:
428,731 – 175,842= 252,889
400,000 – 200,000= 200,000.

Question 3.
920,026 – 535,722
Estimate: ______
Difference: ______

Answer:
Estimate: 400,000.
Difference: 384,304.

Explanation:
920,026 – 535,722= 384,304
900,000 – 500,000= 400,000.

Question 4.
253,495 – 48,617
Estimate: ______
Difference: ______

Answer:
Estimate: 200,000.
Difference: 204,878.

Explanation:
253,495 – 48,617= 204,878.
250,000 – 50,000= 200,000.

Subtract. Add to check.

Question 5.
735,249 – 575,388 = ______
______ + ______ = ______

Answer: 159,861.
575,388+159,861= 735,249.

Explanation:
735,249 – 575,388= 159,861.
575,388+159,861= 735,249.

Question 6.
512,724 – 96,473 = ______
______ + ______ = ______

Answer: 416,251
96,473+416,251= 512,724.

Explanation:
512,724 – 96,473 = 416,251
96,473+416,251= 512,724.

Question 7.
600,000 – 145,782 = _______
_______ + ______ = _______

Answer: 454,218.
145,782+454,218= 600,000.

Explanation:
600,000 – 145,782 = 454,218.
145,782+454,218= 600,000.

Problem Solving
Use the table for 8 and 9.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 33$

Question 8.
How many more people attended the Magic’s games than attended the Pacers’ games?
_______ people

Answer: 133,606 people.

Explanation: The number of people attended for Magic’s game is 715,901 and the number of people attended for Pacer’s games is 582,295. So the number of people more attended for the Magic’s games than attended the Pacers’ games are 715,901-582,295=133,606.

Question 9.
How many fewer people attended the Pacers’ games than attended the Clippers’ games?
_______ people

Answer: 87,768 people

Explanation: The number of people attended for Indiana Pacers game is 582,295 and the number of people attended for Los Angeles Clippers is 670,063. So 670,063- 582,295= 87,768 people attended the Pacers’ games than attended the Clippers’ games.

Question 10.
Have students write a story problem that can be solved by finding the difference of 432,906 and 61,827. Then have them solve the problem.

Answer: The number of people who attended the football game is 432,906 and the number of people who attended the basketball game is 61,287. How many fewer people attended the football game than attended the basketball game?

Explanation: The number of people who attended the football game is 432,906 and the number of people who attended the basketball game is 61,287. So 432,906- 61,287= 371,619 people attended the Pacers’ games than attended the Clippers’ games.

Common Core – Subtract Whole Numbers (Page 48)

Lesson Check

Question 1.
This year, a farm planted 400,000 corn stalks. Last year, the farm planted 275,650 corn stalks. How many more corn stalks did the farm plant this year than last year?
(a) 124,350
(b) 125,450
(c) 235,450
(d) 275,650

Answer: 124,350.

Explanation: A farm planted 400,000 corn stalks this year and 275,650 corn stalks last year, so 400,000-275,650= 124,350 many more corn stalks did the farm plant this year than last year.

Question 2.
One machine can make 138,800 small paper clips in one day. Another machine can make 84,250 large paper clips in one day. How many more small paper clips than large paper clips are made by the two machines in one day?
(a) 44,550
(b) 54,550
(c) 54,650
(d) 154,650

Answer: 54,550.

Explanation: As machine one makes 138,800 small paper clips in one day and the machine makes 84,250 paper clips in one day, so
138,800-84,250= 54,550 many more small paper clips than large paper clips are made by the two machines in one day.

Spiral Review

Question 3.
In three baseball games over a weekend, 125,429 people came to watch. The next weekend, 86,353 came to watch the games. How many people in all watched the six baseball games?
(a) 201,782
(b) 211,772
(c) 211,782
(d) 211,882

Answer: 211,782.

Explanation: The number of people attended for three baseball games is 125,429 and 86,353 in next weekend, so
125,429+86,353= 211,782 people watched the six baseball games.

Question 4.
Kevin read the number “two hundred seven thousand, forty-eight” in a book. What is this number in standard form?
(a) 27,048
(b) 27,480
(c) 207,048
(d) 207,480

Answer: 207,048.

Explanation: The standard form of “two hundred seven thousand, forty-eight” is 207,048.

Question 5.
A museum had 275,608 visitors last year. What is this number rounded to the nearest thousand?
(a) 275,600
(b) 276,000
(c) 280,000
(d) 300,000

Answer: 276,000.

Explanation: The nearest thousand of the number 275,608 is 276,000.

Question 6.
At the Millville Theater, a play ran for several weeks. In all, 28,175 people saw the play. What is the value of the digit 8 in 28,175?
(a) 8
(b) 800
(c) 8,000
(d) 80,000

Answer: 8,000.

Explanation: The value of the digit 8 in 28,175 is 8,000.

Problem Solving • Comparison Problems with Addition and Subtraction (Page 50)

During an event, a hot air balloon traveled a distance of 5,110 feet during the first trip and 850 feet more during the second trip. How far did it travel during the second trip?

Question 1.
What do I need to find?

Answer: We need to find the number of feet the balloon traveled during the second trip.

Question 2.
What information do I need to use?

Answer: We will use the facts that the ballon traveled 5,110 feet during the first trip and 850 feet more during the second trip.

Question 3.
How will I use the information?

Answer: We can draw a diagram or use a bar model to help me find how many feet the ballons traveled during the second trip.

Explanation: As hot air balloon traveled a distance of 5,110 feet in the first trip and 850 more in the second trip, so the second trip is 5,110+850= 5,960 feet. So, the balloon traveled 5,960 feet during the second trip.

Question 4.
How far did it travel during the second trip? And
______ feet

Answer: The ballon traveled 5,960 feet during the second trip.

Question 5.
Is your answer reasonable? Explain how you know.

Answer: Yes, the answer is reasonable.

Explanation: As 5,960 feet is reasonable because 5,000+1,000= 6,000 and 5,960 is close to 6,000. Since addition and subtraction are inverse operations, we can subtract 850 from the sum to see if we get 5,110.

Problem Solving • Comparison Problems with Addition and Subtraction (Page 51)

Hot air balloons are able to fly at very high altitudes. A world record height of 64,997 feet was set in 1988. In 2005, a new record of 68,986 feet was set. How many feet higher was the 2005 record than the 1988 record?

Question 1.
First, draw a diagram to show the parts of the problem.

Answer: 3,989 feet higher.

Explanation: 68,986-64,997= 3,989 feet.

Question 1.
Next, write the problem you need to solve.

Answer: 3,989 feet higher.

Explanation: The 2005 record was 68,986-64,997= 3,989 feet higher.

Question 1.
Last, solve the problem to find how many feet higher the 2005 record was than the 1988 record
______ feet higher

Answer: 3,989 feet higher.

Explanation: The 2005 record was 68,986-64,997= 3,989 feet higher.

Question 2.
What if a new world altitude record of 70,000 feet was set? How many feet higher would the new record be than the 2005 record?
______ feet

Answer: 1,014 feet.

Explanation: The new world altitude record is 70,000 feet, so the new record is 70,000-68,986= 1,014 feet higher.

Question 3.
Last year, the ticket sales for a commercial hot air balloon ride were $109,076. This year, the ticket sales were $125,805. How much more were the ticket sales this year?
$ ______

Answer: $16,729.

Explanation: The ticket sale for last year is $109,076 and this year is $125,805, so $125,805- $109,076= $16,729 much more tickets are sold this year.

Question 4.
There were 665 hot air balloon pilots at a hot air balloon race. There were 1,550 more ground crew members than there were pilots. How many ground crew members were there in all?

______ ground crew members

Answer: 2,215 ground crew members.

Explanation: There were 1,550 more ground crew members and 665 hot air ballon pilots at a hot air ballon. So 1,550+665= 2,215 ground crew members.

Problem Solving • Comparison Problems with Addition and Subtraction (Page 52)

Question 5.
Steve Fossett attempted to fly around the world in a balloon several times before he succeeded in 2002. How many more miles did he fly during the 2002 flight than during the August 1998 flight?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 34$
______ miles

Answer: 6,247 miles.

Explanation: Number of miles did he flew are during 2002 are 20,482-14,235= 6,247 miles.

Question 6.
Is the combined distance for the 1998 flights more or less than the distance for the 2002 flight?

Answer: The combined distance is 20,038 miles, which is less than 20,482 miles.

Question 7.
Estimate the total number of miles Fossett flew during the six hot air balloon flights. Explain how you estimated.
______ miles

Answer: 55,000 miles.

Explanation: Round off each distance to the greatest place value position, then add 2,000+10,000+6,000+14,000+3,000+20,000= 55,000 miles.

Question 8.
Rusty wants to buy a small hot air balloon that costs $23,950. The cost of training for a license is $2,750. How much will Rusty pay for the balloon and the training?
(a) $21,200
(b) $26,600
(c) $26,700
(d) $36,700

Answer: $26,700

Explanation: Rusty wants to buy a small hot air balloon that costs $23,950 and the cost of training for a license is $2,750, so total Rusty pay is $23,950+$2,750= $26,700.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 53)

Problem Solving • Comparasion Problems with Addition and Substraction

Use the information in the table for 1–3.

Question 1.
How many square miles larger is the surface area of Lake Huron than the surface area of Lake Erie?

Think: How can a bar model help represent the problem? What equation can be written?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 35$

Question 1.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million 36$

Question 2.
Which lake has a surface area that is 14,938 square miles greater than the surface area of Lake Ontario? Draw a model and write a number sentence to solve the problem.

Answer: Lake Michigan 22,278 square miles.

Explanation: 7,340+14,938= 22,278.

Question 3.
Lake Victoria has the largest surface area of all lakes in Africa. Its surface area is 26,828 square miles. How much larger is the surface area of Lake Superior than that of Lake Victoria?
______ square milles

Answer: 4,872 square miles.

Explanation: The Surface area of Lake Victoria is 26,828 square miles and the surface area of the Lake Superior is 31,700 square miles. So 31,700-26,828= 4,872 square miles larger.

Question 4.
At 840,000 square miles, Greenland is the largest island in the world. The second-largest island is New Guinea, at 306,000 square miles. How much larger is Greenland than New Guinea?
______ square miles

Answer: 534,000 square miles.

Explanation: The surface area of Greenland is 840,000 square miles and New Guinea is 306,000 square miles. So 840,000-306,000= 534,000 square miles.

Problem Solving • Comparison Problems with Addition and Subtraction (Page 54)

Lesson Check

Question 1.
The Mariana Trench in the Pacific Ocean is about 36,201 feet deep. The Puerto Rico Trench in the Atlantic Ocean is about 27,493 feet deep. Based on these data, how many feet deeper is the Mariana Trench than the Puerto Rico Trench?
(a) 8,708 feet
(b) 9,718 feet
(c) 9,808 feet
(d) 63,694 feet

Answer: 8,708 feet.

Explanation: The Mariana Trench in the Pacific Ocean is about 36,201 feet deep and the Atlantic Ocean is about 27,493 feet deep. So 36,201-27,493= 8,708 feet.

Question 2.
At 1,932 feet, Crater Lake, Oregon, is the deepest lake in the United States. The world’s deepest lake, Lake Baykal in Russia, is 3,383 feet deeper. How deep is Lake Baykal?
(a) 3,383 feet
(b) 4,215 feet
(c) 4,315 feet
(d) 5,315 feet

Answer: 5,315 feet

Explanation: Crater Lake is 1,932 feet and Lake Baykal is 3,383 feet, so 1,932+3,383= 5,315 feet deeper.

Spiral Review

Question 3.
Which of the following amounts is greater than $832,458?
(a) $82,845
(b) $832,458
(c) $823,845
(d) $832,485

Answer: $832,485.

Explanation: $832,458 is greater than $832,485.

Question 4.
A stadium in Pennsylvania seats 107,282 people. A stadium in Arizona seats 71,706 people. Based on these facts, how many more people does the stadium in Pennsylvania seat than the stadium in Arizona?
(a) 35,576
(b) 35,586
(c) 36,576
(d) 178,988

Answer: 35,576.

Explanation: A stadium in Pennsylvania seats 107,282 people and a stadium in Arizona seats 71,706 people. So 107,282-71,706= 35,576 people seat in the stadium in Arizona.

Question 5.
Which of the following numbers is 399,713 rounded to the place value of the underlined digit?
(a) 390,000
(b) 398,000
(c) 399,800
(d) 400,000

Answer: 400,000.

Explanation: The number 399,713 rounded to the nearest thousand is 400,000.

Question 6.
About 400,000 people visited an art museum in December. Which number could be the exact number of people who visited the art museum?
(a) 478,051
(b) 452,223
(c) 352,483
(d) 348,998

Answer: 352,483.

Explanation: The exact number of people who visited the art museum is 352,483.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 55)

Question 1.
Select a number for ■ that will make a true comparison. Mark all that apply.
703,209 > ■
Options:
(a) 702,309
(b) 703,029
(c) 703,209
(d) 703,290
(e) 730,029
(f) 730,209

Answer: 703,209>702,309, 703,209>703,029.

Explanation: The numbers 702,309, 703,029 are less than 703,209.

Question 2.
Nancy wrote the greatest number that can be made using each of these digits exactly once.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 37$
Part A
What was Nancy’s number? How do you know this is the greatest possible number for these digits?

Answer: 985,431.

Explanation: Here we will use place value and we will take the greatest digit and place it in the spot furthest to the left, the hundred thousands column. And place the next greatest digit in the ten thousands column and so on. We know that the place value of each digit to the left is ten times the place value of the digit to its right.

Question 2.
Part B
What is the least number that can be made using each digit exactly once? Explain why the value of the 4 is greater than the value of the 5.

Answer: 134,589.

Explanation: The 4 represents 4,000 and 5 represents 500.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 56)

For 3–4, use the table.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 38$

Question 3.
Write the name of each mountain peak in the box that describes its height, in feet.
Between 14,000 feet and Between 14,301 feet and
14,300 feet 14,500 feet

Answer:
Between 14,000 feet and 14,300 feet- Crestone Peak, Humboldt Peak, White Mountain.
Between 14,301 feet and 14,500 feet- Blanca Peak, University Peak, Mount Whitney.

Explanation:
Between 14,000 feet and 14,300 feet- Crestone Peak 14,294 ft, Humboldt Peak 14,064 ft, White Mountain 14,246 ft.
Between 14,301 feet and 14,500 feet- Blanca Peak 14,345 ft, University Peak 14,470 ft, Mount Whitney 14,494 ft.

Question 4.
Circle the name of the tallest peak. Explain how you know which of the mountain peaks is the tallest.

Answer: Mount Whitney.

Explanation: Comparing the heights by place value position.

Question 5.
Mr. Rodriguez bought 420 pencils for the school. If there are 10 pencils in a box, how many boxes did he buy?
Options:
(a) 42
(b) 420
(c) 430
(d) 4,200

Answer: 42 boxes.

Explanation: Mr. Rodriguez bought 420 pencils and in a box, there are 10 pencils. So the number of boxes did he bought is
420÷10= 42 boxes.

Question 6.
Bobby and Cheryl each rounded 745,829 to the nearest ten thousand. Bobby wrote 750,000 and Cheryl wrote 740,000. Who is correct? Explain the error that was made.
_________

Answer: Bobby is correct.

Explanation: Cheryl left the ten thousands digit the same instead of increasing it by 1. The digit in the thousands place is 5, so to round to the nearest ten thousand, Cheryl should have increased the ten thousands digit, 4 by 1.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 57)

Question 7.
The total season attendance for a college team’s home games, rounded to the nearest ten thousand, was 270,000. For numbers 7a–7d, select Yes or No to tell whether the number could be the exact attendance.
a. 265,888
i. yes
ii. no

Answer: Yes.

Explanation: When 265,888 is rounded off to the nearest ten thousand we will get 270,000.

Question 7.
b. 260,987
i. yes
ii. no

Answer: No.

Explanation: When 260,987 is rounded off to the nearest ten thousand we will get 260,000.

Question 7.
c. 274,499
i. yes
ii. no

Answer: Yes.

Explanation: When 274,499 is rounded off to the nearest ten thousand we will get 270,000.

Question 7.
d. 206,636
i. yes
ii. no

Answer: No.

Explanation: When 206,636 is rounded off to the nearest ten thousand we will get 210,000.

For 8–10, use the table.

The table shows recent population data for Sacramento, California.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 39$

Question 8.
How many children are under 10 years old? Show your work.
_____ children

Answer: 66,416 children.

Explanation: Children under 10 years old are 35,010+31,406= 66,416 children.

Question 9.
How many people are between the ages of 20 and 49? Show your work.
_____ people

Answer: 207,909 people.

Explanation: People between the ages of 20 and 49 are 115,279+92,630= 207,909 people.

Question 10.
How many more children are under the age of 5 than between the ages of 10 and 14? Show your work.
_____ children

Answer: 4,757 children.

Explanation: The children 35,010-30,253= 4,757 children are under the age of 5 than between the ages of 10 and 14.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 58)

Question 11.
For numbers 11a–11d, select True or False for each sentence.
a. The value of 7 in 375,092 is 7,000.
i. True
ii. False

Answer: False.

Explanation: False, because the value of the digit 7 in 375,092 is 70,000.

Question 11.
b. The value of 5 in 427,593 is 500.
i. True
ii. False

Answer: True.

Explanation: As 5 is in hundreds place, so the value of the digit 5 in 427,593 is 500.

Question 11.
c. The value of 2 in 749,021 is 200.
i. True
ii. False

Answer: False.

Explanation: False, because the value of the digit 2 in 749,021 is 20.

Question 11.
d. The value of 4 in 842,063 is 40,000.
i. True
ii. False

Answer: True.

Explanation: The value of the digit 4 in the digit 842,063 is 40,000.

Question 12.
Select another way to show 403,871. Mark all that apply.
Options:
(a) four hundred three thousand, eight hundred one
(b) four hundred three thousand, seventy-one
(c) four hundred three thousand, eight hundred seventy-one
(d) 400,000 + 38,000 + 800 + 70 + 1
(e) 400,000 + 3,000 + 800 + 70 + 1
(f) 4 hundred thousands + 3 thousands + 8 hundreds + 7 tens + 1 one

Answer: c, e, f

Explanation: four hundred three thousand, eight hundred seventy-one, 400,000 + 3,000 + 800 + 70 + 1, 4 hundred thousands + 3 thousands + 8 hundreds + 7 tens + 1 one are the another way of 403,871.

Question 13.
Lexi, Susie, and Rial are playing an online word game. Rial scores 100,034 points. Lexi scores 9,348 fewer points than Rial and Susie scores 9,749 more points than Lexi. What is Susie’s score? Show your work.
_____

Answer: 100,435 points.

Explanation: Rial score is 100,034 points and Lexi scores 9,348 fewer points which means 100,034-9,348= 90686 and Susie scores 9,749 more points than Lexi which means 90,686+9,749= 100,435 points are scored by Susie.

Question 14.
There were 13,501 visitors to a museum in June. What is this number rounded to the nearest ten thousand? Explain how you rounded.
_____

Answer: 10,000.

Explanation: There is a 1 in the ten thousands place. The digit to its right is 3, so the 1 stays the same.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 59)

Question 15.
New Mexico has an area of 121,298 square miles. California has an area of 155,779 square miles. How much greater is the area, in square miles, of California than the area of New Mexico? Show your work and explain how you know the answer is reasonable.
______ square miles

Answer: 34,481 square miles.

Explanation: The area of New Mexico is 121,298 square miles and the area of California is 155,779 square miles. So
155,779- 121,298= 34,481 square miles greater.

Question 16.
Circle the choice that completes the statement.
10,000 less than 24,576 is $Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 40$ 1,000 less than 14,576.
_________

Answer: 10,000 less than 24,576 is greater than 1,000 less than 14,576.

Explanation:
10,000 less than 24,576 is 1,000 less than 14,576.

Question 17.
Match the number to the value of its 5.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 41$
Type below:
__________

Answer: 45,678 – 5,000 757,234 – 50,000 13,564 – 500. 3,450 – 50.

Explanation:

Problem Solving • Comparasion Problems with Addition and Substraction (Page 60)

Question 18.
During September and October, a total of 825,150 visitors went to Grand Canyon National Park. If 448,925 visitors went to the park in September, how many visitors went to the park in October? Show your work.
_____ people

Answer:

Explanation: The total number of visitors in September and October is 825,150 visitors and 448,925 visitors visited the park in September, so 825,150-448,925= 376,225 visitors visited in October.

Question 19.
A college baseball team had 3 games in April. Game one had an attendance of 14,753 people. Game two had an attendance of 20,320 people. Game three had an attendance of 14,505 people. Write the games in order from the least attendance to the greatest attendance. Use pictures, words, or numbers to show how you know.
Game _____ ; _____ ; _____

Answer: Game 3; Game 1; Game2.

Explanation: The number of people who attended for game one is 14,753 and game two is 20,320 people, game three is 14,505 people. So the order from the least attendance to the greatest attendance is 14,505<14,753<20,320.

Question 20.
Caden made a four-digit number with a 5 in the thousands place, a 5 in the ones place, a 6 in the tens place, and a 4 in the hundreds place. What was the number?
_____

Answer: 5,465.

Explanation: The four-digit number with 5 in the thousands place, 4 in the hundreds place, 6 in the tens place, and 5 in the ones place made by Caden is 5,465.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 65)

Question 1.
There are 8 students in the art club. There are 3 times as many students in chorus. How many students are in chorus?
So, there are _____ students in chorus.

Answer: There are 24 students in the chorus.

Explanation: The number of students in the art club is 8 students and there are 3 times as many students in the chorus. So number of students in the chorus is 8×3= 24 students. So, there are 24 students in the chorus.

Draw a model and write an equation.

Question 2.
6 times as many as 2 is 12.

Answer: 6×2= 12

Explanation: 6×2= 12

Question 3.
20 is 4 times as many as 5.

Answer: 20= 4×5.

Explanation: 20= 4×5.

Write a comparison sentence.

Question 4.
18 = 9 × 2
_____ is _____ times as many as _____ .

Answer: 18 is 9 times as many as 2.

Question 5.
8 × 4 = 32
_____ times as many as _____ is _____

Answer: 8 times as many as 4 is 32.

Write a comparison sentence.

Question 6.
5 × 7 = 35
_____ times as many as _____ is _____ .

Answer: 5 times as many as 7 is 35.

Question 7.
54 = 6 × 9
_____ is _____ times as many as _____ .

Answer: 54 is 6 times as many as 9.

Question 8.
One week, Jake and Sally collected canned goods for a food drive. On Monday, Jake collected 4 boxes and Sally collected 2 boxes. At the end of the week, Jake had 3 times as many boxes as he had on Monday. Sally had 4 times as many boxes as she had on Monday. Together, how many boxes of canned goods did they have at the end of the week?
_____ boxes

Answer: 20 boxes.

Explanation:
The number of boxes Jake collected on Monday is 4 boxes and at the end of the week, he collected 3 times as many boxes as he had on Monday, which means 3×4= 12. Sally collected 2 boxes on Monday and at the end of the week, Sally collected 4 times as many boxes as she had on Monday which means 4×2= 8 boxes. So 12 boxes+8 boxes= 20 boxes of canned goods they have collected at the end of the week.

Question 9.
Nando has 4 goldfish. Jill has 3 goldfish. Cooper has 2 times as many goldfish as Nando and Jill combined. Write an equation that compares the number of goldfish Cooper has with the number of goldfish that Nando and Jill have.

Answer: 14 goldfish.

Explanation: Nando has 4 goldfish, Jill has 3 goldfish and Cooper has 2 times as many goldfish as Nando and Jill combined which means the total goldfish Nando and Cooper has are 4+3= 7, so Cooper had 2×7= 14 goldfish.

Question 10.
Represent a Problem Write a comparison sentence about pet food that could be represented using the equation 12 = 4 × 3.

Answer: Cooper bought 12 cans of cat food, which is 4 times the number of cans that he has now.

Problem Solving • Comparasion Problems with Addition and Substraction (Page 66)

Question 11.
Luca has 72 baseball cards. This is 8 times as many cards as Han has. How many baseball cards does Han have?
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 42$
a. What do you need to find?

Answer: We need to find how many baseball cards Han has.

Question 11.
b. How can you use a model to find the number of cards Han has?

Answer: By drawing a comparison model we can find the number of cards Han has.

Question 11.
c. Draw the model.

Answer:

Question 11.
d. Write an equation and solve.

Answer: Han has 9 baseball cards.

Explanation:
72= 8×n
n= 72÷8
= 9.
So, Han has 9 baseball cards.

Question 12.
Complete the statements to describe each model.
$Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million img 43$
24 is _____ times as many as _____ . 24 is _____ times as many as _____ .

Answer:
24 is 6 times as many as 4.
24 is 4 times as many as 6.

Conclusion:

Enhance your math skills by preparing from the Go Math Answer Key Chapter 1. Also, get some subject knowledge after performing the chapter practice test in the HMH Go Math Grade 4 Answer Key Chapter 1 Place Value, Addition, and Subtraction to One Million.

Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test

April 7, 2022March 27, 2022 by Go Math Answer Key

Improve your Math Skills by referring to the Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test. Take the help of this Go Math Grade 3 Ch 1 Assessment Test Answer Key, and attain good scores in your exams.

Go Math Grade 3 Answer Key Chapter 1 contains different topics which you can see in the below modules. Through this 3rd Grade Go Math Answer Key Ch 1 Addition and Subtraction within 1,000 Assessment Test, you can test your preparation standard and understand where you went wrong. Clear all your queries and understand the concepts then and there itself.

Chapter 1: Addition and Subtraction within 1,000 Assessment Test

Test – Page 1 – Page No. 11
Test – Page 2 – Page No. 12
Test – Page 3 – Page No. 13
Test – Page 4 – Page No. 14
Test – Page 5 – Page No. 15
Test – Page 6 – Page No. 16

Test – Page 1 – Page No. 11

Question 1.
For numbers 1a–1d, choose Yes or No to tell whether the sum is even.
a. 8 + 3
i. yes
ii. no

Answer: No

Explanation: As 8 + 3 = 11 which is odd number. So the answer is no.

Question 1.
b. 6 + 6
i. yes
ii. no

Answer: Yes

Explanation: As 6 + 6= 12 which is even number. So the answer is true.

Question 1.
c. 4 + 5
i. yes
ii. no

Answer: No

Explanation: As 4 + 5 = 9 which is odd number. So the answer is No.

Question 1.
d. 2 + 6
i. yes
ii. no

Answer: Yes

Explanation: As 2 + 6 = 8 which is even number. So the answer is Yes.

Question 2.
Select the number sentences that show the Commutative Property of Addition. Mark all that apply.
Options:
a. 9 + 7 = 16 + 0
b. 9 + 7 = 7 + 9
c. (4 + 5) + 7 = (5 + 4) + 7
d. 7 + (4 + 5) = (7 + 4) + 5

Answer: b.

Explanation: The “Commutative Laws” say we can swap numbers over and still get the same answer when we add a + b = b+a. Therefore 9 + 7 = 7 + 9 and (4 + 5) + 7 = (5 + 4) + 7 shows the Commutative Property of Addition.

Question 3.
Select the numbers that round to 500 when rounded to the nearest hundred. Mark all that apply.
Options:
a. 438
b. 542
c. 450
d. 483
e. 567

Answer: options b, c, d.

Explanation: We know that 542, 450, and 483 are between 400 and 500 and it is closer to 500. So, 483 rounded off to the nearest hundred is 500.

Question 4.
There are 165 cars in the parking lot. Complete the chart to show 165 rounded to the nearest 10.
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 1 img 1$

Answer: 170.

Explanation: Rounding 165 to nearest 10 = 170.
1 hundred, 7 tens, and 0 ones = 170.

Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test

Test – Page 2 – Page No. 12

Question 5.
Write each number sentence in the box below the better estimate of the sum.
281 + 125 = ■ 236 + 119 = ■
242 + 128 = ■ 309 + 135 = ■
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 2 img 2$

Answer:
281 + 125 = 300 + 100 = 400 236 + 119 = 200 + 100 = 300
242 + 128 = 200 + 100 = 300 309 + 135 = 300 + 100 = 400

Explanation:

Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test

Question 6.
Abby and Cruz are playing a game. Abby’s score is 586 points. Cruz’s score is 754. Abby estimates she needs about 200 points more to reach Cruz’s score. How did she estimate? Explain.

Answer: Cruz rounded the estimates points to the nearest hundred.

Explanation: Cruz rounded 586 to 600 and 754 to 800. Then she calculated the difference to estimate points = 800 – 600 = 200.

Question 7.
The table shows how many shells each person collected.
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 2 img 3$
For numbers 7a–7d select True or False for each statement.
a. Melba collected about 40 more shells than Pablo.
i. True
ii. False

Answer: True

Explanation:
Melba collected 455 shells and Pablo collected 421 shells
Difference between both = 455 – 421 = 34 which is near to 40.

Question 7.
b. Melba and Pablo collected more than 800 shells.
i. True
ii. False

Answer: True

Explanation: Sum of shells collected by Melba and Pablo = 455 + 421 = 876.

Question 7.
c. Amber collected about 60 fewer shells than Pablo.
i. True
ii. False

Answer: False

Explanation: Difference between Amber and Pablo collected shells = 421 – 382 = 39.

Question 7.
d. Amber, Melba, and Pablo collected over 1,100 shells.
i. True
ii. False

Answer: True

Explanation: Sum of shells collected all three = 382 + 455 + 421 = 1258.

Test – Page 3 – Page No. 13

Question 8.
Mikio drove 58 miles on Saturday. On Sunday he drove 23 miles. How many miles did he drive on Saturday and Sunday? Explain how you solved the problem.
_____ miles

Answer: 81 miles.

Explanation:
No of miles drove on Saturday = 58 miles
No of miles drove on Sunday = 23 miles
Total no of miles he drove on both Saturday and Sunday = 58 + 23 = 81 miles.

Question 9.
Choose the property that makes the statement true.
The $Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 3 img 4$ Property of Addition describes the number sentence 17 + 1 = 1 + 17.
________

Answer:

The Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Property of Addition describes the number sentence 17 + 1 = 1 + 17.

Use the table for 10–12.
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 3 img 5$

Question 10.
The table shows the number of students visiting the zoo each day.
How many students visited the zoo on Wednesday and Thursday?
_____ students

Answer: 857 students.

Explanation: No of students visited zoo on Wednesday and Thursday = 349 + 508 = 857 students.

Question 11.
How many more students visited the zoo on Wednesday than on Monday?
_____ students

Answer: 103 students.

Explanation: No of students visited the zoo on Wednesday than on Monday = 349 – 246 = 103.

Question 12.
How many more students visited the zoo on Monday and Tuesday than on Wednesday?
_____ students

Answer: 315 students.

Explanation: No of students visited the zoo on Monday and Tuesday than on Wednesday = (246+418) – 349 = 315.

Test – Page 4 – Page No. 14

Question 13.
Help Ben find the sum.
2 4 6
3 2 1
+1 2 8
———-
695

For numbers 13a–13d choose Yes or No to tell Ben when to regroup.
a. Regroup the ones.
i. yes
ii. no

Answer: Yes

Question 13.
b. Add the regrouped ten.
i. yes
ii. no

Answer: Yes.

Question 13.
c. Regroup the tens.
i. yes
ii. no

Answer: No.

Question 13.
d. Add the regrouped hundred.
i. yes
ii. no

Answer: No.

Question 14.
Avery sent 58 email invitations to a party. So far, 37 people replied. How many people still need to reply? Draw jumps and label the number line to show your thinking.
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 4 img 6$
_____ emails.

Answer: 21 people.

Explanation:
Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test
Given that total 58 email invitations are sent to a party
No of people replied so far = 37
From the below figure no of people remained to reply =1 + 10 + 10
= 21 people.

Question 15.
There are 842 seats in the school auditorium. 138 seats need repairs. How many seats do not need repairs? Show your work.
_____ seats

Answer: 704 seats.

Explanation: Total seats in school auditorium = 842
No of seats need to be repaired = 138
Therefore no of seats not required to repair = 842 – 138 = 704 seats.

Question 16.
Madison solves this problem. She says the difference is 419. Explain the mistake Madison made. What is the correct difference?
6 4 5
−2 3 6
———–
_____

Answer: 409

Explanation: When Madison combined the tens and ones, she should have regrouped 1 ten as 10 ones to subtract 36 from 45. Then she would have 0 tens and 9 ones left. The difference is 409, not 419.

Test – Page 5 – Page No. 15

Question 17.
Radburn School recycles aluminum cans to raise money. The third graders have collected 329 cans so far. Their goal is to collect more than 500 cans. What is the least number of cans they need to collect to reach their goal? Complete the bar model and explain how to use it to find the unknown part.
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 5 img 7$
_____ cans

Answer: 172 cans.

Explanation:
Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test
The given model shows a whole of 500 and a part of 329. The unknown part represents the number of cans still to be collected.By solving using subtraction: 500 − 329 = 171. So, they need to collect 1 more can than 171, which is 172.

Question 18.
The Science Center displays 236 butterflies. The number of beetles on display is 89 less than the number of butterflies.
Part A
About how many beetles are on display at the Science Center? Explain.
about _____ beetles

Answer: About 150 beetles.

Explanation:
Given that 236 butterflies have displayed in the Science Center, rounding to nearest value = 240
No of displayed beetles are 89 less than the number of butterflies, after rounding = 90
Therefore no of beetles displayed = 240 – 90 = 150.

Question 18.
Part B
How many butterflies and beetles are on display at the Science Center? Show your work.
_____ butterflies and beetles

Answer: 383 butterflies and beetles.

Explanation:
Given no of butterflies = 236
No of beetles = 236 – 89 = 147
Total no of beetles and butterflies = 236 + 147 = 383.

Test – Page 6 – Page No. 16

Question 19.
Elena used 74 + 37 = 111 to check her subtraction. Which math problem could she be checking? Mark all that apply.
Options:
a. 74 − 37 = ■
b. 111 − 74 = ■
c. 111 + 37 = ■
d. 111 − 37 = ■

Answer: options b and d.

Explanation: She could use either option b. 111 – 74 = 37 or option d. 111 – 37 = 74.

Question 20.
Shawn and Steve are rock hunters. The tables show the kinds of rocks they collected.
$Go Math Grade 3 Answer Key Chapter 1 Addition and Subtraction within 1,000 Assessment Test Test - Page 6 img 8$
Part A
Who collected more rock samples? How many did he collect? About how many more did he collect? Explain how you solved the problem.
__________

Answer: Shawn collected more rock samples which are 288.

Explanation:
Sum of rock samples collected by Shawn = (127+65+96) = 288
Sum of rock samples collected by Steve = (79 + 109 + 93) = 281
Therefore Shawn collected more rock samples compared to Steve
By subtracting 288 – 281 = 9 (after rounding) => 10
Shawn has about 10 more rock samples.

Question 20.
Part B
Shawn and Steve have the greatest number of what kind of rock? How many rocks of that kind do they have? Show your work.

Answer: Quartz rocks, 236 rocks; 127 + 109 = 236.

Explanation:
Shawn collected 127 quartz rocks where Steve collected 109 quartz rocks.
Total they both collected 236 Quartz rocks which are greatest in number compared to other types.

Conclusion

Improve your math skills by using the Go Math 3rd Grade Chapter 1 Addition and Subtraction within 1,000 Assessment Test. For more help, you can always look up to HMH Go Math Chapter 1 Addition and Subtraction within 1,000 and clear your doubts instantly.

Go Math Grade 7 Answer Key Chapter 12 Experimental Probability

April 7, 2022March 26, 2022 by Go Math Answer Key

$go-math-grade-7-chapter-12-experimental-probability-answer-key$

Go Math Grade 7 Answer Key Chapter 12 Experimental Probability helps the students to score best in the examinations. Download Go Math Answer Key Chapter 12 Experimental Probability for free. We provide a detailed explanation for all the questions which makes students understand the concepts in an easy manner. Students feel that probability is difficult among all the chapters but it is an interesting and easy chapter. Refer Go Math Grade 7 Answer Key Chapter 12 Experimental Probability while doing your homework.

Go Math Grade 7 Answer Key Chapter 12 Experimental Probability

Below we have provided the links according to the list of the chapters. Get the solutions for all Guided Practice and Independent Practice. Just tap the links and get the answers in Go Math Grade 7 Answer Key Chapter 12 Experimental Probability. Improve your math skills with the help of HMH Go Math Grade 7 Solution Key Chapter 12 Experimental Probability.

Chapter 12– Lesson 1:

Guided Practice – Page No. 372
Independent Practice – Page No. 373
Page No. 374

Chapter 12– Lesson 2:

Guided Practice – Page No. 378
Independent Practice – Page No. 379
Page No. 380

Chapter 12– Lesson 3:

Guided Practice – Page No. 384
Independent Practice – Page No. 385
H.O.T. – Page No. 386

Chapter 12– Lesson 4:

Guided Practice – Page No. 390
Independent Practice – Page No. 391
Page No. 392
12.1 Probability – Page No. 393
Selected Response – Page No. 394

Guided Practice – Page No. 372

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0, close to 0, $\frac{1}{2}$ , close to 1, or 1.

Question 2.
randomly picking a green card from a standard deck of playing cards
_____

Answer: Probability is 0.

Explanation: A standard deck of play cards does not have green cards, so the probability is 0.

Question 3.
randomly picking a red card from a standard deck of playing cards
_____

Answer: Probability is 1/2.

Explanation: As half of the cards are from a standard deck of playing cards are red, so the probability is 1/2.

Question 4.
picking a number less than 15 from a jar with papers labeled from 1 to 12
_____

Answer: The probability of picking a number less than 15 is 1.

Explanation: All papers have a number less than 15, so the probability of picking a number less than 15 is 1.

Question 5.
picking a number that is divisible by 5 from a jar with papers labeled from 1 to 12
close to _____

Answer: The probability is 1/6.

Explanation: The numbers divisible by 5 from 1 to 12 are 5 and 10, so there are two positive numbers from a total of 12 positive numbers and the probability of picking a number that is divisible by 5 is 2/12= 1/6.

Find each probability. Write your answer in simplest form.

Question 6.
spinning a spinner that has 5 equal sections marked 1 through 5 and landing on an even number
$\frac{□}{□}$

Answer: The spinner landing on an even number is 2/5.

Explanation: As there are 5 possible outcomes when spinning the spinner and there are two even numbers on the spinner 2 and 4. So the probability of the spinner landing on an even number is 2/5.

Question 7.
picking a diamond from a standard deck of playing cards which has 13 cards in each of four suits: spades, hearts, diamonds and clubs
$\frac{□}{□}$

Answer: The probability is 1/4.

Explanation: As the dek of cards contains 52 cards. so there are 52 possible outcomes in the situation and there are 13 cards with diamonds. So the probability is 13/52= 1/4.

Use the complement to find each probability.

Question 8.
What is the probability of not rolling a 5 on a standard number cube?
$\frac{□}{□}$

Answer: The probability of not rolling a 5 is 5/6.

Explanation: A standard number cube has six sides and marked from 1 to 6, so the probability of rolling a 5 is 1/6. And the probability of not rolling a 5 is
P(rolling a 5) + P(not rolling a 5 ) = 1
1/6 + P(not rolling a 5 )= 1
P(not rolling a 5 ) = 1- 1/6
= (6-1)/6
= 5/6.

Question 9.
A spinner has 3 equal sections that are red, white, and blue. What is the probability of not landing on blue?
$\frac{□}{□}$

Answer: The probability of not landing on blue is 2/3.

Explanation: As spinner has 3 equal sections, so possible outcomes are 3. The probability of landing on blue is 1/3, so the probability of not landing on blue is
P(landing on blue) + P(not landing on blue ) = 1
1/3 + P(not landing on blue )= 1
P(not landing on blue ) = 1- 1/3
= (3-1)/3
= 2/3.

Question 10.
A spinner has 5 equal sections marked 1 through 5. What is the probability of not landing on 4?
$\frac{□}{□}$

Answer:

Explanation: As spinner has 5 equal sections, so possible outcomes are 5. The probability of landing on 4 is 1/5, so the probability of not landing on 4 is
P(landing on 4) + P(not landing on 4 ) = 1
1/5 + P(not landing on blue )= 1
P(not landing on blue ) = 1- 1/5
= (5-1)/5
= 4/5.

Question 11.
There are 4 queens in a standard deck of 52 cards. You pick one card at random. What is the probability of not picking a queen?
$\frac{□}{□}$

Answer: The probability of not picking a queen is 12/13.

Explanation: The deck has 52 cards, so there are 52 possible outcomes. And there are 4 queens in the deck, so the probability of picking a queen is 4/52= 1/13. And the probability of not picking a queen is
P(picking queen) + P(not picking queen ) = 1
1/13 + P(not picking queen )= 1
P(not picking queen ) = 1- 1/13
= (13-1)/13
= 12/13.

Essential Question Check-In

Question 12.
Describe an event that has a probability of 0% and an event that has a probability of 100%.

Answer: An event with a probability of 0% would be picking a number card labeled 15 from a standard deck of cards. And an event with a probability of 100% would be picking a red marble from a bowl filled only with red marbles.

Independent Practice – Page No. 373

Question 13.
There are 4 aces and 4 kings in a standard deck of 52 cards. You pick one card at random. What is the probability of selecting an ace or a king? Explain your reasoning.
$\frac{□}{□}$

Answer: The probability of selecting an ace or king from the deck is 2/13.

Explanation: There are 52 possible outcomes when picking from a deck of cards and there are 8 cards that have an ace or king, so the probability of selecting an ace or king from the deck is 8/52= 2/13.

Question 14.
There are 12 pieces of fruit in a bowl. Seven of the pieces are apples and two are peaches. What is the probability that a randomly selected piece of fruit will not be an apple or a peach? Justify your answer.
$\frac{□}{□}$

Answer: The probability of not picking an apple or a peach is 1/4.

Explanation: There are 12 possible outcomes and 9 out of 12 fruits are apples or peaches, so the probability of picking an apple or a peach is 9/12 = 3/4. And the probability of not picking an apple or a peach is
P(picking an apple or a peach ) + P(not picking an apple or a peach ) = 1
3/4 + P(not picking an apple or a peach)= 1
P(not picking an apple or a peach) = 1- 3/4
= (4-3)/4
= 1/4.

Question 15.
Critique Reasoning
For breakfast, Clarissa can choose from oatmeal, cereal, French toast, or scrambled eggs. She thinks that if she selects a breakfast at random, it is likely that it will be oatmeal. Is she correct? Explain your reasoning.
_____

Answer: Clarissa will unlikely to have oatmeal.

Explanation: As Clarissa has 4 breakfast choices, the probability of choosing oatmeal is 1/4, so it is unlikely that Clarissa will have oatmeal.

Question 16.
Draw Conclusions
A researcher’s garden contains 90 sweet pea plants, which have either white or purple flowers. About 70 of the plants have purple flowers, and about 20 have white flowers. Would you expect that one plant randomly selected from the garden will have purple or white flowers? Explain.
_____

Answer: The one plant randomly selected from the garden will be pruple flowers.

Explanation: The probability of selecting a white flowered plant is 20/90= 2/9 and the probability of selecting purple flowered plant is 70/90= 7/9. So, it is more likely to select a purple plant when randomly choosing from the garden

Question 17.
The power goes out as Sandra is trying to get dressed. If she has 4 white T-shirts and 10 colored T-shirts in her drawer, is it likely that she will pick a colored T-shirt in the dark? What is the probability she will pick a colored T-shirt? Explain your answers.
_____

Answer: The probability of selecting a colored T-shirt is 5/7.

Explanation: The total number of T-shirts in Sandra’s drawer are 14, and the probability of selecting a white T-shirt is 4/14= 2/7. And the probability of selecting a colored T-shirt is 10/14= 5/7. So, it is more likely to choose a colored T-shirt when randomly choosing from the drawer.

Page No. 374

Question 18.
James counts the hair colors of the 22 people in his class, including himself. He finds that there are 4 people with blonde hair, 8 people with brown hair, and 10 people with black hair. What is the probability that a randomly chosen student in the class does not have red hair? Explain.
_____

Answer: The probability that a randomly chosen student in the class does not have red hair is 1.

Explanation: As there is no student with red hair in James class and that means the probability that a randomly chosen student in the class does not have red hair is 1.

Question 19.
Persevere in Problem Solving
A bag contains 8 blue coins and 6 red coins. A coin is removed at random and replaced by three of the other color.
a. What is the probability that the removed coin is blue?
$\frac{□}{□}$

Answer: The probability that the blue coin is removed is 8/14= 4/7.

Explanation: The total number of coins in the bag is 14, so there are 14 possible outcomes. As there are 8 blue coins and 6 red coins, so the probability that the blue coin is removed is 8/14= 4/7.

Question 19.
b. If the coin removed is blue, what is the probability of drawing a red coin after three red coins are put in the bag to replace the blue one?
$\frac{□}{□}$

Answer: The probability of choosing a red coin is 9/16.

Explanation: The total number of coins in the bag is 14 and one blue coin was removed which means 8-1= 7 and three red coins are added, so 6+3= 9 the total number of coins is 7+9= 16. And there are 7 blue coins and 9 red coins, so the probability of choosing a red coin is 9/16.

Question 19.
c. If the coin removed is red, what is the probability of drawing a red coin after three blue coins are put in the bag to replace the red one?
$\frac{□}{□}$

Answer: The probability of choosing a red coin is 5/16.

Explanation: The total number of coins in the bag is 14 and one red coin was removed which means 6-1= 5 and three blue coins are added, so 8+3= 11 the total number of coins is 5+11= 16. And there are 11 blue coins and 5 red coins, so the probability of choosing a red coin is 5/16.

H.O.T.

Focus on Higher Order Thinking

Question 20.
Draw Conclusions
Give an example of an event in which all of the outcomes are not equally likely. Explain.

Answer: A bag of coins with 5 red coins and 11 blue coins are not equally likely.

Explanation: All the outcomes are not equally likely would be having a bag of coins with 5 red coins and 11 blue coins. Since these are not the same number of coins of each color, so the probability of choosing a certain color are not equal.

Question 21.
Critique Reasoning
A box contains 150 black pens and 50 red pens. Jose said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1. Explain whether you agree.

Answer: Jose is correct and the probability of choosing a pen that is not black and the probability of choosing the pen that is not red is 1.

Explanation: Since the pens are either red or black, the probability of choosing a pen that is not black is equal to the probability of choosing a pen that is red and the probability of choosing a pen that is not red is equal to the probability of choosing a pen that is black. So the probability of choosing a pen that is not black and the probability of choosing the pen that is not red is
P(not red)+P(not black)= 150/200 + 50/200
= 200/200
= 1.

Question 22.
Communicate Mathematical Ideas
A spinner has 7 identical sections. Two sections are blue, 1 is red, and 4 of the sections are green. Suppose the probability of an event happening is $\frac{2}{7}$. What does each number in the ratio represent? What outcome matches this probability?

Answer: The probability outcome match is 2/7.

Explanation: As the spinner has 7 identical sections. The numerator of the ratio represents the number of sections with color and the denominator represents the total number of sections on the spinner. And there are 2 blue sections, so the probability of the spinner landing on the blue is 2/7 matches.

Guided Practice – Page No. 378

Question 1.
A spinner has four sections lettered A, B, C, and D. The table shows the results of several spins. Find the experimental probability of spinning each letter as a fraction in simplest form, a decimal, and a percent.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 1$

Answer:
The probability of letter A is 35%.
The probability of letter B is 17.5%.
The probability of letter C is 27.5%.
The probability of letter D is 20%.

Explanation:
The total number of spins is 14+7+11+8= 40.
The probability for the letter A is 14/40= 7/20
= 0.35
= 35%.
The probability for the letter B is 7/40= 0.175
= 17.5%.
The probability for the letter C is 11/40= 0.275
= 27.5%.
The probability for the letter D is 8/40= 1/5
= 0.2
= 20%.

Question 2.
Rachel’s free-throw average for basketball is 60%. She wants to predict how many times in the next 50 tries she will make a free throw. Describe how she could use 10 index cards to predict the answer.

Answer: As Rachel has a 60% success rate, she could write Successful on 6 cards and Unsuccesful on 4 cards. She then needs to draw cards at random 50 times and record the number of times she gets a Succesful card.

Essential Question Check-In

Question 3.
Essential Question Follow Up
How do you find an experimental probability of a simple event?

Answer: To find the experimental probability of a simple event, divide the number of successful outcomes by the total number of outcomes in the experiment.

Explanation: To find the experimental probability of a simple event, divide the number of successful outcomes by the total number of outcomes in the experiment. For example, if a person makes 10 free throws out of 18, attempts, the experimental probability of making the next free throw is 10/18 = 5/9.

Independent Practice – Page No. 379

Question 4.
Dree rolls a strike in 6 out of the 10 frames of bowling. What is the experimental probability that Dree will roll a strike in the first frame of the next game? Explain why a number cube would not be a good way to simulate this situation.
$\frac{□}{□}$

Answer: The experimental probability is 6/10 = 3/5. And the number of possible outcomes should be a multiple of 5.

Experiment:
The experimental probability is 6/10 = 3/5. As the denominator of the probability is either 5 or 10, a number cube would not be able to represent the outcomes because it has 6 faces.

Question 5.
To play a game, you spin a spinner like the one shown. You win if the arrow lands in one of the areas marked “WIN”. Lee played this game many times and recorded her results. She won 8 times and lost 40 times. Use Lee’s data to explain how to find the experimental probability of winning this game.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 2$
$\frac{□}{□}$

Answer: The experimental probability is 8/48= 1/6.

Explanation: As Lee won 8 times and lost 40 times, the number of spins that Lee played is 8+40= 48. So the experimental probability is 8/48= 1/6.

Question 6.
The names of the students in Mr. Hayes’ math class are written on the board. Mr. Hayes writes each name on an index card and shuffles the cards. Each day he randomly draws a card, and the chosen student explains a math problem at the board. What is the probability that Ryan is chosen today? What is the probability that Ryan is not chosen today?
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 3$
Chosen: $\frac{□}{□}$

Answer: The probability of the teacher not choosing Ryan is 19/20.

Explanation: As there are 20 students, so possible outcomes are 20. And Ryan is 1 student, the probability of the teacher choosing Ryan is 1/20. And the probability of the teacher not choosing Ryan is
= 1- 1/20
= (20-1)/20
= 19/20.

Question 7.
Critique Reasoning
A meteorologist reports an 80% chance of precipitation. Is this an example of experimental probability, written as a percent? Explain your reasoning.
______

Answer: Yes, the given example is the experimental probability.

Explanation: Experimental probability uses past data to predict future data. The probability that it will rain is based on historical data. So it is an experimental probability written as a percent.

Page No. 380

Question 8.
Mica and Joan are on the same softball team. Mica got 8 hits out of 48 times at bat, while Joan got 12 hits out of 40 times at bat. Who do you think is more likely to get a hit her next time at bat? Explain.
______

Answer: Joan is more likely to get hit her next time at the bat.

Explanation:
As Mica got 8 hits out of 48 times, so the experimental probability of getting a hit is 8/48= 1/6.
And Joan got 12 hits out of 40 times, the experimental probability of getting a hit is 12/40= 3/10.
Therefore Joan is more likely to get hit her next time at the bat.

Question 9.
Make a Prediction
In tennis, Gabby serves an ace, a ball that can’t be returned, 4 out of the 10 times she serves. What is the experimental probability that Gabby will serve an ace in the first match of the next game? Make a prediction about how many aces Gabby will have for the next 40 serves. Justify your reasoning.
$\frac{□}{□}$

Answer: The experimental probability of her serving an ace is 2/5. In 40 serves, she will serve an ace about 2/5×40 = 16 times.

Explanation: To find the experimental probability we need to divide the number of tries by the number of aces. As Gabby serves 4 aces out of 10 times, the experimental probability of her serving an ace is 4/10= 2/5. Next, to make a prediction about how many aces Gabby will have for the next 40 serves, we need to multiply the number of servers 40 by the experimental probability. In her next 40 serves, she will serve an ace about 2/5×40 = 16 times.

Question 10.
Represent Real-World Problems
Patricia finds that the experimental probability that her dog will want to go outside between 4 P.M. and 5 P.M. is $\frac{7}{12}$. About what percent of the time does her dog not want to go out between 4 P.M. and 5 P.M.?
______ %

Answer: 41.67%

Explanation: As the sum of the probabilities of an event and its complement is always equal to 1 and P(dog want to go outside) is $\frac{7}{12}$.
So P(dog want to go outside)+P(dog does not want to go outside) = 1
$\frac{7}{12}$ + P(dog does not want to go outside) = 1
P(dog does not want to go outside) = 1-$\frac{7}{12}$
= $\frac{12-7}{12}$
= $\frac{5}{12}$
= 0.4167
= 41.67%

H.O.T.

Focus on Higher Order Thinking

Question 11.
Explain the Error
Talia tossed a penny many times. She got 40 heads and 60 tails. She said the experimental probability of getting heads was $\frac{40}{60}$. Explain and correct her error.

Answer: Talia is not correct.

Explanation: As Taila got 40 heads and 60 tails, which means that she did 100 tosses of the coin. So the experimental probability of getting heads was $\frac{40}{100}$

Question 12.
Communicate Mathematical Ideas
A high school has 438 students, with about the same number of males as females. Describe a simulation to predict how many of the first 50 students who leave school at the end of the day are female.

Answer: Since high school has about the same number of male students as female students, the probability of a student leaving school at the end of the day being female is about 50%. And a possible simulation could be using a coin toss, with heads representing males and tails representing females. Toss the coin 50 times and use the results to make a prediction.

Question 13.
Critical Thinking
For a scavenger hunt, Chessa put one coin in each of 10 small boxes. Four coins are quarters, 4 are dimes, and 2 are nickels. How could you simulate choosing one box at random? Would you use the same simulation if you planned to put these coins in your pocket and choose one? Explain your reasoning.

Answer: A possible simulation could be using 10 index cards. Four of the cards could be labeled as quarters, four as dimes, and two nickels. Then cards can be drawn and recorded to simulate choosing a box at random. This simulation could not be used if you planned to put these coins in your pocket and choose one. This is because the size of the coins vary. As we would be able to tell what coin it was in the pocket by feeling its size. And picking one of out your pocket is different than picking a box out of 10 boxes of the same size.

Guided Practice – Page No. 384

Question 1.
A dentist has 400 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table. What is the experimental probability that the next patient will be female and in the age range 22–39?
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 4$
$\frac{□}{□}$

Answer: The experimental probability is $\frac{1}{8}$

Explanation: The total male and female patients are 400.
The age range 22-39 is 50 females
The experimental probability is $\frac{50}{400}$
= $\frac{1}{8}$.

Question 2.
At a car wash, customers can choose the type of wash and whether to use the interior vacuum. Customers are equally likely to choose each type of wash and whether to use the vacuum. Use a simulation to find the experimental probability that the next customer purchases a deluxe wash and no interior vacuum. Describe your simulation.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 5$

Answer: The experimental probability is $\frac{11}{50}$.

Explanation: A possible simulation could be using a standard cube and flipping a coin. If the number cube rolls 1 or 2 it is recorded as a standard wash, if the number cube rolls 3 or 4 it is recorded as a deluxe wash, if the number cube rolls 5 or 6 it is recorded as a superior wash. For the coin toss, heads count as vacuum and tails count as no vacuum.
For example:

So the experimental probability that the next customer purchases a deluxe and no interior vacuum is $\frac{11}{50}$.

Essential Question Check-In

Question 3.
How do you find the experimental probability of a compound event?

Answer: To find the experimental probability of a compound event, determine the number of occurrences that satisfies both events and then divide it by the total number of trails.

Independent Practice – Page No. 385

Question 4.
Represent Real-World Problems
For the same food trailer mentioned in Example 1, explain how to find the experimental probability that the next order is two pieces of chicken with a green salad.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 6$
$\frac{□}{□}$

Answer: The experimental probability is $\frac{1}{10}$.

Explanation: The total number of orders is 330 and in that 33 orders are with 2 pieces green salad, so the experimental probability is
P(2 pieces + green salad) = $\frac{33}{330}$
= $\frac{1}{10}$.

The school store sells spiral notebooks in four colors and three different sizes. The table shows the sales by size and color for 400 notebooks.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 7$

Question 5.
What is the experimental probability that the next customer buys a red notebook with 150 pages?
$\frac{□}{□}$

Answer: The experimental probability is $\frac{3}{20}$.

Experiment: The total number of notebooks sold is 400 and in that, red notebooks with 150 pages sold are 60.
So the experimental probability is $\frac{60}{400}$
= $\frac{3}{20}$.

Question 6.
What is the experimental probability that the next customer buys any red notebooks?
$\frac{□}{□}$

Answer: The experimental probability is $\frac{69}{200}$.

Explanation: The total number of notebooks sold is 400 and in that, red notebooks sold are 138.
So the experimental probability that the next customer buys any red notebooks is $\frac{138}{400}$
= $\frac{69}{200}$.

Question 7.
Analyze Relationships
How many possible combined page count and color choices are possible? How does this number relate to the number of page size choices and to the number of color choices?

Answer: 12 is the product of the number of page size choices and the number of color choices.

Explanation: As there are 12 entries in the table, there are 12 possible page count and color combinations. This number relates to the number of page size choices and to the number of color choices by the fact that there are 3-page count choices and 4 colors.
So 3×4= 12.

A middle school English teacher polled random students about how many pages of a book they read per week.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 8$

Question 8.
Critique Reasoning
Jennie says the experimental probability that a 7th grade student reads at least 100 pages per week is $\frac{16}{125}$. What is her error and the correct experimental probability?
$\frac{□}{□}$

Answer: The correct experimental probability $\frac{17}{50}$.

Explanation:
The total number of students is 24+22+30+18+32+53+22+24+25= 250. And the total number of 7th graders that reads at least 100 pages is 32+53= 85. Jennie’s error not including the 7th-grade students that read 150 pages a week. So the experimental probability is
P(7th grade+ al least 100 pages)= $\frac{85}{250}$
= $\frac{17}{50}$.

Question 9.
Analyze Relationships
Based on the data, which group(s) of students should be encouraged to read more? Explain your reasoning.

Answer: 6th and 8th grade should be encouraged to read more.

Explanation: Based on the data, 6th and 8th grade should be encouraged to read more as 6th and 8th grades read 150 pages per week than 7th grade.

H.O.T. – Page No. 386

Focus on Higher Order Thinking

Question 10.
Make a Conjecture
Would you expect the probability for the simple event “rolling a 6” to be greater than or less than the probability of the compound event “rolling a 6 and getting heads on a coin”? Explain.

Answer: Rolling a 6 to be greater than the probability of the compound event.

Explanation: The simple event would have a greater probability than the probability of the compound event. Because to find a compound event you have to multiply the two probabilities in fraction form. Multiplying two fractions that are less than 1 gives a fraction answer that is smaller than the original two fractions. The probability for the simple event of rolling a 6 is 1/6. The probability of the compound event is 1/6×1/2= 1/12 < 1/6.

Question 11.
Critique Reasoning
Donald says he uses a standard number cube for simulations that involve 2, 3, or 6 equal outcomes. Explain how Donald can do this.

Answer:
If a simulation has two options A and B, Donald can let the even number be A and the odd number be B. If a stimulation has 3 outcomes A, Band C Donald can let 1 and 2 be A, 3 and 4 be B, and 5 and 6 be C. If a stimulation has 6 outcomes A, B, C, D, E, and F Donald can let 1 be A 2 be B, 3 be C 4 be D 5 be E, and 6 be F

Question 12.
Draw Conclusions
Data collected in a mall recorded the shoe styles worn by 150 male and for 150 female customers. What is the probability that the next customer is male and has an open-toe shoe (such as a sandal)? What is the probability that the next male customer has an open-toe shoe? Are the two probabilities the same? Explain.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 9$

Answer: The probability of the next customer is male and has an open-toe shoe is 11/300. And the probability of male customers having open-toe shoes is 11/150.

Explanation:
The total number of customers is 300 and 11 male customers are with open-toe shoes. So the probability of the next customer is male and has an open-toe shoe is 11/300. And the probability of male customers having open-toe shoes is 11/150. The probabilities are not the same, the first one being a compound event and the second one being a simple event.

Question 13.
What If?
Suppose you wanted to perform a simulation to model the shoe style data shown in the table. Could you use two coins? Explain.
______

Answer: No, two coins cannot be used.

Explanation: No, coins cannot be used for this simulation. As there are two options male and female, for the type of customers and two options open and close toe for the type of shoe. It is not given that the customers are equally likely to wear each kind of shoe. So a coin can only be used to simulate male or female.

Question 14.
Represent Real-World Problems
A middle school is made up of grades 6, 7, and 8, and has about the same number of male and female students in each grade. Explain how to use a simulation to find the experimental probability that the first 50 students who arrive at school are male and 7th graders.

Answer: A possible simulation could be done using a coin to simulate a male or female and a standard number of the cube to simulate a grade. Let tails be the male and heads be the female. 1 and 2 be 6th grade, 3 and 4 be 7th grade, and 5 and 6 be the 8th grade. After flipping the coin and rolling the number cube 50 times and recording the results each time and count the number of times you got male and 7th grade out of 50 trails.

Guided Practice – Page No. 390

Question 1.
A baseball player reaches first base 30% of the times he is at bat. Out of 50 times at bat, about how many times will the player reach first base?
______

Answer: So 15 times will the player reach the first base.

Explanation: As the baseball player reaches first base at 30% out of 50 times at bat, so
30% of 50= 0.3×50
= 15.
So 15 times will the player reach the first base.

Question 2.
The experimental probability that it will rain on any given day in Houston, Texas, is about 15%. Out of 365 days, about how many days can residents predict rain?
______

Answer: 55 days can residents predict rain.

Explanation: As the experimental probability that it will rain is 15% out of 365 days, so
15% of 365= 0.15×365
= 54.75
= 55 days.
So 55 days can residents predict rain.

Question 3.
A catalog store has 6% of its orders returned for a refund. The owner predicts that a new candle will have 812 returns out of the 16,824 sold. Do you agree with this prediction? Explain.
______

Answer: The prediction is incorrect.

Explanation: As the catalog store has 6% of its order and 16,824 are sold, so
6% of 16,824 = 0.06×16,824
= 1009 will return.
As the owner predicts that a new candle will have an 812 return which is less than 1009, so the prediction is incorrect.

Question 4.
On a toy assembly line, 3% of the toys are found to be defective. The quality control officer predicts that 872 toys will be found defective out of 24,850 toys made. Do you agree with this prediction? Explain.
______

Answer: The prediction is incorrect.

Explanation: As 3% are found defective out of 24,850 toys, so
3% of 24,850 = 0.03×24850
= 746 will be defective.
As the quality control officer predicts that 872 toys will be found defective which is greater than 746, so the prediction is incorrect.

Question 5.
A light-rail service claims to be on time 98% of the time. Jeanette takes the light-rail 40 times one month, how many times can she predict she will be on time? Is the light-rail’s claim accurate if she is late 6 times?
______

Answer: Jeanette will be on time about 39 times.

Explanation: As light-rail service claims to be on time 98%, and Jeanette takes the light-rail 40 times one month. So
98% of 40= 0.98×40
= 39.
So Jeanette will be on time about 39 times. if she is late 6 times, then the claim is not accurate. Being late 6 times means she was on-time 34 times and $\frac{34}{40}$= 85% which is not close to 98%.

Question 6.
On average, a college claims to accept 18% of its applicants. If the college has 5,000 applicants, predict how many will be accepted. If 885 applicants are accepted, is the college’s claim accurate?
______

Answer: 900 applicants will be accepted.

Explanation: As the college claims to accept 18% of its applicants of 5000 applicants, so 18% of 5000 is
0.18×5000= 900.
About 900 applicants will be accepted. If 885 applicants are accepted, the claim is accurate because 885 is close to 900.

Essential Question Check-In

Question 7.
How do you make predictions using experimental probability?

Answer: To make a prediction using experimental probability multiply the experimental probability by the number of trails to get the prediction number.

Independent Practice – Page No. 391

The table shows the number of students in a middle school at the beginning of the year and the percentage that can be expected to move out of the area by the end of the year.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 10$

Question 8.
How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th grade students move than expected? Justify your answer.
______ students

Answer: 8 students from 7th grade are expected to move by the end of the year.

Explanation: As 4% of 7th grades are expected to move by the end of the year, so 4% of 200 is
0.04×200= 8.
If 12 students actually moved, then more than expected would have moved.

Question 9.
Critique Reasoning
The middle school will lose some of its funding if 50 or more students move away in any year. The principal claims he only loses about 30 students a year. Do the values in the table support his claim? Explain.
______

Answer: Yes, the table supports the principal’s claim of 30 students.

Explanation: 2% of 6th graders and 8% of 8th graders are expected to move. So
2% of 250= 0.02×250
= 5.
8% of 150= 0.08×150
= 12
So in total 5+8+12= 25 students are expected to move. And the table supports the principal’s claim of 30 students.

Question 10.
Represent Real-World Problems
An airline knows that, on average, the probability that a passenger will not show up for a flight is 6%. If an airplane is fully booked and holds 300 passengers, how many seats are expected to be empty? If the airline overbooked the flight by 10 passengers, about how many passengers are expected to show up for the flight? Justify your answer.
______

Answer: The number of passengers expected to show up is then 310-19= 291 passengers.

Explanation: As 6% of the 300 seats are expected to be empty, so
6% of 300 = 0.06×300
= 18.
18 seats are expected to be empty. If the airline overbooked the flight by 10 passengers then 300+10= 310 passengers were booked, then 310×0.06= 18.6
= 19
So the number of passengers expected to show up is then 310-19= 291 passengers.

Question 11.
Draw Conclusions
In a doctor’s office, an average of 94% of the clients pay on the day of the appointment. If the office has 600 clients per month, how many are expected not to pay on the day of the appointment? If 40 clients do not pay on the day of their appointment in a month, did more or fewer than the average not pay?
______

Answer:

Explanation: 94% of the clients pay on the day of the appointment for 600 clients, so
94% of 600= 0.94 × 600
= 564
As 564 clients are expected to pay so 600- 564= 36 clients are expected not to pay on the day of the appointment. So if 40 clients do not pay, then this a little more than the average.

Page No. 392

Question 12.
Counterexamples
The soccer coach claimed that, on average, only 80% of the team come to practice each day. The table shows the number of students that came to practice for 8 days. If the team has 20 members, how many team members should come to practice to uphold the coach’s claim? Was the coach’s claim accurate? Explain your reasoning.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 11$

Answer: As all the values in the table are greater than 16 except for one value, the claim is not accurate.

Explanation: As the soccer coach claimed that only 80% of the team come to practice each day, and the team has 20 members. So
80% of 20= 0.8×20
= 16.
So 16 players in the team should come to practice to uphold the coach’s claim. As all the values in the table are greater than 16 except for one value, the claim is not accurate. More than 80% come on average to practice each day and more than 16 members on average come to practice.

Question 13.
What’s the Error?
Ronnie misses the school bus 1 out of every 30 school days. He sets up the proportion $\frac{1}{30}$ = $\frac{180}{x}$ to predict how many days he will miss the bus in the 180-day school year. What is Ronnie’s error?

Answer: The proportion he sets up is $\frac{1}{30}$ = $\frac{180}{X}$ is Ronnie’s error.

Explanation: As Ronnie misses the school bus 1 out of every 30 school days, and the proportion he sets up is $\frac{1}{30}$ = $\frac{180}{X}$ which is incorrect. As it should be $\frac{1}{30}$ = $\frac{X}{180}$ to respect the form of $\frac{number of days missed}{total number of days}$

H.O.T.

Focus on Higher Order Thinking

Question 14.
Persevere in Problem Solving
A gas pump machine rejects 12% of credit card transactions. If this is twice the normal rejection rate for a normal gas pump, how many out of 500 credit cards transactions would a normal gas pump machine reject?
______

Answer: The normal gas machine rejects 30 transactions.

Explanation: If 12% is twice the normal rate, then the normal rate is 6%, so 6% of 500 is
0.06×500= 30.
So the normal gas machine rejects 30 transactions.

Question 15.
Make Predictions
An airline’s weekly flight data showed a 98% probability of being on time. If this airline has 15,000 flights in a year, how many flights would you predict to arrive on time? Explain whether you can use the data to predict whether a specific flight with this airline will be on time.
______

Answer: 14,700 flights we can predict to arrive on time.

Explanation: The airline’s weekly flight data is a 98% probability of being on time, and there are 15,000 flights in a year. So 98% of 15,000 is 0.98×15000 = 14,700.
So 14,700 flights are expected to be on time and 15,000-14,700= 300 flights will not be on time. And we can use the data to predict whether a specific flight with this airline will be on time by determining the number of flights that have not been on time. If about 300 flights have not been on time then we can predict that the specific flight will be on time. If less than 300 flights have not been on time, then you can’t predict with absolute certainty if the specific flight will be on time.

Question 16.
Draw Conclusions
An average response rate for a marketing letter is 4%, meaning that 4% of the people who receive the letter respond to it. A company writes a new type of marketing letter, sends out 2,400 of them, and gets 65 responses. Explain whether the new type of letter would be considered to be a success.

Answer: As we have received fewer responses than expected and thus a new type of letter would be considered to be not successful.

Explanation: The company sends 2400 letters. And the average response rate for marketing is 4%, so we can expect only a 4% response to the 2400 letters. So
4% of 2400= $\frac{4}{100}$ × 2400
= 4×24
= 96.
Since 96 is greater than 65, we have received fewer responses than expected and thus a new type of letter would be considered to be not successful. We should receive more responses than expected if the letter was successful.

12.1 Probability – Page No. 393

Question 1.
Josue tosses a coin and spins the spinner at the right. What are all the possible outcomes?
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 12$

Answer: The possible outcomes are heads and 1, heads and 2, tails and 1, tails and 2.

Explanation: The spinner can land on 1 or 2 so the outcomes for the spinner 1 and 2. So the coin can land on heads or tails so the outcomes for the coin are heads and tails. The outcomes for tossing a coin and spinning the spinner are heads and 1, heads and 2, tails and 1, tails and 2.

12.2 Experimental Probability of Simple Events

Question 2.
While bowling with friends, Brandy rolls a strike in 6 out of 10 frames. What is the experimental probability that Brandy will roll a strike in the first frame of the next game?
$\frac{□}{□}$

Answer: The experimental probability is $\frac{3}{5}$.

Explanation: As there are 10 frames, so possible outcomes are 10. And Brandy rolls a strike in 6, so the experimental probability that Brandy will roll a strike in the first frame of the next game is $\frac{6}{10}$= $\frac{3}{5}$.

Question 3.
Ben is greeting customers at a music store. Of the first 20 people he sees enter the store, 13 are wearing jackets and 7 are not. What is the experimental probability that the next person to enter the store will be wearing a jacket?
$\frac{□}{□}$

Answer: The experimental probability $\frac{13}{20}$.

Explanation: The total number of people is 20, and Ben sees 13 people were wearing jackets. So the experimental probability that the next person to enter the store will be wearing a jacket is $\frac{13}{20}$.

12.3 Experimental Probability of Compound Events

Question 4.
Auden rolled two number cubes and recorded the results.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 13$
What is the experimental probability that the sum of the next two numbers rolled is greater than 5?
$\frac{□}{□}$

Answer: The experimental probability is latex]\frac{3}{7}[/latex].

Explanation:
The sum of two numbers for every roll is
Roll #1 is 2+1= 3.
Roll #2 is 4+5= 9.
Roll #3 is 3+2= 5.
Roll #4 is 2+2= 4.
Roll #5 is 1+3= 4
Roll #6 is 6+2= 8.
Roll #7 is 5+3= 8.
As there are 7 rolls, so the possible outcomes are 7, so the experimental probability that the sum of the next two numbers rolled is greater than 5 is $\frac{3}{7}$.

12.4 Making Predictions with Experimental Probability

Question 5.
A player on a school baseball team reaches first base $\frac{3}{10}$ of the time he is at bat. Out of 80 times at bat, about how many times would you predict he will reach first base?
______

Answer: We can predict that he will reach first base 24 times out 80 times at the bat.

Explanation:
We need to write a proportion:
latex]\frac{3}{10}[/latex]= latex]\frac{X}{80}[/latex].
10×X= 80×3
10×X= 240
X= 24.
So we can predict that he will reach first base 24 times out 80 times at the bat.

Essential Question

Question 6.
How is experimental probability used to make predictions?

Answer:

Selected Response – Page No. 394

Question 1.
A frozen yogurt shop offers scoops in cake cones, waffle cones, or cups. You can get vanilla, chocolate, strawberry, pistachio, or coffee flavored frozen yogurt. If you order a single scoop, how many outcomes are in the sample space?
Options:
a. 3
b. 5
c. 8
d. 15

Answer: The possible outcomes are 3×5= 15.

Explanation: As there is three option for the scoops are cake cones, waffle cones, or cups. And the five flavors are vanilla, chocolate, strawberry, pistachio, or coffee. So the possible outcomes are 3×5= 15.

Question 2.
A bag contains 7 purple beads, 4 blue beads, and 4 pink beads. What is the probability of not drawing a pink bead?
Options:
a. $\frac{4}{15}$
b. $\frac{7}{15}$
c. $\frac{8}{15}$
d. $\frac{11}{15}$

Answer: The probability of not drawing a pink bead is $\frac{11}{15}$.

Explanation: The total number of beads in the bag are 7+4+4= 15 beads. And the pink beads are 4 beads.
The probability of not drawing a pink bead is
P(pink)+P(not pink)= 1
$\frac{4}{15}$+ P(not pink)= 1
P(not pink)= 1- $\frac{4}{15}$
= $\frac{15-4}{15}$
= $\frac{11}{15}$.

Question 3.
During the month of June, Ava kept track of the number of days she saw birds in her garden. She saw birds on 18 days of the month. What is the experimental probability that she will see birds in her garden on July 1?
Options:
a. $\frac{1}{18}$
b. $\frac{2}{5}$
c. $\frac{1}{2}$
d. $\frac{3}{5}$

Answer: The experimental probability that she will see birds in her garden on July 1 is $\frac{3}{5}$.

Explanation:
As there are 30 days in the month of June, so if Ava saw birds of those days, the experimental probability that she will see birds in her garden on July 1 is $\frac{18}{30}$= $\frac{3}{5}$.

Question 4.
A rectangle has a width of 4 inches and a length of 6 inches. A similar rectangle has a width of 12 inches. What is the length of the similar rectangle?
Options:
a. 8 inches
b. 12 inches
c. 14 inches
d. 18 inches

Answer: The length is 18 inches.

Explanation: The length of the rectangle is 6 inches and the width is 4 inches and similarly width of the other rectangle is 12 inches so the length is
$\frac{Length}{Width}$= $\frac{6}{4}$= $\frac{X}{12}$.
4×X= 12×6
4X= 72
X= 18 inches.

Question 5.
The experimental probability of hearing thunder on any given day in Ohio is 30%. Out of 600 days, on about how many days can Ohioans expect to hear thunder?
Options:
a. 90 days
b. 180 days
c. 210 days
d. 420 days

Answer: The number of days is 180 days.

Explanation: We need to find 30%. Out of 600 days
= 0.3×600
= 180 days.
The number of days is 180 days.

Question 6.
Isidro tossed two coins several times and then recorded the results in the table below.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 14$
What is the experimental probability that both coins will land on the same side on Isidro’s next toss?
Options:
a. $\frac{1}{5}$
b. $\frac{2}{5}$
c. $\frac{3}{5}$
d. $\frac{4}{5}$

Answer: The experimental probability that both coins will land on the same side on Isidro’s next toss is $\frac{2}{5}$.

Explanation: As there are 5 tosses and possible outcomes are 5. As the coin was landed twice on the same side, so the experimental probability is $\frac{2}{5}$.

Mini-Task

Question 7.
Magdalena had a spinner that was evenly divided into sections of red, blue, and green. She spun the spinner and tossed a coin several times. The table below shows the results.
$Go Math Grade 7 Answer Key Chapter 12 Experimental Probability img 15$
a. What are all the possible outcomes?

Answer: The possible outcomes are RH,RT,BH,BT,GH,GT.

Explanation:
The spinner can land on red, blue, and green and the coin can land heads or tails so the possible outcomes are red and heads, red and tails, blue and heads, blue and tails, green and heads and green and tails.

Question 7.
b. What experimental probability did Magdalena find for spinning blue? Give your answer as a fraction in simplest form, as a decimal, and as a percent.

Answer: The experimental probability is 40%.

Explanation: The total trails are 5 and Magdalena spun blue twice,
so the experimental probability is 2/5 = 0.4
= 40%

Question 7.
c. Out of 90 trials, how many times should Magdalena predict she will spin green while tossing tails?
______ times

Answer: We can predict that she will spin green 36 times.

Explanation: The total trails are 5 and Magdalena spun green twice,
so the experimental probability is 2/5.
And out of 90 trails, we can predict that she will spin green
2/5×90
= 18×2
= 36 times.

Conclusion:

We believe the information provided in this article is helpful for you. Refer Go Math Answer Key Grade 7 Chapter 12 Experimental Probability and enhance your math skills. You can also test your skills by solving the questions which are provided at the end of the chapter. All the Best!!!

Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test

April 7, 2022March 26, 2022 by Go Math Answer Key

$go-math-grade-4-chapter-5-factors-multiples-and-patterns-review-test-answer-key$

Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test includes all the topics of chapter 5. In Practice Test, Chapter Test, Cumulative Practice, etc., we have compiled detailed Solutions for all the Questions. So, check out the 4th Grade Go math Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test & cross-check your knowledge & math skills.

Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test

Improve your subject Skills with the help of Go Math Grade 4 Answer Key Homework FL Review/Test and score better grades in your exams. Also, you can take help from the 4th Grade Go Math Ch 5 Review/Test Solution Key for effective preparation and better practice sessions. Moreover, it let students know where they went wrong and clear their doubts. Hence, this guide is so helpful for 4th standard students to score high in exams.

Chapter 5: Review/Test

Review/Test – Page No. 219
Review/Test – Page No. 220
Review/Test – Page No. 221
Review/Test – Page No. 222

Review/Test – Page No. 219

Choose the best term from the box.
$Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 1$

Question 1.
The product of two numbers is a _______________ of both numbers.

Answer:
The product of two numbers is a multiple of both numbers.

Question 2.
A _______________ has exactly two factors.

Answer:
A prime has exactly two factors.

Question 3.
A number is always a multiple of its ____________ .

Answer:
A number is always a multiple of its multiple.

List all the factor pairs in the table.

Question 4.
$Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 2$

Answer:
Factors of 48 are 1,2,3,4,6.

Explanation:
1×48= 48 1,48.
2×24= 48 2,24.
3×16= 48 3,16.
4×12= 48 4,12.
6×8= 48 6,8

Question 5.
$Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 3$

Answer:
Factors of 81 are 1,3,9.

Explanation:
1×81= 81 1,81
3×27= 81 3,27
9×9= 81 9,9

Is the number a multiple of 9? Write yes or no.

Question 6.
3 _____

Answer: No

Explanation:
The number 3 is a factor of 9 but not a multiple of 9.

Question 7.
39 _____

Answer: No

Explanation:
The number 39 is not a multiple of 39.

Question 8.
45 _____

Answer: Yes

Explanation:
9×5= 45, so the number 45 is a multiple of 9.

Question 9.
93 _____

Answer: No.

Explanation:
The number 93 is not a multiple of 9.

Tell whether the number is prime or composite.

Question 10.
65 _________

Answer: Composite number.

Explanation:
As the number 65 factors are 1,5,13,65. So the number 65 is a composite number as it has more than two factors.

Question 11.
37 _________

Answer: Prime number.

Explanation:
The number 37 has only two factors 1 and 37, so the number is a prime number.

Question 12.
77 _________

Answer: Composite number.

Explanation:
The factors of 77 are 1,7,11 and 77, so the number 77 is a composite number.

Use the rule to write the first twelve terms in the pattern.
Describe another pattern in the numbers.

Question 13.
Rule: Add 10, subtract 5.

Answer:
1,6,11,16,21,26,31,36,41,46,51,56.

Explanation:
1
(1+10)-5= 11-5= 6
(6+10)-5= 16-5= 11
(11+10)-5= 21-5= 16
(16+10)-5= 26-5= 21
(21+10)-5= 31-5= 26
(26+10)-5= 36-5= 31
(31+10)-5= 41-5= 36
(36+10)-5= 46-5= 41
(41+10)-5= 51-5= 46
(46+10)-5= 56-5= 51
(51+10)-5= 61-5= 56.

Review/Test – Page No. 220

Question 14.
Erica knits 18 squares on Monday. She knits 7 more squares each day for the rest of the week. How many squares does Erica have on Friday?
Options:
a. 36
b. 46
c. 54
d. 90

Answer: b

Explanation:
As Erica knits 18 squares on Monday and she knits 7 more squares each day for the rest of the week, so on Friday Erica have 18+7+7+7+7= 46.

Question 15.
James works in a flower shop. He will put 36 tulips in vases for a wedding. He must use the same number of tulips in each vase. How many tulips could be in each vase?
Options:
a. 1, 2, 8
b. 2, 4, 8
c. 2, 4, 9
d. 6, 12, 16

Answer: c

Explanation:
As James put 36 tulips in vases for a wedding and he must use the same number of tulips in each vase, so we must find the factors of 36 to find how many tulips could be in each vase. So the factors of 36 are 1,2,3,4,6,9,12,18,36. So
2 tulips in 18 vases each
4 tulips in 9 vases each
9 tulips in 4 vases each.

Question 16.
What multiple of 7 is a factor of 7?
Options:
a. 0
b. 1
c. 7
d. 14

Answer: c

Explanation:
The number 7 is multiple and a factor of 7.

Question 17.
Hot dogs come in packages of 6. Hot dog buns come in packages of 8. Antonio will buy the same number of hot dogs as hot dog buns. How many hot dogs could he buy?
Options:
a. 6
b. 8
c. 18
d. 24

Answer: 24.

Explanation:
As hot dogs come in packages of 6, and hot dog buns come in packages of 8. So to find how many hot dogs could Antonio bought we must find the multiples of 6 and 8. So multiples of 6 and 8 are
Multiples of 6 are 6, 12, 18, 24, 30
Multiples of 8 are 8, 16, 24, 32, 40.
So Antonio bought 24 hot dogs.

Question 18.
Sean has 54 flower bulbs. He planted all the bulbs in rows. Each row has the same number of bulbs. How many bulbs could be in each row?
Options:
a. 6
b. 8
c. 12
d. 26

Answer: a

Explanation:
As Sean has 54 flower bulbs and planted all the bulbs in rows and each row has the same number of bulbs, so we will find the factors of 54. And the factors of 54 are 1,2,3,6,9,18,27, and 54. So Sean will plant 6 bulbs in each row.

Review/Test – Page No. 221

Question 19.
An ice-cream truck visits Julio’s street every 3 days and Lara’s street every 4 days. The truck visits both streets on April 12. When will the truck visit both streets next?
Options:
a. April 15
b. April 16
c. April 19
d. April 24

Answer: d

Explanation:
As an ice-cream truck visits Julio’s street every 3 days and Lara’s street every 4 days, and the truck visits both streets on April 12, so the next visit will be on April 24. By finding the multiples of 3 and 4 we will get the answer.
Multiples of 3 are 3,6,9,12,15,18,21,24
Multiples of 6 are 6,12,18,24.

Question 20.
The factors of a number include 2, 3, 4, 6, 8, 12, 16, 32, and 48. Which could be the number?
Options:
a. 32
b. 64
c. 96
d. 98

Answer: 96

Explanation:
As the number 96 is divisible by all the given numbers.

Question 21.
Ms. Booth has 16 red buttons and 24 blue buttons. She is making finger puppets. Each puppet has the same number of blue buttons and red buttons. How many puppets can she make if she uses all of the buttons?
Options:
a. 1, 2, 4, or 8
b. 1, 2, 4, 8, or 16
c. 1, 2, 4, 8, or 24
d. 1, 2, 4, 8, 16, or 24

Answer: a

Explanation:
As Ms. Booth has 16 red buttons and 24 blue buttons and she is making finger puppets and each puppet has the same number of blue buttons and red buttons, so to find how many puppets can she make if she uses all of the buttons we will find the factors of 16 and 24
so the factors of 16 are 1,2,4,8,16
Factors of 24 are 1,2,3,4,6,8,12,24.
So the common factors in both 16 and 24 are 1,2,4,8,16.

Review/Test – Page No. 222

Question 22.
I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number. What number am I?
Explain.
_____

Answer: 97.

Explanation:
Let’s name the digit:
X be one’s digit and y be tens digit
we know that X=Y-2. Now, Y can be 6,7,8,9 the number is between 60 and 100
As the possibilities with x=y-2, the numbers would be 64,75,86,97.
And 64 and 86 are even, so they can’t be prime. 75 is a composite number as there are more than two factors. So the remaining number is 97.

Question 23.
The number of pieces on display at an art museum is shown in the table.
$Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review Test img 4$
A. The museum’s show for July features 30 oil paintings by different artists. All artists show the same number of paintings and each artist shows more than 1 painting. How many artists could be featured in the show?

Answer:
15 artists with 2 paintings per artist.
10 artists with 3 paintings per artist.
6 artists with 5 paintings per artist.
5 artists with 6 paintings per artist.
3 artists with 10 paintings per artist.
2 artists with 15 paintings per artist.

Explanation:
As the museum’s show for July features 30 oil paintings by different artists and all artists show the same number of paintings and each artist shows more than 1 painting, so the number of artists are
15 artists with 2 paintings per artist.
10 artists with 3 paintings per artist.
6 artists with 5 paintings per artist.
5 artists with 6 paintings per artist.
3 artists with 10 paintings per artist.
2 artists with 15 paintings per artist.

Question 23.
B. The museum wants to display all the art pieces in rows. Each row has the same number of pieces and the same type of pieces. How many pieces could be in each row?

Answer: 3

Explanation:
Given that 30 oil paintings, 24 photographs, and 21 sketches that a museum wants a display. The arrangement of all these art pieces must be in rows such that each row has the same number and same type of art piece displayed. And the greatest common factor of 30,24,21 is 3. So 3 pieces could be in each row.

Question 23.
C. The museum alternates between adding 3 new pieces one month and retiring one piece the following month. If the museum starts with 75 pieces and the pattern continues, write the numbers in the pattern for the next 8 months. Describe other patterns in the numbers.

Answer: 78, 77, 80, 79, 82, 81, 84, 83.

Explanation:
As the museum alternates between adding 3 new pieces one month and retiring one piece the following month and if the museum starts with 75 pieces and the pattern continues, so the numbers are 78, 77, 80, 79, 82, 81, 84, 83. Here the pattern is every other number differs by 2 and the numbers alternate between even and odd.

Conclusion:

Students are recommended to use this Go Math Grade 4 Answer Key Homework FL Chapter 5 Factors, Multiples, and Patterns Review/Test and identify their lag areas and cover them properly. If you have any doubts leave a comment below and we will sort it out very soon. Also, visit our site for more questions to practice from Go Math Grade 4 Answer Key Homework practice FL Chapter 5 and enhance your problem-solving skills.

Go Math Grade 3 Answer Key Chapter 10 Time, Length, Liquid Volume, and Mass Assessment Test

April 7, 2022March 26, 2022 by Go Math Answer Key

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
Test – Page 2 – Page No. 102
Test – Page 3 – Page No. 103
Test – Page 4 – Page No. 104
Test – Page 5 – Page No. 105
Test – Page 6 – Page No. 106

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 8 Answer Key Chapter 12 The Pythagorean Theorem

Guided Practice – The Pythagorean Theorem – Page No. 378

12.1 Independent Practice – The Pythagorean Theorem – Page No. 379

FOCUS ON HIGHER ORDER THINKING – The Pythagorean Theorem – Page No. 380

Guided Practice – Converse of the Pythagorean Theorem – Page No. 384

12.2 Independent Practice – Converse of the Pythagorean Theorem – Page No. 385

Converse of the Pythagorean Theorem – Page No. 386

Guided Practice – Distance Between Two Points – Page No. 390

12.3 Independent Practice – Distance Between Two Points – Page No. 391

Distance Between Two Points – Page No. 392

Ready to Go On? – Model Quiz – Page No. 393

Selected Response – Mixed Review – Page No. 394

Final Words

Download Go Math Grade 7 Answer Key Chapter 9 Circumference, Area, and Volume Pdf

Guided Practice – Page No. 268

Independent Practice – Page No. 269

Page No. 270

Guided Practice – Page No. 274

Independent Practice – Page No. 275

Page No. 276

Guided Practice – Page No. 280

Independent Practice – Page No. 281

H.O.T. – Page No. 282

Guided Practice – Page No. 286

Independent Practice – Page No. 287

Page No. 288

Guided Practice – Solving Volume Problems – Page No. 292

Independent Practice – Page No. 293

Page No. 294

9.1, 9.2 Circumference and Area of Circles – Page No. 295

Page No. 296

EXERCISES – Page No. 298

Page No. 300

Page No. 301

Unit 4 Performance Tasks (cont’d) – Page No. 302

Selected Response – Page No. 303

Page No. 304

Go Math Grade 4 Answer Key Homework FL Chapter 3 Multiply 2-Digit Numbers Review/Test

Review/Test – Page No. 131

Review/Test – Page No. 132

Review/Test – Page No. 133

Review/Test – Page No. 134

Conclusion:

Go Math Grade 4 Answer Key Homework FL Chapter 7 Add and Subtract Fractions Review/Test

Review/Test – Page No. 309

Review/Test – Page No. 310

Review/Test – Page No. 311

Review/Test – Page No. 312

Conclusion:

Test – Page 1 – Page No. 31

Test – Page 2 – Page No. 32

Test – Page 3 – Page No. 33

Test – Page 4 – Page No. 34

Test – Page 5 – Page No. 35

Test – Page 6 – Page No. 36

Summary

Test – Page 1 – Page No. 91

Test – Page 2 – Page No. 92

Test – Page 3 – Page No. 93

Test – Page 4 – Page No. 94

Test – Page 5 – Page No. 95

Test – Page 6 – Page No. 96

Test – Page 1 – Page No. 61

Test – Page 2 – Page No. 62

Test – Page 3 – Page No. 63

Test – Page 4 – Page No. 64

Test – Page 5 – Page No. 65

Test – Page 6 – Page No. 66

Conclusion

Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns

Lesson 1: Model Factors

Lesson 2: Factors and Divisibility

Lesson 3: Problem Solving • Common Factors

Lesson 4: Factors and Multiples

Lesson 5: Prime and Composite Numbers

Lesson 6: Algebra • Number Patterns

Chapter 5 Review/Test

Common Core – Model Factors – Page No. 283

Common Core – Factors – Page No. 284

Page No. 287