Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 3 Sprint Answer Key

A
Add Equal Groups

Question 1.
2 + 2 =
2 + 2 = 4,

Explanation:
Given 2 + 2 we add 2 with 2,
we get 4 as 2 + 2 = 4.

Question 2.
2 twos =
2 twos = 4,

Explanation:
Given 2 twos means 2 by 2 times as
2 X 2 we get 4 so 2 twos = 4.

Question 3.
5 + 5 =
5 + 5 = 10,

Explanation:
Given 5 + 5 we add 5 with 5,
we get 10 as 5 + 5 = 10.

Question 4.
2 fives =
2 fives = 10,

Explanation:
Given 2 fives means 2 by 5 as
2 X 5 we get 10 so 2 fives = 10.

Question 5.
2 + 2 + 2 =
2 + 2 + 2 = 6,

Explanation:
Given 2 + 2 + 2 we add 2 thrice
we get 6 as 2 + 2 + 2 = 6.

Question 6.
3 twos =
3 twos = 6,

Explanation:
Given 3 twos means 3 by 2 as
3 X 2 we get 6 so 3 twos = 6.

Question 7.
2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 = 8,

Explanation:
Given 2 + 2 + 2 + 2 we add 2 four times
we get 8 as 2 + 2 + 2 + 2 = 8.

Question 8.
4 twos =
4 twos = 8,

Explanation:
Given 4 twos means 4 by 2 as
4 X 2 we get 8 so 4 twos = 8.

Question 9.
5 + 5 + 5 =
5 + 5 + 5 = 15,

Explanation:
Given 5 + 5 + 5 we add 5 thrice
we get 15 as 5 + 5 + 5 = 15.

Question 10.
3 fives =
3 fives = 15,

Explanation:
Given 3 fives means 3 by 5 as
3 X 5 we get 15 so 3 fives = 15.

Question 11.
5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 = 20,

Explanation:
Given 5 + 5 + 5 + 5 we add 5 four times
we get 20 as 5 + 5 + 5 + 5 = 20.

Question 12.
4 fives =
4 fives = 20,

Explanation:
Given 4 fives means 4 by 5 as
4 X 5 we get 20 so 4 fives = 20.

Question 13.
2 fours=
2 fours = 8,

Explanation:
Given 2 fours means 2 by 4 as
2 X 4 we get 8 so 2 fours = 8.

Question 14.
4 + 4 =
4 + 4 = 8,

Explanation:
Given 4 + 4 we add 4 with 4,
we get 8 as 4 + 4 = 8.

Question 15.
2 threes =
2 threes = 6,

Explanation:
Given 2 threes means 2 by 3 as
2 X 3 we get 6 so 2 threes = 6.

Question 16.
3 + 3 =
3 + 3 = 6,

Explanation:
Given 3 + 3 we add 3 with 3,
we get 6 as 3 + 3 = 6.

Question 17.
2 sixes =
2 sixes = 12,

Explanation:
Given 2 sixes means 2 by 6 as
2 X 6 we get 12 so 2 sixes = 12.

Question 18.
6 + 6 =
6 + 6 = 12,

Explanation:
Given 6 + 6 we add 6 with 6,
we get 12 as 6 + 6 = 12.

Question 19.
5 twos =
5 twos = 10,

Explanation:
Given 5 twos means 5 by 2 as
5 X 2 we get 10 so 5 twos = 10.

Question 20.
2 + 2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 + 2 = 10,

Explanation:
Given 2 + 2 + 2 + 2 + 2  we add 2 five times
we get 10 as 2 + 2 + 2 + 2 + 2 = 10.

Question 21.
5 fives =
5 fives = 25,

Explanation:
Given 5 fives means 5 by 5 as
5 X 5 we get 25 so 5 fives = 25.

Question 22.
5 + 5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 + 5 = 25,

Explanation:
Given 5 + 5 + 5 + 5 + 5  we add 5 five times
we get 25 as 5 + 5 + 5 + 5 + 5 = 25.

Question 23.
7 + 7 =
7 + 7 = 14,

Explanation:
Given 7 + 7 we add 7 with 7,
we get 14 as 7 + 7 = 14.

Question 24.
2 sevens =
2 sevens = 14,

Explanation:
Given 2 sevens means 2 by 7 as
2 X 7 we get 14 so 2 sevens = 14.

Question 25.
9 + 9 =
9 + 9 = 18,

Explanation:
Given 9 + 9 we add 9 with 9,
we get 18 as 9 + 9 = 18.

Question 26.
2 nines =
2 nines = 18,

Explanation:
Given 2 nines means 2 by 9 as
2 X 9 we get 18 so 2 nines = 18.

Question 27.
8 + 8 =
8 + 8 = 16,

Explanation:
Given 8 + 8 we add 8 with 8,
we get 16 as 8 + 8 = 16.

Question 28.
2 eights =
2 eights = 16,

Explanation:
Given 2 eights means 2 by 8 as
2 X 8 we get 16 so 2 eights = 16.

Question 29.
3 + 3 + 3 =
3 + 3 + 3 = 9,

Explanation:
Given 3 + 3 + 3 we add 3 thrice
we get 9 as 3 + 3 + 3 = 9.

Question 30.
3 threes =
3 threes = 9,

Explanation:
Given 3 threes means 3 by 3 as
3 X 3 we get 9 so 3 threes = 9.

Question 31.
4 + 4 + 4 =
4 + 4 + 4 = 12,

Explanation:
Given 4 + 4 + 4 we add 4 thrice
we get 12 as 4 + 4 + 4 = 12.

Question 32.
3 fours =
3 fours = 12,

Explanation:
Given 3 fours means 3 by 4 as
3 X 4 we get 12 so 3 fours = 12.

Question 33.
3 + 3 + 3 + 3 =
3 + 3 + 3 + 3 = 12,

Explanation:
Given 3 + 3 + 3 + 3 we add 3 four times
we get 12 as 3 + 3 + 3 + 3= 12.

Question 34.
4 threes =
4 threes = 12,

Explanation:
Given 4 threes means 4 by 3 as
4 X 3 we get 12 so 4 threes = 12.

Question 35.
4 fives =
4 fives = 20,

Explanation:
Given 4 fives means 4 by 5 as
4 X 5 we get 20 so 4 fives = 20.

Question 36.
5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 = 20,

Explanation:
Given 5 + 5 + 5 + 5 we add 5 four times
we get 20 as 5 + 5 + 5 + 5 = 20.

Question 37.
3 sixes =
3 sixes = 18,

Explanation:
Given 3 sixes means 3 by 6 as
3 X 6 we get 18 so 3 sixes = 18.

Question 38.
6 + 6 + 6 =
6 + 6 + 6 = 18,

Explanation:
Given 6 + 6 + 6 we add 6 thrice
we get 18 as 6 + 6 + 6 = 18.

Question 39.
3 eights =
3 eights = 24,

Explanation:
Given 3 eights means 3 by 8 as
3 X 8 we get 24 so 3 eights = 24.

Question 40.
8 + 8 + 8 =
8 + 8 + 8 = 24,

Explanation:
Given 8 + 8 + 8 we add 8 thrice
we get 24 as 8 + 8 + 8 = 24.

Question 41.
3 sevens =
3 sevens = 21,

Explanation:
Given 3 sevens means 3 by 7 as
3 X 7 we get 21 so 3 sevens = 21.

Question 42.
7 + 7 + 7 =
7 + 7 + 7 = 21,

Explanation:
Given 7 + 7 + 7 we add 7 thrice
we get 21 as 7 + 7 + 7 = 21.

Question 43.
3 nines =
3 nines = 27,

Explanation:
Given 3 nines means 3 by 9 as
3 X 9 we get 27 so 3 nines = 27.

Question 44.
9 + 9 + 9 =
9 + 9 + 9 = 27,

Explanation:
Given 9 + 9 + 9 we add 9 thrice
we get 27 as 9 + 9 + 9 = 27.

B
Add Equal Groups

Question 1.
5 + 5 =
5 + 5 = 10,

Explanation:
Given 5 + 5 we add 5 with 5,
we get 10 as 5 + 5 = 10.

Question 2.
2 fives =
2 fives = 10,

Explanation:
Given 2 fives means 2 by 5 as
2 X 5 we get 10 so 2 fives = 10.

Question 3.
2 + 2 =
2 + 2 = 4,

Explanation:
Given 2 + 2 we add 2 with 2,
we get 4 as 2 + 2 = 4.

Question 4.
2 twos =
2 twos = 4,

Explanation:
Given 2 twos means 2 by 2 times as
2 X 2 we get 4 so 2 twos = 4.

Question 5.
5 + 5 + 5 =
5 + 5 + 5 = 15,

Explanation:
Given 5 + 5 + 5 we add 5 thrice
we get 15 as 5 + 5 + 5 = 15.

Question 6.
3 fives =
3 fives = 15,

Explanation:
Given 3 fives means 3 by 5 as
3 X 5 we get 15 so 3 fives = 15.

Question 7.
5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 = 20,

Explanation:
Given 5 + 5 + 5 + 5 we add 5 four times
we get 20 as 5 + 5 + 5 + 5 = 20.

Question 8.
4 fives =
4 fives = 20,

Explanation:
Given 4 fives means 4 by 5 as
4 X 5 we get 20 so 4 fives = 20.

Question 9.
2 + 2 + 2 =
2 + 2 + 2 = 6,

Explanation:
Given 2 + 2 + 2 we add 2 thrice
we get 6 as 2 + 2 + 2 = 6.

Question 10.
3 twos =
3 twos = 6,

Explanation:
Given 3 twos means 3 by 2 as
3 X 2 we get 6 so 3 twos = 6.

Question 11.
2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 = 8,

Explanation:
Given 2 + 2 + 2 + 2 we add 2 four times
we get 8 as 2 + 2 + 2 + 2 = 8.

Question 12.
4 twos =
4 twos = 8,

Explanation:
Given 4 twos means 4 by 2 as
4 X 2 we get 8 so 4 twos = 8.

Question 13.
2 threes =
2 threes = 6,

Explanation:
Given 2 threes means 2 by 3 as
2 X 3 we get 6 so 2 threes = 6.

Question 14.
3 + 3 =
3 + 3 = 6,

Explanation:
Given 3 + 3 we add 3 with 3,
we get 6 as 3 + 3 = 6.

Question 15.
2 sixes =
2 sixes = 12,

Explanation:
Given 2 sixes means 2 by 6 as
2 X 6 we get 12 so 2 sixes = 12.

Question 16.
6 + 6 =
6 + 6 = 12,

Explanation:
Given 6 + 6 we add 6 with 6,
we get 12 as 6 + 6 = 12.

Question 17.
2 fours =
2 fours = 8,

Explanation:
Given 2 fours means 2 by 4 as
2 X 4 we get 8 so 2 fours = 8.

Question 18.
4 + 4 =
4 + 4 = 8,

Explanation:
Given 4 + 4 we add 4 with 4,
we get 8 as 4 + 4 = 8.

Question 19.
5 fives =
5 fives = 25,

Explanation:
Given 5 fives means 5 by 5 as
5 X 5 we get 25 so 5 fives = 25.

Question 20.
5 + 5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 + 5 = 25,

Explanation:
Given 5 + 5 + 5 + 5 + 5 we add 5 five times
we get 25 as 5 + 5 + 5 + 5 + 5 = 25.

Question 21.
5 twos =
5 twos = 10,

Explanation:
Given 5 twos means 5 by 2 as
5 X 2 we get 10 so 5 twos = 10.

Question 22.
2 + 2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 + 2 = 10,

Explanation:
Given 2 + 2 + 2 + 2 + 2 we add 2 five times
we get 10 as 2 + 2 + 2 + 2 + 2 = 10.

Question 23.
8 + 8 =
8 + 8 = 16,

Explanation:
Given 8 + 8 we add 8 with 8,
we get 16 as 8 + 8 = 16.

Question 24.
2 eights =
2 eights = 16,

Explanation:
Given 2 eights means 2 by 8 as
2 X 8 we get 16 so 2 eights = 16.

Question 25.
7 + 7 =
7 + 7 = 14,

Explanation:
Given 7 + 7 we add 7 with 7,
we get 14 as 7 + 7 = 14.

Question 26.
2 sevens =
2 sevens = 14,

Explanation:
Given 2 sevens means 2 by 7 as
2 X 7 we get 14 so 2 sevens = 14.

Question 27.
9 + 9 =
9 + 9 = 18,

Explanation:
Given 9 + 9 we add 9 with 9,
we get 18 as 9 + 9 = 18.

Question 28.
2 nines =
2 nines = 18,

Explanation:
Given 2 nines means 2 by 9 as
2 X 9 we get 18 so 2 nines = 18.

Question 29.
3 + 3 + 3 + 3 =
3 + 3 + 3 + 3 = 12,

Explanation:
Given 3 + 3 + 3 + 3 we add 3 four times
we get 12 as 3 + 3 + 3 + 3= 12.

Question 30.
4 threes =
4 threes = 12,

Explanation:
Given 4 threes means 4 by 3 as
4 X 3 we get 12 so 4 threes = 12.

Question 31.
4 + 4 + 4 =
4 + 4 + 4 = 12,

Explanation:
Given 4 + 4 + 4 we add 4 thrice
we get 12 as 4 + 4 + 4 = 12.

Question 32.
3 fours =
3 fours = 12,

Explanation:
Given 3 fours means 3 by 4 as
3 X 4 we get 12 so 3 fours = 12.

Question 33.
3 + 3 + 3 =
3 + 3 + 3 = 9,

Explanation:
Given 3 + 3 + 3 we add 3 thrice
we get 9 as 3 + 3 + 3 = 9.

Question 34.
3 threes =
3 threes = 9,

Explanation:
Given 3 threes means 3 by 3 as
3 X 3 we get 9 so 3 threes = 9.

Question 35.
4 fives =
4 fives = 20,

Explanation:
Given 4 fives means 4 by 5 as
4 X 5 we get 20 so 4 fives = 20.

Question 36.
5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 = 20,

Explanation:
Given 5 + 5 + 5 + 5 we add 5 four times
we get 20 as 5 + 5 + 5 + 5 = 20.

Question 37.
3 sevens =
3 sevens = 21,

Explanation:
Given 3 sevens means 3 by 7 as
3 X 7 we get 21 so 3 sevens = 21.

Question 38.
7 + 7 + 7 =
7 + 7 + 7 = 21,

Explanation:
Given 7 + 7 + 7 we add 7 thrice
we get 21 as 7 + 7 + 7 = 21.

Question 39.
3 nines =
3 nines = 27,

Explanation:
Given 3 nines means 3 by 9 as
3 X 9 we get 27 so 3 nines = 27.

Question 40.
9 + 9 + 9 =
9 + 9 + 9 = 27,

Explanation:
Given 9 + 9 + 9 we add 9 thrice
we get 27 as 9 + 9 + 9 = 27.

Question 41.
3 sixes =
3 sixes = 18,

Explanation:
Given 3 sixes means 3 by 6 as
3 X 6 we get 18 so 3 sixes = 18.

Question 42.
6 + 6 + 6 =
6 + 6 + 6 = 18,

Explanation:
Given 6 + 6 + 6 we add 6 thrice
we get 18 as 6 + 6 + 6 = 18.

Question 43.
3 eights =
3 eights = 24,

Explanation:
Given 3 eights means 3 by 8 as
3 X 8 we get 24 so 3 eights = 24.

Question 44.
8 + 8 + 8 =
8 + 8 + 8 = 24,

Explanation:
Given 8 + 8 + 8 we add 8 thrice
we get 24 as 8 + 8 + 8 = 24.

Eureka Math Grade 3 Module 1 Lesson 3 Problem Set Answer Key

Solve Problems 1–4 using the pictures provided for each problem.

Question 1.
There are 5 flowers in each bunch.
How many flowers are in 4 bunches?

a. Number of groups: _____4______
Size of each group: _____5________
b. 4 × 5 = ___20_______
c. There are ___20______ flowers altogether.

a. Number of groups are 4,
b. 4 X 5 = 20,
c. There are 20 flowers altogether.

Explanation:
Given there are 5 flowers in each bunch.
a. Number of groups are 4 and
size of each group:  5 as shown in the picture,

b. Multiplication sentence is 4 X 5 = 20,

c. As there are 4 groups of 5 flowers each we have
4 X 5 = 20 flowers altogether.

Question 2.
There are ___3____ candies in each box.
How many candies are in 6 boxes?

a. Number of groups: _____6______
Size of each group: ______3_______
b. 6 × ____3______ = ____18_______
c. There are ___18______ candies altogether.

a. Number of groups: 6 and
size of each group: 3
b. 6 X 3 = 18
c. There are 18 candies altogether.

Explanation:
Given there are 3 candies in each box,
a. Number of groups are 6 and
size of each group is 3 as shown in the picture,

b. Multiplication sentence is 6 X 3 = 18,

c. As there are 6 groups of 3 candies each we have
6 X 3 = 18 candies altogether.

Question 3.
There are 4 oranges in each row. How many
oranges are there in ___3___ rows?
a. Number of rows: ______3_____ Size of each row: ____4______

b. _____3______ × 4 = _____12______
c. There are ____12_____ oranges altogether.

a. Number of rows: 3 and size of each row: 4,
b. 3 X 4 = 12,
c. There are 12 oranges altogether.

Explanation:
Given there are 4 oranges in each row,
a. Number of rows are 3 and
size of each row is 4 as shown in the picture,

b. Multiplication sentence is 3 X 4 = 12,

c. As there are 3 rows of 4 oranges each we have
3 X 4 = 12 oranges altogether.

Question 4.
There are ____2____ loaves of bread in each row.
How many loaves of bread are there in 5 rows?
a. Number of rows: _____5______ Size of each row: _____2_____
b. ____5______ × _____2_____ = ____10_______

c. There are ___10__ loaves of bread altogether.

a. Number of rows: 5 and size of each row: 2,
b. 5 X 2 = 10,
c. There are 10 loaves of bread altogether.

Explanation:
Given there are 2 loaves of bread in each row
a. Number of rows are 5 and
size of each row is 2 as shown in the picture,

b. Multiplication sentence is 5 X 2 = 10,

c. As there are 5 rows of 2 loaves of bread each
we have 5 X 2 = 10 loaves of bread altogether.

Question 5.
a. Write a multiplication equation for the array shown below.

b. Draw a number bond for the array where each
part represents the amount in one row.

a. Multiplication equation : 4 X 3 = 12,

Explanation:
As shown in the picture there are 4 rows of 3 X
in each row, So the multiplication equation is 4 X 3 = 12.

b.

Explanation:
Drawn a number bond for the array where each
part represents the amount in one row.

Question 6.
Draw an array using factors 2 and 3.
Then, show a number bond where each part
represents the amount in one row.

Explanation:
Drawn an array using factors 2 and 3 as
2 X 3 = 6, 2 rows of 3 each and showed
a number bond where each part represents
the amount in one row as shown in the picture above.

Eureka Math Grade 3 Module 1 Lesson 3 Exit Ticket Answer Key

Draw an array that shows 5 rows of 3 squares.
Then, show a number bond where each part
represents the amount in one row.

Explanation:
Drawn an array that shows 5 rows of 3 squares as
5 X 3 = 15 and showed a number bond where
each part represents the amount in one row as
shown in the picture above.

Solve Problems 1–4 using the pictures provided for each problem.

Question 1.
There are 5 pineapples in each group.
How many pineapples are there in 5 groups?

a. Number of groups: _______5______ Size of each group: ____5________
b. 5 × 5 = _____25_______
c. There are ____25______ pineapples altogether.

a. Number of groups : 5 and size of each group: 5,
b. 5 X 5 = 25,
c. There are 25 pineapples altogether.

Explanation:
Given there are 5 pineapples in each group
a. Number of groups are 5 and
size of each group is 5 as shown in the picture,

b. Multiplication sentence is 5 X 5 = 25,

c. As there are 5 rows of 5 pineapples each
we have 5 X 5 = 25 pineapples altogether.

Question 2.
There are ____4___ apples in each basket.
How many apples are there in 6 baskets?

a. Number of groups: _______6______ Size of each group: _____4_______
b. 6 × ____4______ = _____24_______
c. There are ____24______ apples altogether.

a. Number of groups : 6 and size of each group: 4,
b. 6 X 4 = 24,
c. There are 24 apples altogether.

Explanation:
Given there are 6 baskets with 4 apples
in each basket  as shown in the picture
a. Number of groups are 6 and
size of each group is 4,

b. Multiplication sentence is 6 X 4 = 24,

c. As there are 4 apples each in 6 baskets
we have 6 X 4 = 24 apples altogether.

Question 3.
There are 4 bananas in each row. How many
bananas are there in _4_ rows?
a. Number of rows: _____4______ Size of each row: ____4______
b. _____4____ × 4 = ___16_______
c. There are _____16_____ bananas altogether.

a. Number of rows : 4 and size of each row: 4,
b. 4 X 4 = 16,
c. There are 16 bananas altogether.

Explanation:
Given there are 4 rows of 4 bananas
in each row as shown in the picture
a. Number of rows are 4 and
size of each row is 4,

b. Multiplication sentence is 4 X 4 = 16,

c. As there are 4 bananas in 4 rows each
we have 4 X 4 = 16 bananas altogether.

Question 4.
There are _____3______ peppers in each row.
How many peppers are there in 6 rows?
a. Number of rows: ______6_____ Size of each row: ____3______
b. ____6_____ × ____3______ = ____18______
c. There are ____18______ peppers altogether.

a. Number of rows : 6 and size of each row: 3,
b. 6 X 3 = 18,
c. There are 18 peppers altogether.

Explanation:
Given there are 6 rows of 3 peppers
in each row as shown in the picture
a. Number of rows are 6 and
size of each row is 3,

b. Multiplication sentence is 6 X 3 = 18,

c. As there are 3 peppers in 6 rows each
we have 6 X 3 = 18 peppers altogether.

Question 5.
Draw an array using factors 4 and 2.
Then, show a number bond where each part
represents the amount in one row.

Explanation:
Drawn an array that shows factors 4 and 2 as
4 X 2 = 8, 4 rows of 2 each and showed a
number bond where each part represents the
amount in one row as shown in the picture above.

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Big Ideas 5th Grade Chapter 1 Place Value Concepts Math Book Answer Key

Students can learn the quick way to solve problems using Big Ideas Grade 5 Chapter 1 Math Answers. Download Grade 5 Big Ideas Math Answers Chapter 1 Place Value Concepts for free. We provided solutions in an easy manner so that students can solve the problems in less time. Click on the links provided below and find every topic individually. Get the free pdf offline and practice whenever you want it.

Lesson 1: Place Value Patterns

• Lesson 1.1 Place Value Patterns
• Place Value Patterns Homework & Practice 1.1

Lesson 2 Place Value with Whole Numbers

• Lesson 1.2 Place Value with Whole Numbers
• Place Value with Whole Numbers Homework & Practice 1.2

Lesson 3 Patterns and Powers of 10

• Lesson 1.3 Patterns and Powers of 10
• Patterns and Powers of 10 Homework & Practice 1.3

Lesson 4 Decimals to Thousandths

• Lesson 1.4 Decimals to Thousandths
• Decimals to Thousandths Homework & Practice 1.4

Lesson 5 Place Value with Decimals

• Lesson 1.5 Place Value with Decimals
• Place Value with Decimals Homework & Practice 1.5

Lesson 6 Compare Decimals

• Lesson 1.6 Compare Decimals
• Compare Decimals Homework & Practice 1.6

Lesson 7 Round Decimals

• Lesson 1.7 Round Decimals
• Round Decimals Homework & Practice 1.7

Performance Task

• Place Value Concepts Performance Task
• Place Value Concepts Activity
• Place Value Concepts Chapter Practice

Lesson 1.1 Place Value Patterns

Explore and Grow

Write the whole number represented by each base ten block. Then use the base ten blocks to complete the table.

Answer:

Rod is 10 times as much as Unit

The flat is 10 times as much as Rod

Cube is 3 times as much as Flat

Unit is 1/10 of Rod

Rod is 1/10 of Flat

The flat is 3/10 of Cube

Reasoning
Describe the patterns you see in a number as you move from one place value position to another place value position.

Answer: As we move from one place value position to another value position, The place value of a digit increase by ten times as move from the left.

Think and Grow: Place Value Patterns

You can use a place value chart to help write numbers that are 10 times as great as a number or \(\frac{1}{10}\) of a number.

Show and Grow

Question 1.
Complete the statements.

Apply and Grow: Practice

Use a place value chart to answer the question.
Question 2.
What number is 10 times as great as 6,000?
Answer:60,000

If 6,000 is multiplied by 10 times it becomes 60,000

Question 3.
What number is \(\frac{1}{10}\) of 300?
Answer:30

300 x 1/ 10 is 30

Question 4.
80 is 10 times as great as what number?
Answer: 8

if 8 is multiplied by 10 times it becomes 80

Question 5.
40,000 is \(\frac{1}{10}\) of what number?
Answer:4,00,000

4,00,000 x 1/10 is 40,000

The number is 4,00,000

Complete the table.
Question 6.

Answer:

1. 100 ,1 ,

10,  10 times as number is 10 x 10 = 100

1/10 of 10 is 1

2. 4000,40

400, 10 times as number is 400 x 10 = 4000

1/10 of 400 is 40

3. 70,000,700

7,000, 10 times as number is 7,000 x 10 =70,000

1/10 of 7,000 is 700

4. 500,000,    5,000

50,000,10 times as number is 50,000 x 10 = 5,00,000

1/10 of 50,000 is 5,000

Question 7.

Answer:

1. 2,000, 20

200,  10 times as number is 200 x 10 = 2,000

1/10 of 200 is 20

2. 3,00,000,   3,000

30,000,  10 times as number is 30,000 x 10 = 3,00,000

1/10 of  30,000 is 3,000

3. 900, 9

90, 10 times as number is 90 x 10 = 900

1/10 of 90 is 9

4. 80,000, 800

8,000,  10 times as number is 8,0,0 x 10 = 80,000

1/10 of 8,000 is 800

Question 8.
Patterns
Describe the relationship between any place value position and the next greater place value position.
Answer:

The relation between any place value position and next greater place value position increases ten times as we move.

Number Sense
Write whether the statement is true or false. If false, explain why.
Question 9.
600 is 100 times as great as 60,000.
______
Answer: True

600 X 100 = 60,000

Question 10.
9,000 is 1,000 times as great as 9.

_____
Answer: True

9 X 1,000 = 9,000

Think and Grow: Modeling Real Life

Example
Which state is about 10 times larger than Georgia?
The approximate land area of Georgia is 60,000 square miles.
Use a place value chart to find the number that is 10 times as great as 60,000.


6,000_____ is 10 times as great as 60,000.
The land area of _____Alaska__ is about 600,000 square miles.
So, __Alaska____ is about 10 times larger than Georgia.

Show and Grow

Use the table above.
Question 11.
Which state is about 10 times larger than Hawaii?
Answer: Georgia is 10 times larger than Hawaii

Question 12.
Which state is about \(\frac{1}{10}\) the size of Wyoming?
Answer: Maryland is 1/10 the size of Wyoming

Question 13.
DIG DEEPER!
Which state is about 100 times larger than the District of Columbia?
Answer: Hawaii

District of Columbia = 60

100 times larger than the District of Columbia 60 X 100 = 6,000 is Hawaii

Question 14.
DIG DEEPER!
A mother rhinoceros weighs 2 tons. Her baby weighs \(\frac{1}{10}\) as much as her. What is the weight of the baby rhinoceros, in pounds.

Answer: The weight of the baby rhinoceros is 20 Pounds.

2 tons Mother

Baby = 200 x 1/10 = 20 Pounds

Place Value Patterns Homework & Practice 1.1

Complete the statements.

Question 1.
______ is 10 times as great as 2,000.
Answer:   20,000

2,000 x 10 = 20,000

Question 2.
_____ is \(\frac{1}{10}\) of 2,000.
Answer:      200

2,000 x 1/ 10 = 200

Use a place value chart to answer the question.
Question 3.
What number is 10 times as great as 50?
Answer:  500

50 x 10 = 500

Question 4.
What number is \(\frac{1}{10}\) of 4,000?
Answer:  400

4,000 x 1/10 = 400

Question 5.
800 is \(\frac{1}{10}\) of what number?
Answer:8,000

8,000 x 1/10 = 800

Question 6.
60,000 is 10 times as great as what number?
Answer:6,000

6,000 is 10 times means 6,000 x 10 =60,000

Complete the table.
Question 7.

Answer:

1. 400, 4

40, 10 times as number is 40 x 10 = 400

1/10 of 40 is 4

2. 5,000, 50

500, 10 times as number is 500 x 10 = 5,000

1/10 of 500 is 50

3. 10,000  ,  100

1,000, 10 times as number is 1,000 x 10 = 10,000

1/10 of 1,000 is 100

4.8,00,000   , 8,000

80,000, 10 times as number is 80,000 x 10 = 8,00,000

1/10 of 80,000 is 8,000

Question 8.

Answer:

1. 7,00,000   ,   7,000

70,000, 10 times as number is 70,000 x 10 = 7,00,000

1/10 of 70,000 is 7,000

2. 200 ,  2

20, 10 times as number is 20 x 10 = 200

1/10 of 20 is 2

3. 30,000, 300

3,000, 10 times as number is 3,000 x 10 = 30,000

1/10 of 3000 is 300

4. 1,000 ,  10

100, 10 times as number is 100 x 10 = 1,000

1/10 of 100 is 10

Question 9.
Patterns
Describe the relationship between any place value position and the next lesser place value position.

Answer:

The relation between any place value position and next lesser place value position decreases ten times as we move.

Question 10.
YOU BE THE TEACHER
Your friend says 6,700 is \(\frac{1}{10}\) of 67,000. Is your friend correct? Explain.
Answer: Yes My friend is correct, because if we divide 67,000 by 10 we get the result as 6,700 only.

Use the table.

Question 11.
Modeling Real Life
Which city’s population is about 10 times the population of Newark?
Answer: Population of  Oakland.

Newark=40,000

40,000 x 10 = 4,00,000 is Oakland

Question 12.
Modeling Real Life
Which city’s population is about \(\frac{1}{10}\) the population of Marina?
Answer: Population of Del Ray Oaks.

Marina = 20,000

20,000 x 1/10 = 2,000=Del Ray Oaks

Question 13.
DIG DEEPER!
An archaeologist finds a ceramic bowl that is about 400,000 years old. He finds different artifact that is \(\frac{1}{100}\) times as old as the 100ceramic bowl. How much older is the ceramic bowl than the other artifact?
Answer: The Ceramic bowl is 4000 years old.

4,00,000 x 1/100= 4,000

Review & Refresh

Find the factor pairs for the number.
Question 14.
9
Answer: 1,3,9 are factor pairs of 9

Question 15.
24
Answer:  (1,24), (2,12) (3,8) and (4,6) are factor pairs of 24

Question 16.
15
Answer:(1,3,5,15) are factor pairs of 15

Lesson 1.2 Place Value with Whole Numbers

Model the number. Draw your model.
Then write the value of each digit.

Compare the values of the 4s.
Answer: Thousands-4, Hundreds -4 , Tens – 4 and Ones- 2

4 is in thousand, 4 is in Hundreds and 4 is at tens value.

Repeated Reasoning
Is the value of the 4 in the tens place 10 times as much as the value of the 2 in the ones place? Explain.
Answer: No, Why means 4 in tens place means its value is 40 and 2 in ones place means only 2so 4 in the tens place is not 10 times as the value of 2.

Think and Grow: Place Value with Whole Numbers

Key Idea
A place value chart shows the value of each digit in a number. It also shows how the place values are grouped. Each group of three digits is called a period. Ina number, periods are separated by commas.

Example
Write the number in standard form, word form, and expanded form.
Standard form:4,66,900
Word form: Four hundreds sixty six thousand and nine hundred
Expanded form:
4 × 1,00,000 + __6___ × 10,000_____ + ___6__ × _1,000_____ + _9____ × __100____

Show and Grow

Write the number in two other forms.
Question 1.
Standard form: 78,300
Word form:
Expanded form:
Answer:

Word Form : Seventy -Eight Thousand, Three Hundred.

Expanded Form : 7 x 10,000 + 8 x 1000 + 3 x 100=78,300

Question 2.
Standard form:
Word form: three hundred fifty thousand, fifty-eight
Expanded form:
Answer:

Standard Form : 300,50,058

Expanded Form : 3 x 10,00,000+ 5 x 10,000 + 5 x 10 +8=300,50,058

Question 3.
Compare the values of the 6s in the number 466,900.
Answer:

the values of the 6 s are one is in 60 thousand’s place and other is at 6 thousands place.

Apply and Grow: Practice

Write the number in two other forms.
Question 4.
Standard form:
Word form:
Expanded form: 6 × 100,000 + 8 × 1,000 + 4 × 100 + 5 × 10 + 9 × 1
Answer:

Standard Form : 6,08,459

Word Form : 6 hundred / six lakh, eight thousand , four hundred  fifty nine.

Question 5.
Standard form: 45,006,702
Word form:
Expanded form:

Answer:

Word form: forty five lakh ,six thousand seven hundred and two.

Expanded form:4 x 10000000 + 5 x 1000000 + 6 x 1000 +

7 x 100 +2

Question 6.
Compare the values of the 7s in the number 4,877,034.
Answer:

The value’s of 7s is at seventy thousand,(70,000) and again at  seven thousand(7,000).

Question 7.
Compare the values of the 3s in the number 5,338.
Answer:

The values of 3s is at 3-Hundred(300) and at thirty (30)[3 tens)]

or

3 at hundreds and 3 at tens place.

Compare.
Question 8.

Answer:

In 8,046 The value of 4 is in Ten’s place and 6 is in one’ s place

and in 8,460 the value of 4 is in hundreds place and 6 in ten’s place.

Question 9.

Answer:

In 28,517 the value of 2 is at twenty thousand place, 8 at thousands and 5 at hundreds, 1 at tens and 7 at one’s place.

and 28,509 the value of 2 is at twenty thousand place, 8 at thousands and 5 at hundreds, zero at tens and 9 at one’s place.

Question 10.

Answer:

In 5,854,331- Fifty Lakhs , 8 at lakhs, Five at ten thousand, 4 at thousand,3 at hundred, 3 at ten’s and 1 at one’s place.

and in 5,854,231 – Fifty Lakhs , 8 at lakhs, Five at ten thousand, 4 at thousand,2 at hundred, 3 at ten’s and 1 at one’s place.

Question 11.
The white truffle is the world’s most expensive edible fungus, which costs up to three thousand dollars per kilogram. Write this number in standard form.

Answer:

Standard Form: 3000$ per Kg.

the white truffle is 3000$ per kg.

Question 12.
YOU BE THE TEACHER
Your friend says that in the number 45,951, one 5 is 10 times as great as the other 5. Is your friend correct? Explain.
Answer:

Yes,  because  at first the 5 is at tens place and in next time 5 is at thousands place so friend is right 5 is 10 times greater as the other 5 . As we move from right value to left twice tens value place becomes thousand value place.

Question 13.
Logic
Newton is thinking of a 6-digit number in which all of the digits are the same. The value of the digit in the thousands place is 8,000. What is Newton’s number?
Answer:

8,88,888

8 x 1,00,000 + 8 x 10,000+8 x 1,000+8 x 100 + 8 x 10 + 8 x 1

Think and Grow: Modeling Real Life

Example
Compare the values of the 3sin Jupiter’s average distance from the Sun.

Use a place value chart to help you find the value of each 3.

Each place value is 10 times as great as the place value to its right. The digits are two places apart. So, multiply 30,000 by 10 × 10 = 100.
So, the value of the 3 in the millions place is _______ times the value of the 3 in the ten thousands place.

Show and Grow

Use the table above.
Question 14.
Compare the values of the 7s in Mars’s average distance from the Sun.
Answer:

the value of 7 s in first is in thousands place and next 7 s is at hundreds place, the digits are one place apart, so the value of first 7 is in thousands place is 10 times the value of the next 7s in hundreds place.

Question 15.
Compare the values of the 4s in Saturn’s average distance from the Sun.
Answer:

the value of 4 s in first is in four hundred thousands place and next 4 s is at hundreds place, the digits are two places apart, so the value of first  4 is in hundred thousands place is 100 times the value of the next 4s in hundreds place.

Question 16.
DIG DEEPER!
An organization wants to donate all of the money raised through fund raisers and raffles to a children’s charity. Complete the donation check.


Answer:

1.

$ 194,918 + $ 35,187 = $ 230,005

Word Form :  Two Hundred, Thirty thousand and Five dollars.

Standard Form : $ 230,005

Place Value with Whole Numbers Homework & Practice 1.2

Write the value of the underlined digit.
Question 1.
740,225
Answer:

4 is at Forty thousand place

Question 2.
604,197,872
Answer:

6 is at Six Hundred Lakh place

Question 3.
12,405,287
Answer:

2  is at  twenty Lakh or twenty hundred thousand place

Question 4.
392,183
Answer:

3 is at 3 lakhs or 3 hundred thousand place

9  is at ninety thousand place

2 is at 2 thousand place

1 is at one hundred place

8 is at eighty place

3 is at ones place place

Write the number in two other forms.
Question 5.
Standard form: 450,014
Word form:
Expanded form:
Answer:

Word Form : 4 lakhs or 4 hundred thousand ,  fifty thousand and fourteen

Expanded  Form : 4 x 1,00,000 +5 x 10000 + 1 x 10 + 4

Question 6.
Standard form:
Word form: fourteen thousand, two hundred one
Expanded form:
Answer:

Standard Form : 14,201

Expanded Form : 1 X 10000 + 4 X 1000 + 2 X 100 +1

Question 7.
Compare the values of the 9s in the number 537,499.
Answer:

First 9 is at ones place, and second 9 is at tens place.

Question 8.
Compare the values of the 5s in the number 78,550,634.
Answer:

First 5 is at Ten Thousands place,

Second 5 is at Five Hundred Thousands place.

Compare.
Question 9.

Answer:

67,893 < 67,943

6 at sixty thousand place ,6 at sixty thousand place

7 at thousand place, 7 at thousand place

8 at eight hundred place,9 at nine hundred is great

9 at tens place and 4 at four at tens place is less

and 3 at ones place and 3 at ones place is same

Question 10.

Answer:

450,823 > 405,823

4 at Four hundred thousand,

5 at fifty thousand and 0 is smaller at ten thousands place

0 at thousands place is smaller than 5 at thousands place

8  at hundreds place is same as 8 at hundreds place

2 at tens place is same as 2 at tens place

and 3 at ones place is same as 3 at ones place

Question 11.

Answer:

176,994 = 176,994

1 at one hundred thousand, is same at 1 at One Hundred Thousand place

7 at Seventy thousand is same at 7 at Seventy Thousand place

6 at six thousand is same at 6 at six thousand place

9 at hundreds place is same at 9 at hundreds place

9 at ninety or 9 tens place is same as 9 at Ninety or 9 Tens place

and 4 at ones place is same as 4 at Ones place

Question 12.

Your body contains about 60,000 miles of blood vessels. Write this number in word form.
Answer:

60,000 miles of blood vessels in  Word Form : Sixty Thousand miles.

Question 13.
Which One Doesn’t Belong?
Which number does belong with the other three?
1 × 10,000 + 4 × 1,000 + 2 × 100 + 6 × 1 fourteen thousand, two hundred six
140,206

Answer:

No number is repeated, so no number belongs to other

one at tens place

4 at ones place

2 at hundredths place

and 6 at thousandths place.

Question 14.
DIG DEEPER!
Find the difference in the values of the underlined digits.
856,092 37,841
Answer:

8 is at 80 Million,

and

8 is at hundreds value

the difference is 8 X 1,00,00,000 times the other  8 value.

Use the table.

Question 15.
Modeling Real Life
Compare the values of the 3s in the music cost.
Answer: 3 is at 3 millions place and other 3 is at 3 hundreds place.

Question 16.
Modeling Real Life
Compare the values of the 2s in the cost.
Answer:

Costs Places

In cast 2 is at two hundred thousands place and 2 at thousands place.

In Director 2 is at 2 millions place and 2 at thousands place.

In Editing 2 value is not there.

In Music also 2 is not there

In Producers 2 value is at 2 millions place

In Visual effects 2 place is first at thousands place and 2 is in ones place

Question 17.
DIG DEEPER!
What is the total cost for the director and producers? Write your answer in word form.
Answer: Total cost of director-$ 2,712,480+ and cost of roducer –

$ 2,759,981 is $ 5,472,461

Word Form : five million, four hundred thousand, seventy two thousand, four hundred sixty one dollars.

Review & Refresh

Compare
Question 18.

Answer:

0.14 < 0.15

0.14-0+ 1 x 1/10+4/100

0 is at ones place ,1 is at 1/10 place, and 4 is at 1 /100 place is small

0.15-0+1×1/10+5/100

0 is at ones place ,1 is at 1/10 place, and 5 is at 1 / 100 place

Question 19.

Answer:

2.2 = 2.20

2.2-2 is at ones place and .2 is at 2/10 place

2.20- 2 is at ones place ,.2 is at 2/10 place is same

Question 20.

Answer:

5.8 > 5.08

5.8 – 5 is at ones place and .8 is at 1/10 place

5.08  – 5 is at ones place and .8 is at 1/100 place  is small

Lesson 1.3 Patterns and Powers of 10

Explore and Grow

Write a multiplication expression to answer each question.

How many units are in 1 rod?

How many units are in 10 rods?

How many units are in 100 rods?

How many units are in 1,000 rods?
Answer:

In 1 rod its 1 x 10^{0 =}10⁰

In 10 rods its 1 x 10 = 10¹

In 100 rods its 1 x 10 x 10 = 10²

In 1,000 rods it is 1 x 10 x 10 x 10 =10³

Repeated Reasoning
How many tens are in 100? in 1,000? in 10,000?
Answer: In 100 its 10 tens, in 1,000 its 100 tens and in 10,000 its 1000 tens

Think and Grow: Patterns and Powers of 10

Key Idea
A power is a product of repeated factors. The base of a power is the repeated factor. The exponent of a power gives the number of times the base is used as a factor.

Example
Find the value of 4 × 10³.

Multiply 4 by powers of 10. Look for a pattern.
4 × 10¹ = 4 × 10 = _40____
4 × 10² = 4 × 10 × 10 = _400_____
4 × 10³ = 4 × 10 × 10 × 10 = __4,000____
So, 4 × 10³ = ____4,00,000_.
Notice the pattern: In each product, the number of zeros after 4 is equal to the exponent.

Show and Grow

Question 1.
Identify the base, exponent, and power for the expression 10⁶.
Answer:

base : 10,

exponent: 6

power :10⁶⁼ 10 x 10 x 10 x 10 x 10 x 10

Question 2.
Write the product 10 × 10 × 10 × 10 as a power.

Answer:

10 x 10 x 10 x 10  as a power is 10 ⁴

Question 3.
Find the value of 5 × 10².
Answer:

5 × 10^{2 is} 

5 x 10 x 10 = 500

Apply and Grow: Practice

Find each product. Use patterns to help.
Question 4.
2 × 10 = _____
2 × 100 = _____
2 × 1,000 = _____
2 × 10,000 = ____
Answer:

2 x 10 =20

2 x 100=200

2 x 1,000= 2,000

2 x 10,000 = 20,000

Question 5.
9 × 10 = _____
9 × 100 = _____
9 × 1,000 = _____
9 × 10,000 = ____
Answer:

9 x 10 = 90

9 x 100 = 900

9 x 1,000= 9,000

9 x 10,000 = 90,000

Question 6.
5 × 10 = _____
5 × 100 = _____
5 × 1,000 = _____
5 × 10,000 = ____
Answer:

5 x 10 = 50

5 x 100= 500

5 x 1,000 = 5,000

5 x 10,000 = 50,000

Find the value of the expression.
Question 7.
10⁴
Answer:

10⁴⁼ 10 x 10 x 10 x 10 = 10,000

Question 8.
6 × 10⁵
Answer:

6 × 10^{5 =} 6 x 10 x 10 x 10 x 10 x 10 = 6,00,000

Question 9.
7 × 10²
Answer:

7 × 10^{2 =} 7 x 10 x 10 = 700

Question 10.
5 ×10 ⁴
Answer:

5 ×10 ⁴⁼ 5 x 10 x 10 x 10 x 10 = 50,000

Rewrite the number as a whole number multiplied by a power of 10.
Question 11.
20,000
Answer:

20,000=2 x 10⁴

Question 12.
500
Answer:

500=5 X 10²

Question 13.
900,000
Answer:

9,00,000=9 x 10⁵

Number Sense
Write the number in expanded form using exponents.
Question 14.
53,124
(5 × 10⁴) + ______
Answer:

53,214=(5 × 10⁴) +( 3 x 10³)+(1 x 10²) + (2 x10¹)+ (4 x10⁰)

Question 15.
8624
(8 × 10²) + _______
Answer:

8624=(8 x 10³ )+(6 x 10²) +(2 x 10¹)+(4×10⁰)

Question 16.
DIG DEEPER!
Your friend writes (3 × 10⁴) + (5 × 10³) + (2 × 10²) + 4 as the expanded form of thirty-five thousand, twenty-four. Explain what your friend did wrong.
Answer:

(3 × 10⁴) is 3 x 10 x 10 x 10 x 10 = 30,000 is Thirty Thousand

(5 × 10³) is 5 x 10 x 10 x 10 = 5,000 is five thousand

(2 × 10²) is 2 x 10 x 10 = 200 is two hundred not twenty

and 4 is four,

it is  thirty-five thousand, two hundred and four= 35,204

not thirty-five thousand, twenty-four ≠ 35,024

35,204 is right

35,024 is wrong

Think and Grow: Modeling Real Life

Example
Newton and Descartes are running for mayor. How many people voted in the election?
Find the number of votes for each candidate.
Newton: 10⁵ = ______
Descartes: 9 × 10⁴ = ______
Add the votes for Newton and Descartes.

______ people voted in the election.

Newton: 10⁵ =  10 x 10 x 10 x 10 x 10 is 1,00,000

Descartes: 9 × 10⁴ = 9 x 10 x 10 x 10 x 10 is 90,000

so total people voted is 1,00,00 + 90,000 = 1,90,000

1,90,000 Voted in the election.

Show and Grow

Question 17.
A surf shop has been in business for two years. What are the total sales for Year 1 and Year 2 combined?

Answer:

Year 1 $ 10^{4 =} 10 x 10 x 10 x 10 =10,000

Year 2 $ 6 x 10⁵= 6 x 10 x 10 x 10 x 10 x 10 = 6,00,000

there fore total sales for Year 1 and Year 2 combined is  is 6,10,000 .

Question 18.
Which migration is farther? About how much farther is it?

Answer:

Chinook Salmon about 4 x 10^3km

4 X 10 x 10 x 10 = 4000 km

and

Leatherback Turtle about 2 X 10⁴ km

2 x 10 x 10 x 10 x 10 = 20,000 km

So Leatherback Turtle is  farther and

20,000 km – 4000 km = 16,000 km

it is 16,000 km farther

Question 9.
DIG DEEPER!
A human has about 10⁴ taste buds. A cow has about 3 times as many taste buds as a human. About how many taste buds does a cow have? Write your answer as a whole number multiplied by a power of 10.
Answer:

(10⁴) 3 time means (10⁴)³ 

as per the law powers are multiplied 4 x 3

(10^4×3) = (10¹²)

(10^4×3)= 1 X (10⁴) x (10⁴)  x (10⁴)

(10¹²)= 1 x (10 x 10 x 10 x 10 ) x (10 x 10 x 10 x 10 ) x (10  x 10 x 10 x 10)

Patterns and Powers of 10 Homework & Practice 1.3

Question 1.
Identify the base, exponent, and power for the expression 10³.
Answer:

base: 10

exponent:  3

power : 10³⁼ 10 x 10 x 10

Question 2.
Write 10 × 10 × 10 × 10 a power.
Answer:

10 x 10 x 10 x 10 = 10⁴

Find each product. Use patterns to help.
Question 3.
6 × 10 = ______
6 × 100 = _____
6 × 1,000 = _____
6 × 10,000 = _____
Answer:

6 x 10=6 × 10^{1 =} 60

6 x 100 =6 × 10² = 600

6 X 1,000=6 × 10^{3 =}  6,000

6 x 10,000 = 6 × 10⁴= 60,000

Question 4.
8 × 10 = ______
8 × 100 = _____
8 × 1,000 = _____
8 × 10,000 = _____
Answer:

8 x 10=8 × 10^{1 =} 80

8 x 100 =8 × 10² = 800

8 X 1,000=8 × 10^{3 =} 8,000

8 x 10,000 = 8 × 10⁴= 80,000

Question 5.
4 × 10 = ______
4 × 100 = _____
4 × 1,000 = _____
4 × 10,000 = _____
Answer:

4 x 10=4 × 10^{1 =} 40

4 x 100 =4 × 10² = 400

4 X 1,000= 4× 10^{3 =} 4,000

4 x 10,000 = 4 × 10⁴= 40,000

Find the value of the expression.
Question 6.
10³
Answer:

10^{3 =} 10 x 10 x 10 = 1,000

Question 7.
2 × 10⁴
Answer:

2 × 10^{4 =} 2 x 10 x 10 x 10 x 10 = 20,000

Question 8.
9 × 10⁵
Answer:

9 × 10^{5   =}  9 x 10 x 10 x 10 x 10 x 10 = 9,00,000

Question 9.
3 × 10²
Answer:

3 × 10^{2  =} 3 x 10 x 10 = 300

Rewrite the number as a whole number multiplied by a power of 10.
Question 10.
100,000
Answer:

100,000 = 1 x 10 x 10 x 10 x 10 x 10 = 1 × 10⁵

Question 11.
70
Answer:

70 = 7 x 10 = 7 x 10¹

Question 12.
6,000
Answer:

6,000 = 6 x 10 x 10 x 10 = 6 x 10³ 

Number Sense
Write the number in standard form.
Question 13.
(3 × 10²) + (8 × 10¹)
Answer:

(3 × 10²) + (8 × 10¹)  = 3 x 10 x 10 + 8 x 10

3 x 100 + 80

300+ 80 = 380

Question 14.
(2 × 10³) + (5 × 10²) + (4 × 10¹)
Answer:

(2 × 10³) + (5 × 10²) + (4 × 10¹) =  2 x 10 x 10 x 10 + 5 x 10 x 10 + 4 x 10

2,000 + 500 + 40

2,540

Question 15.
YOU BE THE TEACHER
Newton 6 says 10⁶ = 10 × 6. Is he correct? Explain
Answer:

No he is wrong because  10⁶  ≠  10 × 6 it is 10 is to be multiplied by  6 times ,

10^{6 =} 10 x 10 x 10 x 10 x 10 x 10=10,00,000 is correct

Question 16.
Which One Doesn’t Belong?
Which one does not belong with the other three?

Answer:

Both are different blocks , in first block it is  square and next it is cube.  

Question 17.
Modeling Real Life
Each student at an elementary school votes once on this year’s field trip. How many students voted in all?

Answer:

Aquarium = 7 x 10² =   7 x 10 x 10 = 700

Amusement Park = 10^{3  =} 10 x 10 x 10 =  1000

700 + 1000 = 1,700

So total number of students voted are =  1,700.

Question 18.
Modeling Real Life
On which day did more people attend the event? How many more people?

Answer:

Friday = 10 x 10 x 10 = 1,000

Saturday = 5 x 10² = 5 x 10 x 10 = 500

on Friday more people attend the event

and more are 1,000 – 500 = 500 , s0 500 more people attended.

Review & Refresh

Divide. Then check your answer
Question 19.

Answer:

Step 1) Start by dividing 65 by 6 to get the decimal answer as illustrated below. Note that we round the answer if necessary, but don’t worry, the final answer will still be exact.

65 / 6 = 10.83

Step 2) Next we take the Whole part of the answer in Step 1 and multiply it by the Divisor. As you can see, it does not matter if we rounded in the previous step because the Decimal part is ignored. Furthermore, the Divisor in 65 divided by 6 is 6. Thus, the Whole multiplied by the Divisor is:

10 x 6 = 60

Step 3) Finally, we will subtract the answer in Step 2 from the Dividend to get the answer. The Dividend in 65 divided by 6 is 65. Thus, our final calculation to get the answer is:

65 – 60 = 5

the answer is 5.

Question 20.

Answer:

Step 1) Start by dividing 50 by 4 to get the decimal answer as illustrated below. Note that we round the answer if necessary, but don’t worry, the final answer will still be exact.

50 / 4 = 12.50

Step 2) Next we take the Whole part of the answer in Step 1 and multiply it by the Divisor. As you can see, it does not matter if we rounded in the previous step because the Decimal part is ignored. Furthermore, the Divisor in 50 divided by 4 is 4. Thus, the Whole multiplied by the Divisor is:

12 x 4 = 48

Step 3) Finally, we will subtract the answer in Step 2 from the Dividend to get the answer. The Dividend in 50 divided by 4 is 50. Thus, our final calculation to get the answer is:

50 – 48 = 2

the answer is 2.

Question 21.

Answer:

Step 1) Start by dividing 45 by 3 to get the decimal answer as illustrated below. Note that we round the answer if necessary, but don’t worry, the final answer will still be exact.

45 / 3 = 15

the answer is 0.

Lesson 1.4 Decimals to Thousandths

Explore and Grow

Divide the square into10 equal parts. Shade one part. What part of the whole is shaded?
Fraction: Decimal:

Divide each of the 10 parts into 10 equal parts. Shade one part using a different color. What part of the whole is shaded with the second color?

Fraction: Decimal:

If you divide each of the 100 equal parts into10 equal parts, how many parts will the model have?

If you shade one of those parts, what part of the whole is shaded?
Fraction: Decimal:
Answer:

the model will have 10 parts , only 1/ 10th part is shaded, 0.1

Structure
Compare the number of hundredths to the number of tenths. Compare the number of hundredths to the number of thousandths. What do you notice?
Answer:

number of hundredths to the number of tenths is 10 to 100 , 10/100=1/10 = 0.1

number of hundredths to the number of thousandths is

100 to 1000, 100/1000 =1/10= 0.1

both has equal values 1/10 = 0.1

the number of hundredths to the number of tenths is equal to the number of hundredths to the number of thousandths

Think and Grow: Thousandths

Key Idea
In a decimal, the third place to the right of the decimal point is the thousandths place. You can write thousandths as fractions or decimals.

Show and Grow

Write the decimal as a fraction.
Question 1.
0.009

Answer:

0.009= 9 / 1,000 = 9 x 1/1,000

Question 2.
0.063
Answer:

0.063 = 63 / 1,000= 63 x 1/1,000

Question 3.
0.194
Answer:

0.194 = 194 / 1,000= 194 x 1/1,000

Write the fraction as a decimal
Question 4.
\(\frac{3}{1,000}\)
Answer:

\(\frac{3}{1,000}\)= 3 x 1/ 1,000=  0.003

Question 5.
\(\frac{91}{1,000}\)
Answer:

\(\frac{91}{1,000}\)= 91 x 1/ 1,000 = 0.091

Question 6.
\(\frac{607}{1,000}\)
Answer:

\(\frac{607}{1,000}\)= 607 x 1/1,000= 0.607

Apply and Grow: Practice

Write the decimal as a fraction.
Question 7.
0.645
Answer:

0.645= 645x 1/1,000= 645/1,000

Question 8.
0.002
Answer:

0.002=2 x 1/1,000=  2/1,000

Question 9.
0.98
Answer:

0.98= 98 x 1/ 1,000= 98/1,000

Question 10.
0.6
Answer:

0.6 = 6 x 1/10= 0.6/10

Write the fraction as a decimal.
Question 11.
\(\frac{884}{1,000}\)
Answer:

\(\frac{884}{1,000}\)= 884x 1/1,000= 0.884

Question 12.
\(\frac{8}{1,000}\)
Answer:

\(\frac{8}{1,000}\)= 8 x 1/1,000= 0.008

Question 13.
\(\frac{39}{100}\)
Answer:

\(\frac{39}{100}\)= 39 x 1/ 100= 0.39

Question 14.
\(\frac{1}{10}\)
Answer:

\(\frac{1}{10}\)= 1 x 1/10 = 0.1

Question 15.
0.4 is \(\frac{1}{10}\) of what number?
Answer:

\(\frac{4}{10}\) is 0.4

Question 16.
0.52 is 10 times as great as what number?
Answer:

0.52 is 10 times as great as 0.052

Question 17.
You use 47 of the cotton balls for an art project. What portion of the bag of cotton balls do you use? Write your answer as a decimal.

Answer:

47/100= 47 x 1/100= 0.47

Question 18.
Which One Doesn’t Belong?
Which number does not belong with the other three?

Answer:

0.29 does not belongs to other three

Question 19.
YOU BE THE TEACHER
Your friend says the value of the 7 in the hundredths place of 0.877 is 10 times as great as the 7 in the thousandths place. Is your friend correct? Explain.
Answer:

Yes , because the value of 7 in the hundredths place as compared is 10 times as great as the 7 in the thousands place.

Question 20.
Write each fraction as a decimal. What do you notice?
\(\frac{4}{10}\), \(\frac{40}{100}\) and \(\frac{400}{1,000}\)
Answer:

\(\frac{4}{10}\)=0.4

\(\frac{40}{100}\) =0.4

\(\frac{400}{1,000}\)=0.4

number of tenths, tenths number of hundredths and hundredths number of thousandths are same.

Think and Grow: Modeling Real Life

Example
You put together 156 pieces of the puzzle before lunch and 148 pieces of the puzzle after lunch. What portion of the puzzle did you put together? Write your answer as a decimal.


Write the fraction as a decimal.
You put together ____0.304__ of the puzzle.

Show and Grow

Question 21.
You make flash cards out of index cards. You use 50 index cards for social studies and 25 index cards for science. What portion of the pack of index cards do you use? Write your answer as a decimal.

Answer:

50 for social studies, 25 for science total is 50 + 25 = 75, total number of flash cards is 1,000 ,

75 / 1,000 or 75 by 1,000 or 75 x 1/1,000= 0.075

Question 22.
There are 458 knock-knock jokes in the book. not What fraction of the jokes in the book are knock-knock jokes?

Answer:

458/1,000 or 458 x 1/1,000 of jokes books in knock- knock jokes.

Question 23.
DIG DEEPER!
A newly hatched caterpillar was 0.02 inches long. After 2 weeks, the caterpillar grew 10 times as long as its length when it hatched. After another 2 weeks, the caterpillar grew 10 times as long as its length after 2 weeks. How long is the caterpillar now?
Answer: First week it is 0.02 inches,

in two weeks -2 weeks-0.02 x 10 = 0.2 inches

again after 2 weeks -0.2 x 10 = 2 inches

Decimals to Thousandths Homework & Practice 1.4

Write the decimal as a fraction.
Question 1.
0.735
Answer:

0.735= 735 / 1,000= 735 x 1/1,000

Question 2.
0.051
Answer:

0.051= 51 / 1,000= 51 x 1/1,000

Question 3.
0.804
Answer:

0.804 = 804 / 1,000= 804 x 1/ 1,000

Question 4.
0.2
Answer:

0.2 = 2 / 10= 2 x 1/10

Write the fraction as a decimal.
Question 5.
\(\frac{98}{1,000}\)
Answer:

\(\frac{98}{1,000}\)=98 x 1/1,000= 0.098

Question 6.
\(\frac{67}{100}\)
Answer:

\(\frac{67}{100}\)= 67 x 1/100=0.67

Question 7.
\(\frac{4}{100}\)
Answer:

\(\frac{4}{100}\)= 4 x 1/100=0.04

Question 8.
\(\frac{9}{10}\)
Answer:

\(\frac{9}{10}\)= 9 x 1/10= 0.9

Question 9.
0.08 is 10 times as great as what number?
Answer:

0.008

if 0.008 is multiplied by 10 times it becomes 0.08

Question 10.
0.001 is \(\frac{1}{10}\) of what number?
Answer:

0.0001

if 0.0001 is \(\frac{1}{10}\) equals to 0.001

Question 11.
YOU BE THE TEACHER
Your friend says that \(\frac{16}{1,000}\) can be written as 0.16. Is your friend correct? Explain.
Answer: No, because if 16 / 1,000 or 16 x 1/1,000 is 0.016 not 0.16,

0.016 ≠ 0.16

so he is incorrect.

Question 12.
Precision
Thirteen unit cubes are taken from the thousand cube. Write a fraction and a decimal to represent how many unit cubes are left.

Answer:

13 units cubes are taken

Total number of units are  1000

left are from 1,000-13/1,000=87/1000

87 / 1,000 and 0.087 cubes are left

Question 13.
DIG DEEPER!
Write the number represented by each point on the number line.

Point X: _____
Point Y: ___
Answer:

on the number line Point X = 7.633 as we move from 7.63 to three places forward

so Point X is 7.633

on the number line Point Y = 7.638 as we move from 7.63 its eighth place forward

and Point Y is 7.638

Question 14.
Modeling Real Life
A restaurant owner has a 1,000-count box of napkins. She puts 125 of the napkins on tables. What portion of the box of napkins does she use for the tables? Write your answer as a decimal.
Answer:

Restaurant has 1,000 count box of napkins and keeps 125 on table so portion of the box she uses is  125/1,000= 125 x 1/ 1,000= 0.125

Question 15.
DIG DEEPER!
Your friend has a recipe book with 1,000 recipes. She wants to try two new recipes each week. What fraction of the recipes in the book will she have tried after 1 year?
Answer:

In a year there are almost 52 weeks. Each week 2 means 2 x 52 =approximately  104 recipes in a year.

so in a year she would have tired 104 / 1,000= 104 x 1/1,000 = 0.104 recipes.

Review & Refresh

Question 16.
Extend the pattern of shapes by repeating the rule “square, octagon, pentagon, octagon ”What is the 48th shape in the pattern?

Answer:

” square, octagon, pentagon, octagon, hexagon, octagon , heptagon , octagon,

octagon, octagon, nonagon, octagon , decagon, octagon,

Lesson 1.5 Place Value with Decimals

Explore and Grow

Model the number. Draw your model.
Then write the value of each digit.

Answer:

from the model 3.33 =

0nes digit is – 3

tenths digit is 3/10 =0.3

hundredths digit is 3/ 100 = 0.03

Repeated Reasoning
Compare the value of the ones digit to the value of the tenths digit. Then do the same with the tenths and the hundredths digits. Explain why you can use base ten blocks to model ones, tenths, and hundredths.
Answer:

a digit in one place represents one and 10 times more what it represents in the place to its right and that is tenths digit.
Similarly a digit in tenths place represents tenth and 10 times more what it represents in the place to its right and that is hundredths digit.

Each place to the left is 10 times the size of the place to the right, and base 10 blocks are the best way to model ones, tenths, and hundredths.

Think and Grow: Place Value with Decimals

Key Idea
In a place value chart, whole numbers are to the left of the decimal point. Decimals are to the right of the decimal point.

Standard form:2.557
Word form:” Two and five hundred fifty-seven  thousandths”
Expanded form: 2 × 1 + __5__ ×\(\frac{1}{10}\)____ + 5 × \(\frac{1}{100}\) + _7_ × \(\frac{1}{1000}\)__

Show and Grow

Write the number in two other forms.
Question 1.
Standard form: 0.398
Word form:
Expanded form:

Answer:

Word form: “Three hundred ninety – eight thousandths”
Expanded form: 3 x (1/10) + 9 x (1/100) + 8 x (1/1,000)

Question 2.
Standard form:
Word form: eight and forty-six thousandths
Expanded form:
Answer:

Standard form:8.046

Expanded form: 8 x 1 + (4 /100) + (6 / 1,000)

Question 3.
Compare the values of the 5s in the number 2.557.
Answer: at first 5s place value is at tenths and next its place value is at hundredths .

Apply and Grow: Practice

Write the value of the underlined digit.
Question 4.
0.418
Answer:

4 is at tenths value place

Question 5.
5.296
Answer:

9 is at hundredths value place

Question 6.
3.806
Answer:

8 is at tenths value place

6 is at  thousandths value place

Question 7.
0.547
Answer:

7 is at thousandths value place

Write the number in two other forms.
Question 8.
Standard form:
Word form:
Expanded form: 4 × 1 + 9 × \(\frac{1}{10}\) + 8 × \(\frac{1}{1,000}\)
Answer:

Standard form: 4.908
Word form:” Four and nine hundredth – eight thousandths”

Question 9.
Standard form: 0.125
Word form:
Expanded form:
Answer:

Word form: “one hundred twenty – five thousandths”
Expanded form: 1 x (1/10) + 2 x (1 /100) +5 x (1 / 1,000)

Question 10.
Compare the values of the 4s in the number 0.844.
Answer:

at first 4s place value is at hundredths and next 4s place value is at thousandths

Question 11.
Compare the values of the 3s in the number 3.367.
Answer: at first 3s place value is at ones place and next 3s place value is at tenths place

Question 12.
A pygmy jerboa weighs one hundred thirty-two thousandths pound. Write this number in standard form.

Answer:

The Standard Form of pygmy jerboa’s -one hundred thirty-two thousandths pound weighs is  0.132 pound

Question 13.
Reasoning
Is 9.540 equivalent to 9.54? Explain.
Answer:

Yes. 9.540 is equivalent to 9.54 because at thousandths value its 0, so zero multiplied by any number is zero.

Therefore both are equivalent.

Question 14.
DIG DEEPER!
Write three decimals that are equivalent to 6 × 1 + 4 × \(\frac{1}{10}\) .
Answer:

the three equivalent decimals are of 6 .04 are 6.040, 6.0400, 6.04000

Think and Grow: Modeling Real Life

Example
How do the values of the 3s in the masses of the fruits compare?

Use a place value chart to help you find the value of each 3.

The value of the 3 in the mass of the tomato is _one_____ .
The value of the 3 in the mass of the chili pepper is __tenths___.
So, the value of the 3 in the mass of the tomato is __10_____ times the value of the 3 in the mass of the chili pepper. Also, the value of the 3 in the mass of the chili pepper is ___1/10__ the value of the 3 in the mass of the tomato.

Show and Grow

Question 15.
Two baseball players have batting averages of 0.358 and 0.345. How do the values of the 5s in the batting averages compare?
Answer:

In 0.358 the place value of 5s is at tenths place and in

0.345 the place value of 5s  is at thousandths place.

Question 16.
The stopwatch shows a runner’sritethe100-meter dash time. Write the time in words.

Answer:

15.76 seconds time in words  is Fifteen and seven tenths and six hundredths

Question 17.
DIG DEEPER!
You exchange 1 U.S. dollar for Australian dollars and 1 U.S. dollar for Kuwaiti dinars. Do you have 10 times as many Australian dollars as Kuwaiti dinars? Explain.

Answer:

Yes, Because 1 Australian dollars = 1.302 of 0.302 of Kuwaiti dinars,

if we multiply 0.302 by 10 it becomes 1.302 which is equal to 1 Australian dollars.

[0.302 x 10 = 1.302]

so 1 Australian dollars is 10 times more than the 1  Kuwaiti dinars.

Place Value with Decimals Homework & Practice 1.5

Write the value of the underlined digit.
Question 1.
5.437
Answer:

5 at ones place

4 at tenths place

3 at hundredths place

7 at thousandths place

Question 2.
0.852
Answer:

the underlined digit is 2 at thousandths place,

its value is 2 x 1/1000= 2/1000

Question 3.
0.962
Answer:

the underlined digit is 6 at hundredths place

its value is 6 x 1/100= 6 /100

Question 4.
4.165

the underlined digit is 1 at tenths place

its value is 1x 1/10 = 1/10
Answer:

Write the number in two other forms.
Question 5.
Standard form: 9.267
Word form:
Expanded form:
Answer:

Word form:  nine and two tenths six hundredths seven thousandths.

Expanded form : 9+ 2 x 1/10 + 6 x 1/100 + 7 x 1/1000

Question 6.
Standard form:
Word form: two and forty-three thousandths
Expanded form:
Answer:

Standard form : 0.243

Expanded form: 2 x 1/10+4 x 1/100+3 x 1/1000

Question 7.
Compare the values of the 6s in the number 1.668.
Answer:

first 6s at tenths place and next 6s at hundredths place

Question 8.
Compare the values of the 7s in the number 7.704.
Answer:

first 7s at ones place and next 7s at tenths place

Question 9.
A pygmy possum weighs 0.097 pound. Write this number in word form.

Answer:

pygmy weighs 0.097 pound and its

word form is  nine hundredths and seven thousandths

Questio 10.
Which One Doesn’t Belong?
Which one does not belong with the other three?

Answer:

no number belongs to other three because 5 is at tenths place

one at hundredths place and 4 at thousandths all are at different places.

Question 11.
Reasoning
Which number cards are equal to the value of the underlined digit?

Answer:

2 x 1/1,000 , two thousandths and 0.002 are equal to the value of the underlined digit.

Question 12.
Modeling Real Life
How do the values of the 5s in the heights of the plants compare?

Answer:

In Peace lily the 5s place is at  thousandths

and in Venus flytrap the 5s place is at hundredths

Question 13.
Modeling Real Life
The world’s largest gold nugget is located in Las Vegas, Nevada. It has a mass of about 27.247 kilograms. Write how to say the nugget’s mass in words.

Answer:

the mass of gold nugget in Las Vegas is 27.247 kilograms given

In Words form it is twenty seven and two tenths  four hundredths and  seven thousandths

Review & Refresh

Compare.
Question 14.

Answer:

8/10 =0.8

80/100=0.8

both are equal 8/10 = 80/100

Question 15.

Answer:

5/8 = 0.625

3/6= 0.5

0.625 > 0.5,

5/8 > 3/ 6, 5/8 is greater than 3/6

Question 16.

Answer:

7/2= 3.5

10/8=1.25

so 7/2 is greater than 10/8.

7/2 > 10/8

Lesson 1.6 Compare Decimals

Explore and Grow

Use models to compare the decimals.

Answer:

0.62 >0.26, 0.62 is greater than 0.26, 0.6  is greater than o.2

0.80= 0.8, 0.80 both are  equal

3.5 < 3.55, 3.55 is greater than 3.50

Reasoning
How can you use a place value chart to compare two decimals? Use a place value chart to check your answers above.
Answer:

we use another table to compare with the previous and write the answer.

Think and Grow: Compare Decimals

Example
Compare 3.769 and 3.749.
Use a place value chart. Start at the left. Compare the digits in each place until the digits differ.

The digits in the ones place and the tenths place are the same. Compare the hundredths.

Example
Compare 2.4 and 2.405.
Use place value. Line up the decimal points. Start at the left. Compare the digits in each place until the digits differ.

2.4<2.405

Show and Grow

Compare
Question 1.

Answer:

So 9.063 < 9.067

Question 2.

Answer:

So 0.89 > 0.809,

Apply and Grow: Practice
Compare.
Question 3.

Answer:

8.537 < 8.541

Question 4.

Answer:

6.401 < 6.409, since  0.009 is greater than 0.001

Question 5.

Answer:

7.409 > 7.049 since 7.4 is greater than 7.0

Question 6.

Answer:

0.25 = 0.250

Both are equal

Question 7.

Answer:

2.701 >2.700, since 0.001 is greater than 0.000

Question 8.

Answer:

4.006 < 4.61, since 4.6 is greater than 4.0

Question 9.

Answer:

0.041 < 41.6, 41 is greater than 0

Question 10.

Answer:

0.007 < 0.7 as 0.7 is greater than 0.007

Order the decimals from least to greatest.
Question 11.
321.499, 325.499, 321.489
Answer:

321.499, 325.499, 321.489 from least to greatest

as 321.489 is smaller than 321.499 and 321.499 is smaller than 325.499

so 321.489 , 321.499 , 325.499

Question 12.
9.7, 9.64, 9.78
Answer:

9.7, 9.64, 9.78 from least to greatest

9.64 is smaller than 9.7 and  9.7 is smaller than 9.78

so 9.64, 9.7 , 9.78

Open-Ended
Complete the number to make the statement true.
Question 13.

Answer:

10.321 > 10.311

as 10.311 is smaller than 10.321

Question 16.

Answer:

28.60 = 28.600

Both are equal

Question 15.
Number Sense
Is 0.472 greater than or less than \(\frac{47}{1,000}\)? Explain.
Answer:

0.472, 0.047

0.475 is greater than 0.047,

as 4 in the tenths  place is greater than 0 in the others tenth place

Question 16.
YOU BE THE TEACHER
Your friend says that 45.6 is less than 45.57 because 6 is less than 57. Is your friend correct? Explain.
Answer:

Friend says 45.6 is less than 45.57

No ,he is wrong as the 6th in tenths place is greater than 5, in the tenths place

so he is wrong  45.60 > 45.57 not less

Think and Grow: Modeling Real Life

Example
You, your friend, and your cousin compete at a gymnastics competition. Your floor routine score is 15.633. Your friend’s score is 15.533, and your cousin’s score is 15.635. Order the scores from least to greatest.

Use a place value chart. Compare the digits in each place until the digits differ.

_15.533______ is the least
Write the remaining numbers in the place value chart. Compare the digits in each place until the digits differ.

15.633 ,15.635

as 15.533 is less than 15.633 as  5 at tenths place is less than 6 at tenths place

and 15.633 is less than 15.653 as 3 at hundredths place is less than 5 at hundredths place

So, the scores from least to greatest are 15.533, 15.633 and 15.635

Show and Grow

Question 17.
You stand on one leg for 2.75 minutes, your friend stands on one leg for 2 minutes, and your cousin stands on one leg for 2.25 minutes. Order the amounts of time from least to greatest.
Answer:

You – 2.75 min , Friend – 2.00 min and cousin for 2.25 min

2.00< 2.25 ,2.00 is less than 2.25 as 0 at tenths place is less than 2 at tenths place

2.25 < 2.75, 2.25 is less than 2.75 as 2 at tenths place is less than 7 at tenths place

so From Least to Greatest : 2.00 min, 2.25 min, 2.75 min

Question 18.
DIG DEEPER!
You, Newton, Descartes, and your friend each have a tablet. The table shows the screen display sizes. Your friend’s tablet has the greatest display size. Your tablet’s display size is greater than Newton’s but less than Descartes’s. What is the display size of your tablet.

Answer:

Y-Your, N-Newton’s ,F-Friend- 12.9, D-Descartes

Given Friend has greatest display size F= 12.9

Y – N ,given Your tablet’s display size is greater than Newton’s, N< Y and yours is less than Descartes’s Y < D

therefore  N < Y <D < F, Newton’s< Yours<Descartes’s<Friend

so N-Newton’s- 7.9, Y-Your-9.7,D-Descartes-10.5,F-Friend-12.9

Compare Decimals Homework & Practice 1.6

Write which place to use when comparing the numbers.
Question 1.
0.521
0.576
Answer:

2 at hundredths place  is smaller than 7 at hundredths place

so 0.521 < 0.576

Question 2.
17.422
17.946
Answer:

4 at tenths place  is small than 9 at tenths place

so 17.422 < 17.946

Question 3.
9.678
9.67
Answer:

8 at thousandths place is greater than 0 at thousandths place

9.678 > 9.670

Compare.
Question 4.

Answer:

4 at hundredths  place is smaller than 7 at hundredths place

so 3.445 is smaller than 3.472

3.445 < 3.472

Question 5.

Answer:

0 at tenths place is smaller than 4 at tenths place

so 23.049 < 23.409

Question 6.

Answer:

4 at tenths place is greater than 3 at tenths place

75.4 > 75.391

Question 7.

Answer:

All  given place values are same

so 14.100 or 14.10 = 14.100

Question 8.

Answer:

the value of 5s at hundredths place is more than 0 in other hundredths place

4.05> 4.005

Question 9.

Answer:

15.2, 15.002

2 at tenths place is greater than 0 at tenths place

15.2 > 15.002

Question 10.

Answer:

0.021, 0.026

1 at thousandths is smaller than 6 at thousandths place

0.021 < 0.026

Order the decimals from least to greatest.
Question 11.
2.75, 0.2, 0.275
Answer:

0.2 < 0.275 as 0 at hundredths place is less than 7 at hundredths place

0.275<2.75 as 0 at ones place is less than 2 at at ones place

so from least to greatest 0.2, 0.275, 2.75

Question 12.
56.01, 56.1, 56.001
Answer:

56.001 < 56.01 as 0 at hundredths place is less than 1 at hundredths place

56.01 < 56.1 as o at tenths place is less than 1 at tenths place

56.001 , 56.01, 56.1

Open-Ended
Complete the number to make the statement true.
Question 13.

Answer:

29.030 = 29.030

both the place values are same

Question 14.

Answer:

3.562 <3.562

as the value of  6 is at hundredths place so the other value at hundredths place is 6.

Question 15.
YOU BE THE TEACHER
Newton says 8.51 is less than 8.492 because 8.51 has fewer digits after the decimal point than 8.492. Is he correct? Explain.
Answer:

No, he is not correct its not the digits after the decimal point is fewer

but the 5s at tenths place is greater than 4 at the tenths place so

8.51 is greater than 8.492, 8.51 > 8.492

Question 16.
Open-Ended
Descartes is thinking of a number less than 46.922 and greater than 46.915. What could Descartes’s number be?
Answer:

The numbers can be 46.916,  4 6.917, 46.918, 46.919, 46.920 or 46.921 and

all these numbers are less than 46.922 and greater than 46.915.

Question 17.
Modeling Real Life
Player A’s batting average is 0.300, Player B’s batting average is 0.333, and Player C’s batting average is 0.313. Order the batting averages from greatest to least.
Answer:

B- 0.333, C-0.313 , A – 0.300

0.333 is great than 0.313 as 3 at hundredths place is great than 1 at hundredths place

so 0.333>0.313

0.313 is greater than 0.300 as 1 at hundredths place is great than 0 at hundredths place

0.313 > 0.300

the batting averages from greatest to least are B> C> A=0.333 > 0.313 >0.300

batting averages from greatest to least 0.333,0.313,0.300

Question 18.
Modeling Real Life
A gasoline station customer pumps more than 9.487 gallons of gasoline but less than 10 gallons. Which display could be his?

Answer:

Given A gasoline station customer pumps more than 9.487 gallons but less than 10 gallons

as 9.003 is less than 9.487 so not 9.003

as 9.499 is greater than 9.487  and even less than 10.000 so it is 9.499

as 9.406 is less than 9.487 so it cannot be 9.406

as 9.872 is greater than 9.487  and even less than 10.000 so it can be 9.872

so the displays can be  9.499 or 9.82

as both are more than 9.487 gallons and less than 10 gallons

Review & Refresh

Round the number to the place of the underlined digit.
Question 19.
7,851
Answer:

the round place of 5 is 7,850

Question 20.
9,462
Answer:

the round place of 9 means 10,000 or 9,500

Question 21.
4,983
Answer:

the round place of 9 – 5,000

Question 22.
51,504
Answer:

the round place of 1- 52,504

Lesson 1.7 Round Decimals

Explore and Grow

Plot the numbers on the number line. Which numbers round to 3? Which numbers round to4? How do you know?

Answer:

3,  3.09, 3.5, 3.51, 3.6, 3.77, 3.9 , 4

The numbers round to 3 are 3.09

The numbers round to 4 are 3.51, 3.6, 3.77 , 3.9

Repeated Reasoning
Show how you can use a number line to round 3.09, 3.51, and 3.77 to the nearest tenth.
Answer:

3.09 to the nearest tenth is 3.10

3.51 to the nearest tenth is 3.50

3.77 to the nearest tenth is 3.80

Think and Grow: Round Decimal Number

Example
Use a number line to round 7.36 to the nearest tenth.

7.36 is closer to 7.4 than it is to 7.3.
So, 7.36 rounded to the nearest tenth is __7.40____.

Example
Use place value to round 2.185 to the nearest whole number and to the nearest hundredth.

So, 2.185 rounded to the nearest whole number is __2.2_____.
2.185 rounded to the nearest hundredth is ___2.200___.

Show and Grow

Round the number to the place of the underlined digit.
Question 1.
12.67
Answer:

the round place of  digit 6 is 12.70

Question 2.
0.439
Answer:

the round place of  digit 4 is 0.5

the round place of  digit 3 is 0.44

the round place of digit  9 is 0.440

Question 3.
2.555
Answer:

the round place of  digit 2 is 3.000

Question 4.
5.409

the round place of digit 4 is 5.400

Question 5.
Round 0.68 to the nearest tenth.
Answer:

0.68 to the nearest tenth  is 0.70, 6 at tenths place becomes 7

Question 6.
Round 1.715 to the nearest hundredth.
Answer:

1.715 to the nearest hundredth is  1.720, 1 at hundredths place becomes 2

Question 7.
Round 4.07 to the nearest whole number.
Answer:

4.07 to the nearest whole number becomes  4.00 or 4

Question 8.
Round 0.289 to the nearest tenth.
Answer:

0.289 to the nearest tenth is 0.300 as 2 becomes 3 at tenths place.

Apply and Grow: Practice

Round the number to the place of the underlined digit.
Question 9.
1.482
Answer:

the underlined digit is 8 ,so its value becomes 1.490

Question 10.
5.093
Answer:

the underlined digit is 0 so its value  becomes 5.100

Question 11.
8.502
Answer:

the underlined digit is 8 so its value becomes 9.000

Question 12.
34.748
Answer:

if it is underlined at 3 it becomes 35.000

if it is underlined at 4 it becomes 35.000

if it is underlined at 7 it becomes 35.000

if it is underlined at 4 it becomes 34.800

if it is underlined at 8 it becomes 34.750

Question 13.
Round 2.619 to the nearest whole number.
Answer:

the value of 2.619 becomes 3.000

Question 14.
Round 7.825 to the nearest tenth.
Answer:

the value of 7.825 to the nearest tenth is 7.900

Question 15.
Round 92.701 to the nearest ten.
Answer:

the value of 92.701 to the nearest ten 93.000

Question 16.
Round 4.263 to the nearest hundredth.
Answer:

the value of 4.263 to the nearest hundredth is 4.270

Question 17.
Round 0.829.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:

Round 0.829
Nearest whole number:0.900
Nearest tenth:0.830
Nearest hundredth:0.830

Question 18.
Round 18.062.
Nearest whole number:18.100
Nearest tenth:18.070
Nearest hundredth:18.063
Answer:

Question 19.
A baby harp seal weighs 25.482 pounds. Round this weight to the nearest tenth of a pound.

Answer:

Given a baby harp seal weighs 25.482 pounds and the nearest tenth is 25.000 pounds

So the weight of baby harp seal is 25.000 pounds.

Name the place value to which the number was rounded.
Question 20.
8.942 to 8.94
Answer:

It was rounded at hundredths value place

Question 21.
0.164 to 0.2
Answer:

It was rounded at tenths value place

Question 22.
15.826 to 16
Answer:

It was rounded at whole value place

Question 23.
Writing
Explain what happens when you round 2.999 to the nearest tenth.
Answer:

2.999 round value becomes 3.000 as all value places at tenths, hundredths, thousandths are 9 it becomes increased as we move so it ones value increases by 1 and becomes round 3.000.

Question 24.
DIG DEEPER!
To what place should you round 23.459 to get the greatest number? the least number? Explain.
Answer:

To make 23.459 to  greatest number the value of 4s at tenths  becomes 5,

23.500 and to make 23.500 round make 5 at tenths value increased and make ones value 3 as 4 so we get 24.000

and to make 23.459 to least number the value at hundredths 5 becomes 0 ,

23.400  and to make 23.400 round make 4 at tenths value as decreased to 0 and ones value same as 3 it becomes as 23.000

Think and Grow: Modeling Real Life

Example
Gasoline prices are listed to the nearest thousandth of a dollar. The final price is rounded to the nearest hundredth. About how much does a customer pay for 1 gallon of regular gasoline at the station shown?

Think: What do you know? What do you need to find? How will you solve?
Use place value to round the price of 1 gallon of regular gasoline, $2.799, to the nearest hundredth.

So, a customer will pay about $ ___$ 2.800____ for 1 gallon of gasoline.

Show and Grow

Use the table.

Question 25.
What is the length of the praying mantis rounded to the nearest hundredth?
Answer:

Given  praying mantis as 3.254 so the  nearest hundredth becomes 3.26

Praying mantis becomes 3.260

Question 26.
What is the length of the cicada rounded to the nearest tenth?
Answer:

Given cicada 1.48 so rounded to the nearest tenth becomes 1.50

Cicada becomes 1.50

Question 27.
What is the length of the hissing cockroach rounded to the nearest tenth?
Answer:

Given Hissing cockroach 2.682 so rounded to the nearest tenth is 2.700

Hissing cockroach becomes 2.700

Question 28.
DIG DEEPER!
You have about $3 in coins. Write one possible combination of coins that represents the least amount of money you could have. Write another combination of coins for the greatest amount of money you could have.
Answer:

$3 Least amount of money combinations – 1. $ 1.0, $1.0    2.$ 1.0, $1.5

3.$0.5, $ 2.0 all combinations becomes less than $3

$ 3 greatest amount of money combinations- 1. $1.0, $ 2.5   2.$1.5 ,$2.0

3. $2.0 , $ 2.0 all combinations becomes more than $3

Round Decimals Homework & Practice 1.7

Round the number to the place of the underlined digit.
Question 1.
49.012
Answer:

the underline digit is 4 its round number 4 becomes 5 so it is 50.000

Question 2.
2.308
Answer:

the underline digit is 2  its round number 2 becomes as 2.000

Question 3.
9.647
Answer:

the underline digit is 6 its round number 6 becomes 7 so it is 9.700

Question 4.
7.519
Answer:

the underline digit is 1 its round number 1 becomes  2 so it is 7.520

Question 5.
Round 8.436 to the nearest hundredth.
Answer:

8.436 to the nearest hundredth, 3 becomes 4 so it is 8.440

Question 6.
Round 15.159 to the nearest ten.
Answer:

15.159 to the nearest ten ,1 becomes 2 so it is 15.200

Question 7.
Round 1.602 to the nearest whole number.
Answer:

1.602 to the nearest whole number is 2.0

Question 8.
Round 3.619 to the nearest tenth.
Answer:

3.619 to the nearest tenth, so 6 becomes 7 it is 3.700

Question 9.
Round 4.183.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:

Round 4.183.
Nearest whole number:4.000
Nearest tenth:4.200
Nearest hundredth:4.200

Question 10.
Round 9.076.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:

Round 9.076.
Nearest whole number:9.000
Nearest tenth:9.100
Nearest hundredth:9.080

Name the place value to which each number was rounded.
Question 11.
16.932 to 20
Answer:

16.932 at Tens value it is rounded  so it becomes 20

Question 12.
0.581 to 0.58
Answer:

0.581 to 0.58

0.581 at Thousandths value has been rounded so 0.58

Question 13.
7.429 to 7.4
Answer:

7.429 to 7.4

7.429 at Hundredths value has been rounded so 7.4

Question 14.
Structure
Round ★ to the nearest tenth.

Answer:

the nearest tenth * in the number line is showing at 5.64

Question 15.
Precision
The area of a campground is exactly halfway between 25.9 acres and 26 acres. What is the area of the campground?
Answer:

Halfway of 25.9 and 26.0 is 25.90+25.60=51.50/2 = 25.75 acres

So the area of the campground is 25.75 acres.

Question 16.
Open-Ended
Name two different numbers that round to 3.8 when rounded to the nearest tenth.
Answer:

The two numbers that are round to 3.8 when rounded to the nearest tenth place the value becomes 4.0 and  3.90

Question 17.
Open-Ended
Name two different numbers that round to 7.42 when rounded to the nearest hundredth.
Answer:

The two numbers that round to 7.42 when rounded to the nearest hundredth place the value becomes 7.50 and 7.40

Use the table.

Question 18.
Modeling Real Life
Your science class designs and tests four model boats to find out how much weight they can hold without sinking. What is the greatest weight rounded to the nearest tenth that a boat can hold?
Answer:

Given weights held without sinking in kilograms are

0.694,0.605,0.592,0.547 among all the weights the greatest weight rounded to the nearest tenth that a boat can hold is (0.694) i.e  0.7 kilograms

Question 19.
Modeling Real Life
What is the least weight rounded to the nearest hundredth that a boat can hold?
Answer:

The least weight rounded to the nearest hundredth is (0.547)- o.5 kilograms a boat can hold

Review & Refresh

Find the product.
Question 20.
7 × 40
Answer:

The product of 7 X 40 = 280

Question 21.
5,000 × 9
Answer:

The product of 5,000 x 9 = 45,000

Question 22.
8 × 200
Answer:

The product of 8 x 200=1,600

Place Value Concepts Performance Task

There are 18 species of penguins. Scientists have estimated the populations of 16 penguin species.
Question 1.
What fraction of penguin species have unknown populations?
Answer:

Given total is 18 species of penguins out of which Scientists have estimated the populations of 16 penguin species. so unknown is 18-16/18=2/18,

so 2/18=1/9 of penguin species have unknown populations

Question 2.
Several species of penguins and their estimated populations and locations are shown.

a. Are there more emperor penguins or rockhopper penguins? Explain.
b. Which species of penguin has the greatest population? Explain.
c. About how many penguins live in Antarctica? Round your answer to the nearest hundred thousand.

d. The Galápagos penguin is an endangered species. There are about 1,000 times as many macaroni penguins as Galápagos penguins. About how many Galápagos penguins are there?
Answer:

a. Rock hopper penguins are more than Emperor

2,460,000>595,000 as  2,460,000 is greater than 595,000 so Rock hopper penguins are more

B. Macaroni species 18 x 10⁶ of penguin has the greatest population as compared to Emperor 595,000,Adelie 4,000,000+7,00,000+40,000=4,740,000 and

Rockhopper-2,460,000

among all the species Macaroni 18 x 10⁶– species is more.

C. Macaroni + Adelie + Rockhopper +Emperor

18,000,000+4,740,000+ 2,460,000 + 595,000 = 25,795,000

25,785,000  to the nearest hundred thousand is 26,000,000

So there are almost 26,000,000 penguins live in Antarctica.

d. 1,000 times as many macaroni penguins as Galápagos penguins is

18 x 10^{6  x} 1 x 1000 = 18 x 10⁹ 

So there are 18 x 10⁹ Galápagos penguins available

Place Value Concepts Activity

Place Value Plug In
Directions:
1. Players take turns.
2. On your turn, roll six dice. Arrange the dice into a six-digit number that matches one of the descriptions.
3. Write your number on the lines.
4. The first player to fill in all of the numbers wins!

Answer:

Place Value Concepts Chapter Practice

1.1 Place Value Patterns

Use a place value chart to answer the question.
Question 1.
What number is 10 times as great as 4,000?
Answer:

10 times as great as 4,000 is 10 x 4,000= 40,000

Question 2.
What number is \(\frac{1}{10}\) of 8,000?
Answer:

\(\frac{1}{10}\) of 8,000 is 8,000/10 = 800

Question 3.
10,000 is 10 times as great as what number?
Answer:

10,000 is 10 times as great as 1,000

Question 4.
70 is \(\frac{1}{10}\) of what number?
Answer:

70 is \(\frac{1}{10}\) of 700

Question 5.
Complete the table.

Answer:

300 is 10 times as great as 30  and 30 x 1/10 is 3

6,000 is 10 times as great as 600 and 600 x 1/10  is 60

90,000 is 10 times as great as 9,000 and 9,000 x 1/10 is 900

2,00,000 is 10 times as great as 20,000 and 20,000 x 1/10=2,000

Question 6.
YOU BE THE TEACHER
Your friend says 500 is 10 times as great as 5,000. Is your friend correct? Explain.
Answer:

No, My friend is wrong because  500 is not 10 times great as 5,000,

500 < 5,000.

1.2 Place Value with Whole Numbers

Question 7.
Write the number in two other forms.
Standard form: 456,701
Word form:
Expanded form:
Answer:

Word form: Four hundred fifty six thousand, seven hundred and one
Expanded form:4 x 100000 + 5 x 10000 + 6 x 1000 + 7 x 100 + 1

Question 8.
Write the number in two other forms.
Standard form:
Word form: Eight million, sixty thousand, five hundred seventy-three
Expanded form:
Answer:

Standard form:8,060,573
Expanded form:8 x 1000000+6 x 10000 + 5 x 100 + 7 x 10 + 3

Question 9.
Compare the values of the 4s in the number 900,441,358.
Answer:

4s value is at lakh or hundred thousandths place and another 4s place is at ten thousandths place.

Question 10.
Write the values of the 6s in the number 96,672.
Answer:

The values of the 6s in the number 96,672 are

6s place is at thousand and another 6s is at hundreds place

Compare.
Question 11.

Answer:

83,802 > 83,082

The value at hundred 8 is more/great to 0 at hundreds place

Question 12.

Answer:

2,498,576 > 2,477,583

The value at 9 at ten thousands place is more/great than 7 at ten thousands place

1.3 Patterns and Powers of 10

Question 13.
Write 10 × 10 as a power.
Answer:

10 × 10 as a power is 10²

Find each product. Use patterns to help.
Question 14.
4 × 10 = _____
4 × 100 = ______
4 × 1,000 = _____
4 × 10,000 = ______
Answer:

4 × 10 = 40
4 × 100 = 400
4 × 1,000 = 4,000
4 × 10,000 =40,000

Question 15.
3 × 10 = _____
3 × 100 = ______
3 × 1,000 = _____
3 × 10,000 = ______
Answer:

3 × 10 = 30
3 × 100 = 300
3 × 1,000 = 3,000
3 × 10,000 = 30,000

Question 16.
7 × 10 = _____
7 × 100 = ______
7 × 1,000 = _____
7 × 10,000 = ______
Answer:

7 × 10 = 70
7 × 100 = 700
7 × 1,000 = 7,000
7 × 10,000 = 70,000

Find the value of the expression.
Question 17.
10⁵
Answer:

10⁵=1,00,000

Question 18.
8 × 10¹
Answer:

8 × 10¹⁼ 8 x 10 = 80

Question 19.
7 × 10⁴
Answer:

7 × 10⁴ = 7 x  10 x 10 x 10 x 10= 70,000

Question 20.
3 × 10⁵
Answer:

3 × 10⁵ = 3 X 10 X 10 X 10 X 10 X 10=3,00,000

Rewrite the number as a whole number multiplied by a power of 10.
Question 21.
5,000
Answer:

5,000= 5 X 10³

Question 22.
600,000
Answer:

6,00,000= 6 X 10⁵

Question 23.
90
Answer:

90= 90 X 10¹

1.4 Decimals to Thousandths

Write the decimal as a fraction.
Question 24.
0.062
Answer:

0.062= 62 X 1/1,000

Question 25.
0.008
Answer:

0.008= 8 X 1/1,000

Question 26.
0.195
Answer:

0.195= 195 X 1/1,000

Write the fraction as a decimal.
Question 27.
\(\frac{2}{1,000}\)
Answer:

\(\frac{2}{1,000}\) = 2 x 1/1,000= 0.002

Question 28.
\(\frac{37}{1,000}\)
Answer:

\(\frac{37}{1,000}\) = 37 x 1/1,000= 0.037

Question 29.
\(\frac{409}{1,000}\)
Answer:

\(\frac{409}{1,000}\)= 409/1,000=0.409

Question 30.
0.0.7 is 10 times as great as what number?
Answer:

0.07 is 10 times great as 0.007

Question 31.
0.04 is \(\frac{1}{10}\) of what number?
Answer:

0.04 is \(\frac{1}{10}\) of 0.4

1.5 Place Value with Decimals

Write the number in two other forms.
Question 32.
Standard form:
Word form:
Expanded form: 5 × 1 + 3 × \(\frac{1}{10}\) + 8 × \(\frac{1}{100}\) + 4 × \(\frac{1}{1,000}\)
Answer:

Standard form:5+0.3+0.08+0.004=5.384
Word form: five and three tenths, eight hundredths and 4 thousandths

Question 33.
Standard form: 2.059
Word form:
Expanded form:
Answer:

Word form: two and five hundredths and nine thousandths

Expanded form: 2 x 1 + 5 x 1/100 + 9 x 1/1000

Question 34.
Compare the values of the 5s in the number 1.055.
Answer:

5s value is at hundredths and another 5s value is at thousandths place

Question 35.
Compare the values of the 8s in the number 6.884.
Answer:

8s place value is at tenths value and other 8s place value is at hundredths place

1.6 Compare Decimals

Compare.
Question 36.

Answer:

15.891 > 15.791

the 8 value at tenths place is greater than 7 at tenths place

Question 37.

Answer:

8.205 < 8.250

the 0 at hundredths is less than 5 at hundredths

Question 38.

Answer:

Both are same

3.600 = 3.6

Order the decimals from least to greatest.
Question 39.
7.008, 7.09, 7.180
Answer:

7.008<7.09

7.09 <7.18

so the decimals from least to greatest are 7.008 , 7.09, 7.180

Question 40.
50.426, 50.42, 50
Answer:

50 < 50.42

50.42 < 50.426

so the decimals from least to greatest are 50, 50.42, 5.0426

Question 41.
Modeling Real Life
Newton weighs a treat at the pet store. He says it weighs less than 0.519 ounce but more than 0.453 ounce. Which treats could he have weighed?

Answer:

Newton says it weighs less than 0.519 ounce  but more than 0.453 ounce,

so Blue berry waffle 0.512 which is in between 0.453<0.512<0.519

and We have more than 0.453 is 0.459 ounce which is Peanut butter and is less than 0.519 ounce

So Peanut butter 0.453 is in between 0.453<0.459<0.519

so newton would have weighed Peanut butter 0.459 ounce

and it can be even Blueberry  waffle 0.512  ounce

newton’s treats could be Peanut butter ,Blueberry waffle

1.7 Round Decimals

Round the number to the place of the underlined digit.
Question 42.
9.514
Answer:

if 9 is digit then it is rounded as 9.0

if 5 then  it is rounded as 9.500

if 1 then it is rounded as 9.520

if  4 then it is rounded as 9.520,9.510

Question 43.
1.027
Answer:

1.027 at 2 it is rounded as 1.03

Question 44.
8.469
Answer:

8.469, 8 is rounded as 8.500 or 8 or 8.000

Question 45.
32.501
Answer:

in 32.501

3 is rounded as  30.000

2- 33.000

5- 32.6 or 33

0-32.5

1 -32.500

Question 46.
Round 0.176 to the nearest
Answer:

0.200

Question 47.
Round 6.538 to the nearest tenth. hundredth.
Answer:

6.500 

Question 48.
Round 7.425.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:

Nearest whole number:8.000, 8
Nearest tenth:7.500
Nearest hundredth:7.430

Question 49.
Round 2.108.
Nearest whole number:
Nearest tenth:
Nearest hundredth:
Answer:

Nearest whole number:2.000, 2
Nearest tenth:2.100
Nearest hundredth:2.100

Final Words:

It is very important for the students to understand and learn the fundamentals at the primary level itself. Here we have prepared the questions as per the latest edition 2019. Keep the textbook aside and try to solve the problems by referring to our Big Ideas Math Answers Grade 5 Chapter 1 Place Value Concepts. To make you comfortable we have provided the solution key for Big Ideas Math Grade 5 Chapter 1 Place Value Concepts in the pdf format. Stay tuned to our CCSS Math Answers to get the latest updates of BIM Grade 5 Chapters.

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Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 8 Problem Set Answer Key

Question 1.
Draw an array that shows 5 rows of 3.

Explanation:
Drawn an array that shows 5 rows of 3 as
5 X 3 as shown above.

Question 2.
Draw an array that shows 3 rows of 5.

Explanation:
Drawn an array that shows 3 rows of 5 as
3 X 5 as shown above.

Question 3.
Write multiplication expressions for the arrays in
Problems 1 and 2. Let the first factor in each expression
represent the number of rows. Use the commutative property
to make sure the equation below is true.

Explanation:
Wrote multiplication expressions for the arrays in
Problems 1 and 2 as 5 X 3, 3 X 5 and let the first factor
in each expression represent the number of rows.
Used the commutative property to make sure the equation
below is true as 5 X 3 = 15, 3 X 5 = 15,
So,  5 X 3 = 3 X 5 is true equals to 15.

Question 4.
Write a multiplication sentence for each expression.
You might skip-count to find the totals. The first one is done for you.
a. 2 threes: 2 × 3 = 6
b. 3 twos: _________________
c. 3 fours: ________________
d. 4 threes: ________________
e. 3 sevens: ________________
f. 7 threes: ________________
g. 3 nines: _________________
h. 9 threes: ________________
i. 10 threes: _______________

b. 3 twos : 3 x 2 = 6,
Explanation:
Given 3 twos, 3 multiplied by 2 gives 6,
So, 3 X 2 = 6.

c. 3 fours: 3 X 4 = 12,
Explanation:
Given 3 fours, 3 multiplied by 4 gives 12,
So, 3 X 4 = 12.

d. 4 threes: 4 X 3 = 12,
Explanation:
Given 4 threes, 4 multiplied by 3 gives 12,
So, 4 X 3 = 12.

e. 3 sevens:  3 x 7 = 21,
Explanation:
Given 3 sevens, 3 multiplied by 7 gives 21,
So, 3 X 7 = 21.

f. 7 threes:  7 X 3 = 21,
Explanation:
Given 7 threes, 7 multiplied by 3 gives 21,
So, 7 X 3 = 21.

g. 3 nines: 3 X 9 = 27,
Explanation:
Given 3 nines, 3 multiplied by 9 gives 27,
So, 3 X 9 = 27.

h. 9 threes: 9 X 3 = 27,
Explanation:
Given 9 threes, 9 multiplied by 3 gives 27,
So, 9 X 3 = 27.

i. 10 threes: 10 x 3 =30,
Explanation:
Given 10 threes, 10 multiplied by 3 gives 30,
So, 10 X 3 = 30.

Question 5.
Find the unknowns that make the equations true.
Then, draw a line to match related facts.
a. 3 + 3 + 3 + 3 + 3 = _________
b. 3 × 9 = _________
c. 7 threes + 1 three = _________
d. 3 × 8 = _________
e. _________ = 5 × 3
f. 27 = 9 × _________

a. 3 + 3 + 3 + 3 + 3 = 15,

Explanation:
Given 3 + 3 + 3 + 3 + 3  adding 3, 5 times gives 15,
So 3 + 3 + 3 + 3 + 3 = 15.

b. 3 × 9 = 27,

Explanation:
Given 3 X 9, 3 multiplied by 9 gives 27,
So 3 X 9 = 27.

c. 7 threes + 1 three = 8 threes = 24,

Explanation:
Given 7 threes + 1 three = 7 X 3 + 1 X 3 = 21 + 3 = 24,
So, 7 threes + 1 three = 8 threes = 24.

d. 3 X 8 = 24,

Explanation:
Given 3 X 8, 3 multiplied by 8 gives 24,
So 3 X 8 = 24.

e. 15 = 5 × 3,

Explanation:
Given 5 X 3, 5 multiplied by 3 gives 15,
So 15 = 5 X 3.

f. 27 = 9 × 3

Explanation:
Given 27 = 9 X ___, Lets take missing number as x,
27 = 9 X x, So x = 27 ÷ 9 = 3, So 27 = 9 X 3.

Question 6.
Isaac picks 3 tangerines from his tree every day for 7 days.
a. Use circles to draw an array that represents the
tangerines Isaac picks.

Explanation:
Given Isaac picks 3 tangerines from his tree
every day for 7 days.
a. Used circles to draw an array that represents the
tangerines Isaac picks as 3 X 7 as shown above.

b. How many tangerines does Isaac pick in 7 days?
Write and solve a multiplication sentence to find the total.

Isaac picks 21 tangerines in 7 days,
Multiplication sentence to find the total is 3 x 7 = 21.

Explanation:
Wrote and solved a multiplication sentence to
find the total as 3 x 7 = 21,
therefore Isaac picks 21 tangerines in 7 days.

c. Isaac decides to pick 3 tangerines every day for 3 more days.
Draw x’s to show the new tangerines on the array in Part (a).

Explanation:
Given Isaac decides to pick 3 tangerines every day for 3 more days.
Drawn  x’s to show the new tangerines on the array in Part (a) as
shown above in the picture.

d. Write and solve a multiplication sentence to
find the total number of tangerines Isaac picks.

Multiplication sentence is 3 x 10 =
(3 X 7) + (3 X 3) = 21 + 9 = 30,
The total number of tangerines Isaac picks are 30,

Explanation:
Wrote and solved a multiplication sentence as
3 x 10 = (3 X 7) + (3 X 3) = 21 + 9 = 30,
Therefore the total number of tangerines Isaac picks are 30.

Question 7.
Sarah buys bottles of soap. Each bottle costs $2.
a. How much money does Sarah spend if she buys 3 bottles of soap?
_____$2_____ × ____3______ = $___6_____
b. How much money does Sarah spend if she buys 6 bottles of soap?
_____$2_____ × _____6_____ = $__12______

a. Sarah spends $6 if she buys 3 bottles of soap,

Explanation:
Given Sarah buys bottles of soap. Each bottle costs $2,
So money spent by Sarah if she buys 3 bottles of soap are
$2 X 3 = $6.

b. Sarah spends $12 if she buys 6 bottles of soap,

Explanation:
Given Sarah buys bottles of soap. Each bottle costs $2,
So money spent by Sarah if she buys 6 bottles of soap are
$2 X 6 = $12.

Eureka Math Grade 3 Module 1 Lesson 8 Exit Ticket Answer Key

Mary Beth organizes stickers on a page in her sticker book.
She arranges them in 3 rows and 4 columns.
a. Draw an array to show Mary Beth’s stickers.
b. Use your array to write a multiplication sentence to
find Mary Beth’s total number of stickers.
c. Label your array to show how you skip-count to
solve your multiplication sentence.
d. Use what you know about the commutative property
to write a different multiplication sentence for your array.

a.
Explanation:
Given Mary Beth organizes stickers on a page in
her sticker book. She arranges them in 3 rows and
4 columns.
Drawn an array as 3 X 4 to show Mary Beth’s stickers.

b. Mary Beth’s total number of stickers are 12,

Explanation:
Used my array to write a multiplication sentence as 3 X 4 = 12,
in finding Mary Beth’s total number of stickers.

c.

Explanation:
Labeled my array to show skip-count to 12 and
solved my multiplication sentence as 3 x 4 = 12.

d. Commutative property to write a different
multiplication sentence for my array is 3 X 4 = 4 x 3,

Explanation:
Used what I know about the commutative property
to write a different multiplication sentence for my array as
3 X 4 = 4 x 3.

Eureka Math Grade 3 Module 1 Lesson 8 Homework Answer Key

Question 1.
Draw an array that shows 6 rows of 3.

Explanation:
Drawn an array that shows 6 rows of 3 as
6 X 3 as shown above.

Question 2.
Draw an array that shows 3 rows of 6.

Explanation:
Drawn an array that shows 3 rows of 6 as
3 X 6 as shown above.

Question 3.
Write multiplication expressions for the arrays in
Problems 1 and 2. Let the first factor in each expression
represent the number of rows. Use the commutative property
to make sure the equation below is true.


Explanation:
Wrote multiplication expressions for the arrays in
Problems 1 and 2 as 6 X 3, 3 X 6 and let the first factor
in each expression represent the number of rows.
Used the commutative property to make sure the equation
below is true as 6 X 3 = 18, 3 X 6 = 18,
So,  6 X 3 = 3 X 6 is true equals to 18.

Question 4.
Write a multiplication sentence for each expression.
You might skip-count to find the totals. The first one is done for you.
a. 5 threes: 5 × 3 = 15
b. 3 fives: __________________
c. 6 threes: ________________
d. 3 sixes: ___________________
e. 7 threes: __________________
f. 3 sevens: __________________
g. 8 threes: ________________
h. 3 nines: _________________
i. 10 threes: _______________

b. 3 fives: 3 X 5 = 15,

Explanation:
Given 3 fives, 3 multiplied by 5 gives 15,
So, 3 X 5 = 15.

c. 6 threes: 6 X 3 = 18,

Explanation:
Given 6 threes, 6 multiplied by 3 gives 18,
So, 6 X 3 = 18.

d. 3 sixes: = 3 X 6 = 18,

Explanation:
Given 3 sixes, 3 multiplied by 6 gives 18,
So, 3 X 6 = 18.

e. 7 threes: 7 X 3 = 21,

Explanation:
Given 7 threes, 7 multiplied by 3 gives 21,
So, 7 X 3 = 21.

f. 3 sevens: 3 X 7 = 21,

Explanation:
Given 3 sevens, 3 multiplied by 7 gives 21,
So, 3 X 7 = 21.

g. 8 threes: 8 X 3 = 24,

Explanation:
Given 8 threes, 8 multiplied by 3 gives 24,
So, 8 X 3 = 24.

h. 3 nines: 3 X 9 = 27,

Explanation:
Given 3 nines, 3 multiplied by 9 gives 27,
So, 3 X 9 = 27.

i. 10 threes: 10 X 3 = 30,

Explanation:
Given 10 threes, 10 multiplied by 3 gives 30,
So, 10 X 3 = 30.

Question 5.
Find the unknowns that make the equations true. Then, draw a line to match related facts.
a. 3 + 3 + 3 + 3 + 3 + 3 = _________
b. 3 × 5 = _________
c. 8 threes + 1 three = _________
d. 3 × 9 = _________
e. _________ = 6 × 3
f. 15 = 5 × _________

a. 3 + 3 + 3 + 3 + 3 + 3 = 18,

Explanation:
Given 3 + 3 + 3 + 3 + 3 + 3 adding 3, 6 times gives 18,
So 3 + 3 + 3 + 3 + 3 + 3 = 18.

b. 3 × 5 = 15,

Explanation:
Given 3 X 5, 3 multiplied by 5 gives 15,
So 3 X 5 = 15.

c. 8 threes + 1 three =9 threes = 27,

Explanation:
Given 8 threes + 1 three = 8 X 3 + 1 X 3 = 24 + 3 = 27,
So, 8 threes + 1 three = 9 threes = 27.

d. 3 X 9 = 27,

Explanation:
Given 3 X 9, 3 multiplied by 9 gives 27,
So 3 X 9 = 27.

e. 18 = 6 × 3,

Explanation:
Given 6 X 3, 6 multiplied by 3 gives 18,
So 18 = 6 X 3.

f. 15 = 5 × 3,

Explanation:
Given 15 = 5 X ___, Lets take missing number as x,
15 = 5 X x, So x = 15 ÷ 5 = 3, So 15 = 5 X 3.

Question 6.
Fernando puts 3 pictures on each page of his photo album.
He puts pictures on 8 pages.
a. Use circles to draw an array that represents the total number
of pictures in Fernando’s photo album.
b. Use your array to write and solve a multiplication sentence
to find Fernando’s total number of pictures.
c. Fernando adds 2 more pages to his book. He puts 3 pictures
on each new page. Draw x’s to show the new pictures on
the array in Part (a).
d. Write and solve a multiplication sentence to find the new
total number of pictures in Fernando’s album.
a.

Explanation:
Given Fernando puts 3 pictures on each page of his photo album.
He puts pictures on 8 pages.
a. Used circles to draw an array that represents the total number
of pictures in Fernando’s photo album as 3 X 8.

b. Multiplication sentence for Fernando’s total number
of pictures is 3 X 8 = 24,

Explanation:
Used my array to write and solve a multiplication sentence
to find Fernando’s total number of pictures as 3 X 8 = 24.

c.

Explanation:
Fernando adds 2 more pages to his book. He puts 3 pictures
on each new page. Drawn x’s to show the new pictures on
the array in Part (a) as shown above.

d. Multiplication sentence is 3 x 10 =
(3 X 8) + (3 X 2) = 24 + 6 = 30,
The new total number of pictures in Fernando’s album are 30,

Explanation:
Wrote and solved a multiplication sentence as
3 x 10 = (3 X 8) + (3 X 2) = 24 + 6 = 30,
Therefore the new total number of pictures in Fernando’s album are 30.

Question 7.
Ivania recycles. She gets 3 cents for every can she recycles.
a. How much money does Ivania make if she recycles 4 cans?
____3______ × ___4_______ = ___12_____ cents
b. How much money does Ivania make if she recycles 7 cans?
____3______ × ____7______ = ____21____ cents

a. Ivania makes 12 cents if she recycles 4 cans,

Explanation:
Given Ivania recycles and she gets 3 cents for every can she recycles,
So money Ivania makes if she recycles 4 cans is
3 cents X 4 = 12 cents.

b. Ivania makes 21 cents if she recycles 7 cans,

Explanation:
Given Ivania recycles and she gets 3 cents for every can she recycles,
So money Ivania makes if she recycles 7 cans is
3 cents X 7 = 21 cents.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 7 Problem Set Answer Key

Question 1.
a. Draw an array that shows 6 rows of 2.
b. Write a multiplication sentence where the
first factor represents the number of rows.
________ × ________ = ________
a.

Explanation:
Drawn an array that shows 6 rows of 2 as
6 X 2 as shown above in the picture.

b. Multiplication sentence where the first factor represents
the number of rows as 6 X 2 = 12.

Explanation:
Wrote a multiplication sentence where the first factor represents
the number of rows as 6 X 2 = 12.

Question 2.
a. Draw an array that shows 2 rows of 6.
b. Write a multiplication sentence where the first factor
represents the number of rows.
____2____ × ____6____ = ___12_____
a.

Explanation:
Drawn an array that shows 2 rows of 6 as
2 X 6 as shown above in the picture.

b. Multiplication sentence where the first factor represents
the number of rows as 2 X 6 = 12.

Explanation:
Wrote a multiplication sentence where the first factor represents
the number of rows as 2 X 6 = 12.

Question 3.
a. Turn your paper to look at the arrays in Problems 1
and 2 in different ways. What is the same and what is
different about them?
b. Why are the factors in your multiplication sentences
in a different order?

a. Same is the result because both have the same value as 12,
Different is number of rows and number of columns are
not the same,

Explanation:
Turned my paper to look at the arrays in Problems 1
and 2 in different ways.
Is the same because both got same results as 12
and different about them is in problems 1 and 2
the number of rows and number of columns are not the same
as one is 6 rows X 2 columns  and in other it is  2 rows X 6 columns.

b. The factors in my multiplication sentences are
in a different order because first we are taking
6 rows X 2 columns and in other it is  2 rows X 6 columns.

Explanation:
The factors in my multiplication sentences are
in a different order because first we are taking
6 rows X 2 columns  and in other it is  2 rows X 6 columns,
So, rows and columns differ in the both.

Question 4.
Write a multiplication sentence for each expression.
You might skip-count to find the totals.

Explanation:
Wrote a multiplication sentence for each expression as
shown above, might have skipped-count to find the totals.

Question 5.
Write and solve multiplication sentences where the
second factor represents the size of the row.

Explanation:
Wrote and solved multiplication sentences where the
second factor represents the size of the row as
2 X 4 = 8 and 4 X 2= 8.

Question 6.
Ms. Nenadal writes 2 × 7 = 7 × 2 on the board.
Do you agree or disagree? Draw arrays to help
explain your thinking.

Yes, I agree Ms. Nenadal writings as 2 X 7 = 7 X 2,

Explanation:
Given Ms. Nenadal writes 2 X 7 = 7 X 2 on the board,
Yes, I agree because 2 X 7 = 14 and 7 x 2 = 14,
Drawn arrays to help and explained my thinking
as shown above.

Question 7.
Find the missing factor to make each equation true.

Explanation:
Found the missing factor to make each equations true as below
5 X 2 = 2 X 5,
As each equation is true, so the missing factor in 2 X ___ is 5
as LHS is equal to RHS, So 5 X 2 = 2 X 5.

2 X 8 = 8 X 2,
As each equation is true, so the missing factor in ___ X 8 is 2
as LHS is equal to RHS, So 2 X 8 = 8 X 2.

2 X 10 = 10 X 2,
As each equation is true, so the missing factor in ___ X 2  is 10
as LHS is equal to RHS, So 2 X 10 = 10 X 2.

2 X 9 = 9 X 2,
As each equation is true, so the missing factor in 2 X ___ is 9
as LHS is equal to RHS, So 2 X 9 = 9 X 2.

Question 8.
Jada gets 2 new packs of erasers. Each pack has 6 erasers in it.
a. Draw an array to show how many erasers Jada has altogether.
b. Write and solve a multiplication sentence to describe the array.
c. Use the commutative property to write and solve a different
multiplication sentence for the array.

a.

Jada has 12 erasers altogether,

Explanation:
Given Jada gets 2 new packs of erasers. Each pack has 6 erasers in it.
So, drawn an array to show 2 X 6 = 12 number of erasers
Jada has altogether.

b. Multiplication sentence is 2 X 6 = 12, the array has
12 erasers.

Explanation:
Wrote and solved a multiplication sentence as
2 X 6 = 12 erasers, describing the array as 2 packs in rows
and 6 erasers in columns, So 2 packs X 6 erasers = 12 erasers.

c.  Commutative property for multiplication sentence
for the array is 2 X 6 = 6 X 2 = 12.

Explanation:
Used the commutative property to write and solve a different
multiplication sentence for the array as 2 X 6 = 6 x 2 = 12 erasers.

Eureka Math Grade 3 Module 1 Lesson 7 Exit Ticket Answer Key

Do you agree or disagree with the statement in the box?
Draw arrays and use skip-counting to explain your thinking.

Yes, I agree with the statement in the box as 2 x 5 = 5 X 2,

Explanation:
Yes, I agree or disagree with the statement in the box
as 2 X 5 = 10 = 5 X 10,
Drawn arrays and used skip-counting as 2 X 5 = 10 = 5 X 10.

Eureka Math Grade 3 Module 1 Lesson 7 Homework Answer Key

Question 1.
a. Draw an array that shows 7 rows of 2.
b. Write a multiplication sentence where the first factor
represents the number of rows.
____7____ × ___2____ = ____14____

Explanation:
Drawn an array that shows 7 rows of 2 as
7 X 2 as shown above in the picture.

b. Multiplication sentence where the first factor represents
the number of rows as 7 X 2 = 14.

Explanation:
Wrote a multiplication sentence where the first factor represents
the number of rows as 7 X 2 = 14.

Question 2.
a. Draw an array that shows 2 rows of 7.
b. Write a multiplication sentence where the first factor
represents the number of rows.
____2____ × ___7_____ = ___14____

Explanation:
Drawn an array that shows 2 rows of 7 as
2 X 7 as shown above in the picture.

b. Multiplication sentence where the first factor represents
the number of rows as 2 X 7 = 14.

Explanation:
Wrote a multiplication sentence where the first factor represents
the number of rows as 2 X 7 = 14.

Question 3.
a. Turn your paper to look at the arrays in Problems 1 and 2
in different ways. What is the same and what is different about them?
b. Why are the factors in your multiplication sentences in a different order?

a. Same is the result because both have the same value as 14,
Different is number of rows and number of columns are
not the same,

Explanation:
Turned my paper to look at the arrays in Problems 1
and 2 in different ways.
Is the same because both got same results as 14
and different about them is in problems 1 and 2
the number of rows and number of columns are not the same
as one is 7 rows X 2 columns  and in other it is  2 rows X 7 columns.

b. The factors in my multiplication sentences are
in a different order because first we are taking
7 rows X 2 columns and in other it is  2 rows X 7 columns.

Explanation:
The factors in my multiplication sentences are
in a different order because first we are taking
7 rows X 2 columns  and in other it is  2 rows X 7 columns,
So, rows and columns differ in the both.

Question 4.
Write a multiplication sentence to match the number of groups.
Skip-count to find the totals. The first one is done for you.


Explanation:
Wrote a multiplication sentence to match the number of groups
as shown above, might have skipped-count to find the totals.

Question 5.
Write and solve multiplication sentences where
the second factor represents the size of the row.


Explanation:
Wrote and solved multiplication sentences where the
second factor represents the size of the row as
2 X 6 = 12 and 6 X 2= 12.

Question 6.
Angel writes 2 × 8 = 8 × 2 in his notebook.
Do you agree or disagree? Draw arrays to help
explain your thinking.

Explanation:
Given Angel writes 2 X 8 = 8 X 2 in his notebook,
Yes, I agree because 2 X 8 = 16 and 8 x 2 = 16,
Drawn arrays to help and explained my thinking
as shown above.

Question 7.
Find the missing factor to make each equation true.


Explanation:
Found the missing factor to make each equations true as below
2 X 6 = 6 X 2,
As each equation is true, so the missing factor in 6 X ___ is 2
as LHS is equal to RHS, So 2 X 6 = 6 X 2.

7 X 2 = 2 X 7,
As each equation is true, so the missing factor in ___ X 2 is 7
as LHS is equal to RHS, So 7 X 2 = 2 X 7.

9 X 2 = 2 X 9,
As each equation is true, so the missing factor in ___ X 9 is 2
as LHS is equal to RHS, So 9 X 2 = 2 X 9.

2 X 10 = 10 X 2,
As each equation is true, so the missing factor in 2 X ___ is 10
as LHS is equal to RHS, So 2 X 10 = 10 X 2.

Question 8.
Tamia buys 2 bags of candy.
Each bag has 7 pieces of candy in it.
a. Draw an array to show how many pieces of
candy Tamia has altogether.
b. Write and solve a multiplication sentence to
describe the array.
c. Use the commutative property to write and solve a
different multiplication sentence for the array.

a.

Tamia has 14 candy’s altogether,

Explanation:
Given Tamia buys 2 bags of candy. Each bag has
7 pieces of candy in it.
So, drawn an array to show 2 X 7 = 14 number of candy’s
Tamia has altogether.

b. Multiplication sentence is 2 X 7 = 14, the array has
14 candy’s.

Explanation:
Wrote and solved a multiplication sentence as
2 X 7 = 14 candy’s, describing the array as 2 bags in rows
and 7 candy’s in columns, So 2 bags X 7 candy’s = 14 candy’s.

c.  Commutative property for multiplication sentence
for the array is 2 X 7 = 7 X 2 = 14.

Explanation:
Used the commutative property to write and solve a different
multiplication sentence for the array as 2 X 7 = 7 x 2 = 14 candy’s.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 6 Problem Set Answer Key

Question 1.
Rick puts 15 tennis balls into cans. Each can holds 3 balls.
Circle groups of 3 to show the balls in each can.

Rick needs ____5___ cans.
___5___ × 3 = 15
15 ÷ 3 = __5____

Rick needs 5 cans,

Explanation:
Given Rick puts 15 tennis balls into cans and each can
holds 3 balls. Circled groups of 3 to show the balls in each can.
Rick needs 15 ÷ 3 = 5, 5 X 3 = 15,
Therefore Rick needs 5 cans.

Question 2.
Rick uses 15 tennis balls to make 5 equal groups.
Draw to show how many tennis balls are in each group.
There are ____3___ tennis balls in each group.
5 × __3____ = 15
15 ÷ 5 = ___3___

There are 3 tennis balls in each group.

Explanation:
Given Rick uses 15 tennis balls to make 5 equal groups.
Drawn circles to show 3 number of tennis balls are in
each group as 15 ÷ 5 = 3, 5 X 3 = 15,
Therefore, there are 3 tennis balls in each group.

Question 3.
Use an array to model Problem 1.
a. ___5___ × 3 = 15
15 ÷ 3 = ___5___
The number in the blanks represents
_____5 groups___________________.

Explanation:
Used an array to model Problem 1 as
5 X 3 = 15 or 15 ÷ 3 = 5,
The number in the blanks represents groups as
5 groups of balls.

b. 5 × __3____ = 15
15 ÷ 5 = __3____
The number in the blanks represents
____________3 balls in each group________.

The number in the blanks represents 3 balls in each group,

Explanation:
Rick uses 15 tennis balls to make 5 equal groups,
15 ÷ 5 = 3 or 5 X 3= 15, The number in the blanks
represents 3 balls in each group.

Question 4.
Deena makes 21 jars of tomato sauce. She puts 7 jars in
each box to sell at the market. How many boxes does Deena need?
21 ÷ 7 = __3____
___3___ × 7 = 21
What is the meaning of the unknown factor and quotient?
_________3______________

Deena needs 3 boxes,

Explanation:
Given Deena makes 21 jars of tomato sauce and she
puts 7 jars in each box to sell at the market.
So number of boxes Deena needs are 21 ÷ 7 = 3, (3 X 7 = 21)
Therefore, Deena needs 3 boxes.

Question 5.
The teacher gives the equation 4 × __3__ = 12. Charlie
finds the answer by writing and solving 12 ÷ 4 = __3__.
Explain why Charlie’s method works.

Charlie method is 12 ÷ 4 = 3,

Explanation:
Given The teacher gives the equation 4 × ____ = 12.
Charlie finds the answer by writing and solving as
12 ÷ 4 = 3,
because multiplication and division are closely related,
given that division is the inverse operation of multiplication.
When we divide, we look to separate into equal groups,
while multiplication involves joining equal groups.
If we divide this product by one of the factors,
we get the other factor as a result. So Charlie uses
division method to solve missing factor in the given
equation as 3. So the equation is 4 X 3 = 12.

Question 6.
The blanks in Problem 5 represent the size of the groups.
Draw an array to represent the equations.

Explanation:
Drawn an array that represents the equations
as  4 X 3 = 12.

Eureka Math Grade 3 Module 1 Lesson 6 Exit Ticket Answer Key

Cesar arranges 12 notecards into rows of 6 for his presentation.
Draw an array to represent the problem.
12 ÷ 6 = ___2_____
____2____ × 6 = 12
What do the unknown factor and quotient represent?
___2 notecards in each row____

Explanation:
Given Cesar arranges 12 notecards into rows of
6 for his presentation.
Drawn an array to represent the problem as
12 ÷ 6 = 2, 2 X 6 = 12, means 6 rows  and 2 columns
as shown above, The unknown factor and quotient 2
represents 2 notecards in each row.

Eureka Math Grade 3 Module 1 Lesson 6 Homework Answer Key

Question 1.
Mr. Hannigan puts 12 pencils into boxes. Each box holds 4 pencils.
Circle groups of 4 to show the pencils in each box.

Mr. Hannigan needs ___3____ boxes.
___3___ × 4 = 12
12 ÷ 4 = __3____

Mr. Hannigan needs 3 boxes,

Explanation:
Given Mr. Hannigan puts 12 pencils into boxes.
Each box holds 4 pencils.
Circled groups of 4 to show the pencils in each box
as shown above, So Mr. Hannigan needs 12 ÷ 4 = 3 boxes,
( 3 x 4 = 12).

Question 2.
Mr. Hannigan places 12 pencils into 3 equal groups.
Draw to show how many pencils are in each group.
There are ___4____ pencils in each group.
3 × ___4___ = 12
12 ÷ 3 = ___4___

There are 4 pencils in each group,

Explanation:
Given Mr. Hannigan places 12 pencils into 3 equal groups,
Drawn to show 4 number of pencils are in each group
as 12 ÷ 3 = 4, 3 X 4 = 12, Therefore 4 pencils are there in each group.

Question 3.
Use an array to model Problem 1.
a. ___3___ × 4 = 12
12 ÷ 4 = ___3___
The number in the blanks represents
___________3 groups______________.
a.

The number in the blanks represents 3 groups,

Explanation:
Used an array to model Problem 1 as 3 x 4 = 12,
or 12 ÷ 4 = 3, therefore the number in the blanks
represents 3 groups.

b. 3 × ___4___ = 12
12 ÷ 3 = __4____
The number in the blanks represents
___________4 pencils in each group_____________.

The number in the blanks represents 4 pencils in each group,

Explanation:
Given Mr. Hannigan places 12 pencils into 3 equal groups.
12 ÷ 3 = 4 or 3 X 4= 12, The number in the blanks
represents 4 pencils in each group.

Question 4.
Judy washes 24 dishes. She then dries and stacks the dishes
equally into 4 piles. How many dishes are in each pile?
24 ÷ 4 = ___6____
4 × ___6_____ = 24
What is the meaning of the unknown factor and quotient?
__________6 dishes are in each pile____________________

There are 6 dishes in each pile,

Explanation:
Given Judy washes 24 dishes and she then dries and
stacks the dishes equally into 4 piles.
So number of dishes in each pile are 24 ÷ 4 = 6, or
4 X 6 = 24, The meaning of the unknown factor and
quotient is 6 dishes are there in each pile.

Question 5.
Nate solves the equation _____ × 5 = 15 by writing and
solving 15 ÷ 5 = ____. Explain why Nate’s method works.

Nate solves the equation as 3 X 5 = 15,

Explanation:
Given Nate solves the equation _____ × 5 = 15 by writing and
solving as 15 ÷ 5 = 3, Nate’s method is correct because in
the given equation ___ X 5 = 15 , we bring 5 to other side it becomes as
15 ÷ 5 = 3 now we check as 3 X 5 it becomes 15 only,
So Nate’s method work.

Question 6.
The blanks in Problem 5 represent the number of groups.
Draw an array to represent the equations.

Explanation:
Drawn an array to represent the equations as
3 X 5 = 15 or 15 ÷ 5 = 3 as shown in the picture above.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 1 Problem Set Answer Key

Question 1.
Fill in the blanks to make true statements.

a. 3 groups of five = ___15______
3 fives = ____15_____
3 × 5 = ___15______

3 groups of five = 15,
3 fives = 15,
3 X 5 = 15,

Explanation:
Given expressions as
3 groups of five means 3 X 5 = 15,
3 fives = 3 x 5 = 15 and
3 X 5 = 15 as 3 is multiplied by 5 we get 15.

b. 3 + 3 + 3 + 3 + 3 = __15___
5 groups of three = ___15______
5 × 3 = ____15_____

3 + 3 + 3 + 3 + 3 = 15,
5 groups of three = 15,
5 × 3 = 15,

Explanation:
Given expressions as
3 + 3 + 3 + 3 + 3 = 15 as 3 is added 5 times,
5 groups of three = 15 means 5  X 3 = 15,
5 X 3 = 15 as 5 is multiplied by 3 we get 15.

c. 6 + 6 + 6 + 6 = ___24________
____4___ groups of six = ___24_______
4 × __6____ = ____24______

6 + 6 + 6 + 6 = 24,
4 groups of six = 24,
4 X 6 = 24,

Explanation:
Given expressions as
6 + 6 + 6 + 6 = 24 as 6 is added 4 times,
4 groups of six = 24 means 4  X 6 = 24,
4 X 6 = 24 as 4 is multiplied by 6 we get 24.

d. 4 +__4__ + __4__ + __4__ + _4___ + __4__ = ___24______
6 groups of ____4____ = ____24_______
6 × __4____ = ____24______

4 + 4 + 4 + 4 + 4 + 4 = 24,
6 groups of 4 = 24,
6 x 4 = 24,

Explanation:
Given expressions as
4 + ___ + ___ +___ +___ +___ =  means by seeing the picture
4 is added 6 times as 4 + 4 + 4 + 4 + 4 + 4 we get 24,
6 groups of ______ =  means again by seeing the picture
6 X 4 we get 24, So 6 groups of 4 = 24,
6 X 4 = 24 as 6 is multiplied by 4 we get 24.

Question 2.
The picture below shows 2 groups of apples. Does the picture
show 2 × 3? Explain why or why not.

No, the picture does not show 2 X 3,

Explanation:
Given the picture below shows 2 groups of apples but
in the 2 groups the number of apples are not the same
as in group -1 we have 3 apples, group 2 we have 2 apples
in total there are 5 apples and 2 X 3 = 6 whose value is not
same as shown in the picture ,
So, the picture does not show 2 X 3.

Question 3.
Draw a picture to show 2 × 3 = 6.

Explanation:
Drawn a picture above to show 2 X 3 = 6 .

Question 4.
Caroline, Brian, and Marta share a box of chocolates.
They each get the same amount. Circle the chocolates below
to show 3 groups of 4. Then, write a repeated addition sentence
and a multiplication sentence to represent the picture.

Addition sentence is 4 + 4 + 4 = 12,
Multiplication sentence is 3 X 4 = 12,

Explanation:
Given Caroline, Brian, and Marta share a box of chocolates and
they each get the same amount as 12 ÷ 3 = 4 each.
Circled the chocolates above to show 3 groups of 4 and
wrote a repeated addition sentence as  4 + 4 + 4 = 12 and
a multiplication sentence to represent the picture as 3 X 4 = 12.

Eureka Math Grade 3 Module 1 Lesson 1 Exit Ticket Answer Key

Question 1.
The picture below shows 4 groups of 2 slices of watermelon.
Fill in the blanks to make true repeated addition and
multiplication sentences that represent the picture.

True repeated addition is 2 + 2 + 2 + 2 = 8,
Multiplication sentences is 4 X 2 = 8.

Explanation:
Given the picture above shows 4 groups of
2 slices of watermelon.
Filled in the blanks to make true repeated addition
as 2 + 2 + 2 + 2 = 8 and multiplication sentences that
represent the picture as 4 X 2 = 8.

Question 2.
Draw a picture to show 3 + 3 + 3 = 9. Then,
write a multiplication sentence to represent the picture.

Addition sentence is  3 + 3 + 3 = 9,
Multiplication sentences is 3 X 3 = 9.

Explanation:
Drawn a picture above as  3 groups of 3 birds  to show
3 + 3 + 3 = 9 and writing a multiplication sentence to
represent the picture as 3 X 3 = 9 birds in total.

Eureka Math Grade 3 Module 1 Lesson 1 Homework Answer Key

Question 1.
Fill in the blanks to make true statements.

a. 4 groups of five = ____20_____
4 fives = ___20______
4 × 5 = ____20_____

4 groups of five = 20,
4 fives = 20,
4 X 5 = 20,

Explanation:
Given expressions as
4 groups of five means 4 X 5 = 20,
4 fives = 4 x 5 = 20 and
4 X 5 = 20 as 4 is multiplied by 5 we get 20.

b. 5 groups of four = _________
5 fours = _________
5 × 4 = _________

5 groups of four = 20,
5 fours = 20,
5 X 4 = 20,

Explanation:
Given expressions as
5 groups of four means 5 X 4 = 20,
5 fours = 5 x 4 = 20 and
5 X 4 = 20 as 5 is multiplied by 4 we get 20.

c. 6 + 6 + 6 = ___18________
____3___ groups of six = ____18______
3 × __6____ = ____18______

6 + 6 + 6  = 18,
3 groups of 6 = 18,
3 x 6 = 18,

Explanation:
Given expressions as 6 + 6 + 6 = 18 as
6 is added 3 times we get 18,
_____ groups of six =  means again by seeing the picture
3 groups of 6 =  3 X 6 we get 18, So 3 groups of 6 = 18,
3 X 6 = 18 as 3 is multiplied by 6 we get 18.

d. 3 + __3__ + __3__ + __3__ + __3__ + __3__ = ___18____
6 groups of ____3____ = _____18______
6 × __3__ = ____18______

3 + 3 + 3 + 3 + 3 + 3 = 18,
6 groups of 3 = 18,
6 x 3 = 18,

Explanation:
Given expressions as
3 + ___ + ___ +___ +___ +___ =  means by seeing the picture
3 is added 6 times as 3 + 3 + 3 + 3 + 3 + 3 we get 18,
6 groups of ______ =  means again by seeing the picture
6 X 3 we get 18, So 6 groups of 3 = 18,
6 X 3 = 18 as 6 is multiplied by 3 we get 18.

Question 2.
The picture below shows 3 groups of hot dogs.
Does the picture show 3 × 3? Explain why or why not.

Yes, the picture shows 3 X 3,

Explanation:
Given the picture below shows 3 groups of of hot dogs,
In the 3 groups the number of hot dogs are the same as 3,
So in total we have 3 X 3 = 9 hotdogs in the picture
which matches with the given equation as 3 X 3 whose
value is also same 9, So, the picture shows 3 X 3.

Question 3.
Draw a picture to show 4 × 2 = 8,

Explanation:
Drawn picture of flowers as shown above to show 4 X 2 = 8.

Question 4.
Circle the pencils below to show 3 groups of 6.
Write a repeated addition and a multiplication sentence
to represent the picture.


Repeated addition sentence is 6 + 6 + 6 = 18,
Multiplication sentence is 3 X 6 = 18,

Explanation:
Circled the pencils above to show 3 groups of 6.
Wrote a repeated addition as 6 + 6 + 6 = 18 and
a multiplication sentence as 3 X 6 = 18 to represent the picture.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 5 Problem Set Answer Key

Question 1.

Divide 6 tomatoes into groups of 3.
There are ____2_____ groups of 3 tomatoes.
6 ÷ 3 = 2

There are 2 groups of 3 tomatoes,

Explanation:
Dividing 6 tomatoes into groups of 3 we get
6 ÷ 3 = 2 groups,
So there are 2 groups of 3 tomatoes.

Question 2.

Divide 8 lollipops into groups of 2.
There are ____4___ groups.
8 ÷ 2 = ___4____

There are 4 groups,

Explanation:
Dividing 8 lollipops into groups of 2 as
8 ÷ 2 = 4 we get 4 groups,
So, there are 4 groups of 2.

Question 3.

Divide 10 stars into groups of 5.
10 ÷ 5 = ___2____

There are 2 groups,

Explanation:
Dividing 10 stars into groups of 5 as
10 ÷ 5 = 2 we get 2 groups,
So, there are 2 groups of 5.

Question 4.

Divide the shells to show 12 ÷ 3 = ____4____,
where the unknown represents the number of groups.
How many groups are there? ___4_____

There are 4 groups,

Explanation:
Dividing 12 shells into groups of 3 as
12 ÷ 3 = 4 we get 4 groups,
So, there are 4 groups of 3.

Question 5.
Rachel has 9 crackers. She puts 3 crackers in each bag.
Circle the crackers to show Rachel’s bags.

a. Write a division sentence where the answer
represents the number of Rachel’s bags.
b. Draw a number bond to represent the problem.

Division sentence 9 ÷ 3 = 3,
Number of Rachel’s bags are 3,

Explanation:
Given Rachel has 9 crackers.
She puts 3 crackers in each bag.
Circled the crackers to show Rachel’s bags,
a. Division sentence 9 ÷ 3 = 3,
therefore, number of Rachel’s bags are 3.
b.

Explanation:
Drawn a number bond to represent the problem
as shown above

Question 6.
Jameisha has 16 wheels to make toy cars.
She uses 4 wheels for each car.
a. Use a count-by to find the number of cars
Jameisha can build. Make a drawing to match
your counting.
b. Write a division sentence to represent the problem.

a.

Number of cars Jameisha builds are 4,

Explanation:
Given Jameisha has 16 wheels to make toy cars.
She uses 4 wheels for each car.
Used a count-by to find the number of cars
Jameisha can build as 16 ÷ 4 = 4 cars,
Made a drawing to match my counting as shown above.

b. Division sentence to represent the problem is 16 ÷ 4 = 4 cars,

Explanation:
Given Jameisha has 16 wheels to make toy cars.
She uses 4 wheels for each car, So the division sentence
to represent the problem is 16 ÷ 4 = 4 cars.

Eureka Math Grade 3 Module 1 Lesson 5 Exit Ticket Answer Key

Question 1.
Divide 12 triangles into groups of 6.

12 ÷ 6 = ___2____

There are 2 groups of 6,

Explanation:
Dividing 12 triangles into groups of 6 as
12 ÷ 6 = 2 we get 2 groups,
So, there are 2 groups of 6.

Question 2.
Spencer buys 20 strawberries to make smoothies.
Each smoothie needs 5 strawberries.
Use a count-by to find the number of smoothies
Spencer can make.
Make a drawing to match your counting.

Spencer makes 4 smoothies,

Explanation:
Given Spencer buys 20 strawberries to make smoothies.
Each smoothie needs 5 strawberries.
Used a count-by the number of smoothies
Spencer can make are 20 ÷ 5 = 4,
Made a drawing to match my counting as
5 X 4 = 20 strawberries as shown above in the picture.

Eureka Math Grade 3 Module 1 Lesson 5 Homework Answer Key

Question 1.

Divide 4 triangles into groups of 2.
There are _____2____ groups of 2 triangles.
4 ÷ 2 = 2

There are 2 groups of 2 triangles,

Explanation:
Dividing 4 triangles into groups of 2 as
4 ÷ 2 = 2 we get 2 groups,
So, there are 2 groups of 2 triangles.

Question 2.

Divide 9 eggs into groups of 3.
There are ___3____ groups.
9 ÷ 3 = __3_____

There are 3 groups of 3 eggs,

Explanation:
Dividing 9 eggs into groups of 3 as
9 ÷ 3 = 3 we get 3 groups,
So, there are 3 groups of 3 eggs.

Question 3.

Divide 12 buckets of paint into groups of 3.
12 ÷ 3 = __4_____

There are 4 groups of 3 paint buckets,

Explanation:
Divided 12 buckets of paint into groups of 3 as
12 ÷ 3 = 4 we get 4 groups of paint buckets,
So, there are 4 groups of 3 paint buckets.

Question 4.

Group the squares to show 15 ÷ 5 = __3___,
where the unknown represents the number of groups.
How many groups are there? ____3____

There are 3 groups of 5 squares,

Explanation:
Grouped the squares to show 15 ÷ 5 = 3,
where the unknown represents the number of groups
as 3 groups of 5 squares.

Question 5.
Daniel has 12 apples. He puts 6 apples in each bag.
Circle the apples to find the number of bags Daniel makes.

a. Write a division sentence where the answer
represents the number of Daniel’s bags.
b. Draw a number bond to represent the problem.
a.

Daniel’s has 2 bags of 6 apples each,
Division sentence : 12 ÷ 6 = 2 bags,

Explanation:
Daniel has 12 apples and he puts 6 apples in each bag.
Circled the apples to find the number of bags Daniel makes
as 12 ÷ 6 = 2 bags,
a. Writing a division sentence where the answer
represents the number of Daniel’s bags as 12 ÷ 6 = 2 bags.

b.

Explanation:
Drawn a number bond to represent the problem as
shown above in the picture.

Question 6.
Jacob draws cats. He draws 4 legs on each
cat for a total of 24 legs.
a. Use a count-by to find the number of cats
Jacob draws. Make a drawing to match your counting.
b. Write a division sentence to represent the problem.

a.

The number of cats Jacob draws are 6,

Explanation:
Given Jacob draws cats. He draws 4 legs on each
cat for a total of 24 legs.
a. Used a count-by to find the number of cats
Jacob draws as 24 ÷ 4 = 6 cats,
Made a drawing to match my counting as shown above.

b. Division sentence is 24 ÷ 4 = 6 cats,

Explanation:
Wrote a division sentence to represent the problem as
24 ÷ 4 = 6 cats.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 14 Sprint Answer Key

A
Multiply or Divide by 3

Question 1.
2 × 3 =
2 X 3 = 6,

Explanation:
Given 2 X 3 we multiply 2 with 3,
we get 6 as 2 X 3 = 6.

Question 2.
3 × 3 =
3 X 3 = 9,

Explanation:
Given 3 X 3 we multiply 3 with 3,
we get 9 as 3 X 3 = 9.

Question 3.
4 × 3 =
4 X 3 = 12,

Explanation:
Given 4 X 3 we multiply 4 with 3,
we get 12 as 4 X 3 = 12.

Question 4.
5 × 3 =
5 X 3 = 15,

Explanation:
Given 5 X 3 we multiply 5 with 3,
we get 15 as 5 X 3 = 15.

Question 5.
1 × 3 =
1 X 3 = 6,

Explanation:
Given 1 X 3 we multiply 1 with 3,
we get 3 as 1 X 3 = 3.

Question 6.
6 ÷ 3 =
6 ÷ 3 = 2,

Explanation:
Given 6 ÷ 3 we divide 6 by 3,
we get 2 as 6 ÷ 3 = 2.

Question 7.
9 ÷ 3 =
9 ÷ 3 = 3,

Explanation:
Given 9 ÷ 3 we divide 9 by 3,
we get 3 as 9 ÷ 3 = 3.

Question 8.
15 ÷ 3 =
15 ÷ 3 = 5,

Explanation:
Given 15 ÷ 3 we divide 15 by 3,
we get 5 as 15 ÷ 3 = 5.

Question 9.
3 ÷ 1 =
3 ÷ 1 = 3,

Explanation:
Given 3 ÷ 1 we divide 3 by 1,
we get 3 as 3 ÷ 1 = 3.

Question 10.
12 ÷ 3 =
12 ÷ 3 = 4,

Explanation:
Given 12 ÷ 3 we divide 12 by 3,
we get 4 as 12 ÷ 3 = 4.

Question 11.
6 × 3 =
6 X 3 = 18,

Explanation:
Given 6 X 3 we multiply 6 with 3,
we get 18 as 6 X 3 = 18.

Question 12.
7 × 3 =
7 X 3 = 21,

Explanation:
Given 7 X 3 we multiply 7 with 3,
we get 21 as 7 X 3 = 21.

Question 13.
8 × 3 =
8 X 3 = 24,

Explanation:
Given 8 X 3 we multiply 8 with 3,
we get 24 as 8 X 3 = 24.

Question 14.
9 × 3 =
9 X 3 = 27,

Explanation:
Given 9 X 3 we multiply 9 with 3,
we get 27 as 9 X 3 = 27.

Question 15.
10 × 3 =
10 X 3 = 30,

Explanation:
Given 10 X 3 we multiply 10 with 3,
we get 30 as 10 X 3 = 30.

Question 16.
24 ÷ 3 =
24 ÷ 3 = 8,

Explanation:
Given 24 ÷ 3 we divide 24 by 3,
we get 8 as 24 ÷ 3 = 8.

Question 17.
21 ÷ 3 =
21 ÷ 3 = 7,

Explanation:
Given 21 ÷ 3 we divide 21 by 3,
we get 7 as 27 ÷ 3 = 7.

Question 18.
27 ÷ 3 =
27 ÷ 3 = 9,

Explanation:
Given 27 ÷ 3 we divide 27 by 3,
we get 9 as 27 ÷ 3 = 9.

Question 19.
18 ÷ 3 =
18 ÷ 3 = 6,

Explanation:
Given 18 ÷ 3 we divide 18 by 3,
we get 6 as 18 ÷ 3 = 6.

Question 20.
30 ÷ 3 =
30 ÷ 3 = 10,

Explanation:
Given 30 ÷ 3 we divide 30 by 3,
we get 10 as 30 ÷ 3 = 10.

Question 21.
__ × 3 = 15
5 X 3 = 15,

Explanation:
Given __ X 3 = 15, Let us take missing number
as x, So x X  3 = 15, means x = 15 ÷ 3 = 5,
therefore 5 X 3 = 15.

Question 22.
__ × 3 = 12
4 X 3 = 12,
Explanation:
Given __ X 3 = 12, Let us take missing number
as x, So x X  3 = 12, means x = 12 ÷ 3 = 4,
therefore 4 X 3 = 12.

Question 23.
__ × 3 = 30
10 X 3 = 30,

Explanation:
Given __ X 3 = 30, Let us take missing number
as x, So x X  3 = 30, means x = 30 ÷ 3 = 10,
therefore 10 X 3 = 30.

Question 24.
__ × 3 = 6
2 X 3 = 6,

Explanation:
Given __ X 3 = 6, Let us take missing number
as x, So x X  3 = 6, means x = 6 ÷ 3 = 2,
therefore 2 X 3 = 6.

Question 25.
__ × 3 = 9
3 X 3 = 9,

Explanation:
Given __ X 3 = 9, Let us take missing number
as x, So x X  3 = 9, means x = 9 ÷ 3 = 3,
therefore 3 X 3 = 9.

Question 26.
30 ÷ 3 =
30 ÷ 3 = 10,

Explanation:
Given 30 ÷ 3 we divide 30 by 3,
we get 10 as 30 ÷ 3 = 10.

Question 27.
15 ÷ 3 =
15 ÷ 3 = 5,

Explanation:
Given 15 ÷ 3 we divide 15 by 3,
we get 5 as 15 ÷ 3 = 5.

Question 28.
3 ÷ 1 =
3 ÷ 1 = 3,

Explanation:
Given 3 ÷ 1 we divide 3 by 1,
we get 3 as 3 ÷ 1 = 3.

Question 29.
6 ÷ 3 =
6 ÷ 3 = 2,

Explanation:
Given 6 ÷ 3 we divide 6 by 3,
we get 2 as 6 ÷ 3 = 2.

Question 30.
9 ÷ 3 =
9 ÷ 3 = 3,

Explanation:
Given 9 ÷ 3 we divide 9 by 3,
we get 3 as 9 ÷ 3 = 3.

Question 31.
__ × 3 = 18
6 X 3 = 18,

Explanation:
Given __ X 3 = 18, Let us take missing number
as x, So x X  3 = 18, means x = 18 ÷ 3 = 6,
therefore 6 X 3 = 18.

Question 32.
__ × 3 = 21
7 X 3 = 21,

Explanation:
Given __ X 3 = 21, Let us take missing number
as x, So x X  3 = 21, means x = 21 ÷ 3 = 7,
therefore 7 X 3 = 21.

Question 33.
__ × 3 = 27
9 X 3 = 27,

Explanation:
Given __ X 3 = 27, Let us take missing number
as x, So x X  3 = 27, means x = 27 ÷ 3 = 9,
therefore 9 X 3 = 27.

Question 34.
__ × 3 = 24
8 X 3 = 24,

Explanation:
Given __ X 3 = 24, Let us take missing number
as x, So x X  3 = 24, means x = 24 ÷ 3 = 8,
therefore 8 X 3 = 24.

Question 35.
21 ÷ 3 =
21 ÷ 3 = 7,

Explanation:
Given 21 ÷ 3 we divide 21 by 3,
we get 7 as 21 ÷ 3 = 7.

Question 36.
27 ÷ 3 =
27 ÷ 3 = 9,

Explanation:
Given 27 ÷ 3 we divide 27 by 3,
we get 9 as 27 ÷ 3 = 9.

Question 37.
18 ÷ 3 =
18 ÷ 3 = 6,

Explanation:
Given 18 ÷ 3 we divide 18 by 3,
we get 6 as 18 ÷ 3 = 6.

Question 38.
24 ÷ 3 =
24 ÷ 3 = 8,

Explanation:
Given 24 ÷ 3 we divide 24 by 3,
we get 8 as 24 ÷ 3 = 8.

Question 39.
11 × 3 =
11 X 3 = 33,

Explanation:
Given 11 X 3 we multiply 11 with 3,
we get 33 as 11 X 3 = 33.

Question 40.
33 ÷ 3 =
33 ÷ 3 = 11,

Explanation:
Given 33 ÷ 3 we divide 33 by 3,
we get 11 as 33 ÷ 3 = 11.

Question 41.
12 × 3 =
12 X 3 = 36,

Explanation:
Given 12 X 3 we multiply 12 with 3,
we get 36 as 12 X 3 = 36.

Question 42.
36 ÷ 3 =
36 ÷ 3 = 12,

Explanation:
Given 36 ÷ 3 we divide 36 by 3,
we get 12 as 36 ÷ 3 = 12.

Question 43.
13 × 3 =
13 X 3 = 39,

Explanation:
Given 13 X 3 we multiply 13 with 3,
we get 39 as 13 X 3 = 39.

Question 44.
39 ÷ 3 =
39 ÷ 3 = 13,

Explanation:
Given 39 ÷ 3 we divide 39 by 3,
we get 13 as 39 ÷ 3 = 13.

B
Multiply or Divide by 3

Question 1.
1 × 3 =
1 X 3 = 3,

Explanation:
Given 1 X 3 we multiply 1 with 3,
we get 3 as 1 X 3 = 3.

Question 2.
2 × 3 =
2 X 3 = 6,

Explanation:
Given 2 X 3 we multiply 2 with 3,
we get 6 as 2 X 3 = 6.

Question 3.
3 × 3 =
3 X 3 = 9,

Explanation:
Given 3 X 3 we multiply 3 with 3,
we get 9 as 3 X 3 = 9.

Question 4.
4 × 3 =
4 X 3 = 12,

Explanation:
Given 4 X 3 we multiply 4 with 3,
we get 12 as 4 X 3 = 12.

Question 5.
5 × 3 =
5 X 3 = 15,

Explanation:
Given 5 X 3 we multiply 5 with 3,
we get 15 as 5 X 3 = 15.

Question 6.
9 ÷ 3 =
9 ÷ 3 = 3,

Explanation:
Given 9 ÷ 3 we divide 9 by 3,
we get 3 as 9 ÷ 3 = 3.

Question 7.
6 ÷ 3 =
6 ÷ 3 = 2,

Explanation:
Given 6 ÷ 3 we divide 6 by 3,
we get 2 as 6 ÷ 3 = 2.

Question 8.
12 ÷ 3 =
12 ÷ 3 = 4,

Explanation:
Given 12 ÷ 3 we divide 12 by 3,
we get 4 as 12 ÷ 3 = 4.

Question 9.
3 ÷ 1 =
3 ÷ 1 = 3,

Explanation:
Given 3 ÷ 1 we divide 3 by 1,
we get 3 as 3 ÷ 1 = 3.

Question 10.
15 ÷ 3 =
15 ÷ 3 = 5,

Explanation:
Given 15 ÷ 3 we divide 15 by 3,
we get 5 as 15 ÷ 3 = 5.

Question 11.
10 × 3 =
10 X 3 = 30,

Explanation:
Given 10 X 3 we multiply 10 with 3,
we get 30 as 10 X 3 = 30.

Question 12.
6 × 3 =
6 X 3 = 18,

Explanation:
Given 6 X 3 we multiply 6 with 3,
we get 18 as 6 X 3 = 18.

Question 13.
7 × 3 =
7 X 3 = 21,

Explanation:
Given 7 X 3 we multiply 7 with 3,
we get 21 as 7 X 3 = 21.

Question 14.
8 × 3 =
8 X 3 = 24,

Explanation:
Given 8 X 3 we multiply 8 with 3,
we get 24 as 8 X 3 = 24.

Question 15.
9 × 3 =
9 X 3 = 27,

Explanation:
Given 9 X 3 we multiply 9 with 3,
we get 27 as 9 X 3 = 27.

Question 16.
21 ÷ 3 =
21 ÷ 3 = 7,

Explanation:
Given 21 ÷ 3 we divide 21 by 3,
we get 7 as 21 ÷ 3 = 7.

Question 17.
18 ÷ 3 =
18 ÷ 3 = 6,

Explanation:
Given 18 ÷ 3 we divide 18 by 3,
we get 6 as 18 ÷ 3 = 6.

Question 18.
24 ÷ 3 =
24 ÷ 3 = 8,

Explanation:
Given 24 ÷ 3 we divide 24 by 3,
we get 8 as 24 ÷ 3 = 8.

Question 19.
30 ÷ 3 =
30 ÷ 3 = 10,

Explanation:
Given 30 ÷ 3 we divide 30 by 3,
we get 10 as 30 ÷ 3 = 10.

Question 20.
27 ÷ 3 =
27 ÷ 3 = 9,

Explanation:
Given 27 ÷ 3 we divide 27 by 3,
we get 9 as 27 ÷ 3 = 9.

Question 21.
__ × 3 = 12
4 X 3 = 12,

Explanation:
Given __ X 3 = 12, Let us take missing number
as x, So x X  3 = 12, means x = 12 ÷ 3 = 4,
therefore 4 X 3 = 12.

Question 22.
__ × 3 = 15
5 X 3 = 15,

Explanation:
Given __ X 3 = 15, Let us take missing number
as x, So x X  3 = 15, means x = 15 ÷ 3 = 5,
therefore 5 X 3 = 15.

Question 23.
__ × 3 = 6
2 X 3 = 6,

Explanation:
Given __ X 3 = 6, Let us take missing number
as x, So x X  3 = 6, means x = 6 ÷ 3 = 2,
therefore 2 X 3 = 6.

Question 24.
__ × 3 = 30
10 X 3 = 30,

Explanation:
Given __ X 3 = 30, Let us take missing number
as x, So x X  3 = 30, means x = 30 ÷ 3 = 10,
therefore 10 X 3 = 30.

Question 25.
__ × 3 = 9
3 X 3 = 9,

Explanation:
Given __ X 3 = 9, Let us take missing number
as x, So x X  3 = 9, means x = 9 ÷ 3 = 3,
therefore 3 X 3 = 9.

Question 26.
6 ÷ 3 =
6 ÷ 3 = 2,

Explanation:
Given 6 ÷ 3 we divide 6 by 3,
we get 2 as 6 ÷ 3 = 2.

Question 27.
3 ÷ 1 =
3 ÷ 1 = 3,

Explanation:
Given 3 ÷ 1 we divide 3 by 1,
we get 3 as 3 ÷ 1 = 3.

Question 28.
30 ÷ 3 =
30 ÷ 3 = 10,

Explanation:
Given 30 ÷ 3 we divide 30 by 3,
we get 10 as 30 ÷ 3 = 10.

Question 29.
15 ÷ 3 =
15 ÷ 3 = 5,

Explanation:
Given 15 ÷ 3 we divide 15 by 3,
we get 5 as 15 ÷ 3 = 5.

Question 30.
9 ÷ 3 =
9 ÷ 3 = 3,

Explanation:
Given 9 ÷ 3 we divide 9 by 3,
we get 3 as 9 ÷ 3 = 3.

Question 31.
__ × 3 = 18
6 X 3 = 18,

Explanation:
Given __ X 3 = 18, Let us take missing number
as x, So x X  3 = 18, means x = 18 ÷ 3 = 6,
therefore 6 X 3 = 18.

Question 32.
__ × 3 = 24
8 X 3 = 24,

Explanation:
Given __ X 3 = 24, Let us take missing number
as x, So x X  3 = 24, means x = 24 ÷ 3 = 8,
therefore 8 X 3 = 24.

Question 33.
__ × 3 = 27
9 X 3 = 27,

Explanation:
Given __ X 3 = 27, Let us take missing number
as x, So x X  3 = 27, means x = 27 ÷ 3 = 9,
therefore 9 X 3 = 27.

Question 34.
__ × 3 = 21
7 X 3 = 21,

Explanation:
Given __ X 3 = 21, Let us take missing number
as x, So x X  3 = 21, means x = 21 ÷ 3 = 7,
therefore 7 X 3 = 21.

Question 35.
24 ÷ 3 =
24 ÷ 3 = 8,

Explanation:
Given 24 ÷ 3 we divide 24 by 3,
we get 8 as 24 ÷ 3 = 8.

Question 36.
27 ÷ 3 =
27 ÷ 3 = 9,

Explanation:
Given 27 ÷ 3 we divide 27 by 3,
we get 9 as 27 ÷ 3 = 9.

Question 37.
18 ÷ 3 =
18 ÷ 3 = 6,

Explanation:
Given 18 ÷ 3 we divide 18 by 3,
we get 6 as 18 ÷ 3 = 6.

Question 38.
21 ÷ 3 =
21 ÷ 3 = 7,

Explanation:
Given 21 ÷ 3 we divide 21 by 3,
we get 7 as 21 ÷ 3 = 7.

Question 39.
11 × 3 =
11 X 3 = 33,

Explanation:
Given 11 X 3 we multiply 11 with 3,
we get 33 as 11 X 3 = 33.

Question 40.
33 ÷ 3 =
33 ÷ 3 = 11,

Explanation:
Given 33 ÷ 3 we divide 33 by 3,
we get 11 as 33 ÷ 3 = 11.

Question 41.
12 × 3 =
12 X 3 = 36,

Explanation:
Given 12 X 3 we multiply 12 with 3,
we get 36 as 12 X 3 = 36.

Question 42.
36 ÷ 3 =
36 ÷ 3 = 12,

Explanation:
Given 36 ÷ 3 we divide 36 by 3,
we get 12 as 36 ÷ 3 = 12.

Question 43.
13 × 3 =
13 X 3 = 39,

Explanation:
Given 13 X 3 we multiply 13 with 3,
we get 39 as 13 X 3 = 39.

Question 44.
39 ÷ 3 =
39 ÷ 3 = 13,

Explanation:
Given 39 ÷ 3 we divide 39 by 3,
we get 13 as 39 ÷ 3 = 13.

Eureka Math Grade 3 Module 1 Lesson 14 Problem Set Answer Key

Question 1.
Skip-count by fours. Match each answer to the appropriate expression.

Skipped-counts by fours.
Matched each answer to the appropriate expression as
4 = 1 X 4,
8 = 2 X 4,
12 = 3 X 4,
16 = 4 X 4,
20 = 5 X 4,
24 = 6 X 4,
28 = 7 X 4,
32 = 8 X 4,
36 = 9 X 4,
40 = 10 X 4.

Question 2.
Mr. Schmidt replaces each of the 4 wheels on 7 cars.
How many wheels does he replace? Draw and label a tape diagram to solve.
Mr. Schmidt replaces _____28______ wheels.

Mr. Schmidt replaces 28 wheels on 7 cars,

Explanation:
Given Mr. Schmidt replaces each of the 4 wheels on 7 cars.
Drawn and labeled a tape diagram to solve how many wheels
he replaced as shown above, So number of wheels replaced are
7 X 4 = 28, therefore, Mr. Schmidt replaces _____28______ wheels.

Question 3.
Trina makes 4 bracelets. Each bracelet has 6 beads.
Draw and label a tape diagram to show the
total number of beads Trina uses.

Trina uses 24 beads to make 4 bracelets,

Explanation:
Given Trina makes 4 bracelets. Each bracelet has 6 beads.
Draw and label a tape diagram to show the
total number of beads Trina uses as 4 X 6 =24 beads.

Question 4.
Find the total number of sides on 5 rectangles.

Total number of sides on 5 rectangles are 20 side,

Explanation:
We know a rectangle has 4 sides, So number of sides on
5 rectangles are 5 X 4 = 20 sides.

Eureka Math Grade 3 Module 1 Lesson 14 Exit Ticket Answer Key

Arthur has 4 boxes of chocolates. Each box has 6 chocolates inside. How many chocolates does Arthur have altogether? Draw and label a tape diagram to solve.

Eureka Math Grade 3 Module 1 Lesson 14 Homework Answer Key

Question 1.
Skip-count by fours. Match each answer to the appropriate expression.

Skipped-counts by fours.
Matched each answer to the appropriate expression as
4 = 1 X 4,
8 = 2 X 4,
12 = 3 X 4,
16 = 4 X 4,
20 = 5 X 4,
24 = 6 X 4,
28 = 7 X 4,
32 = 8 X 4,
36 = 9 X 4,
40 = 10 X 4.

Question 2.
Lisa places 5 rows of 4 juice boxes in the refrigerator.
Draw an array and skip-count to find the total number of juice boxes.
There are ____20_______ juice boxes in total.

The total number of juice boxes are 20,

Explanation:
Given Lisa places 5 rows of 4 juice boxes in the refrigerator.
Drawn an array and skipped-count for finding the total
number of juice boxes are as 5 X 4 = 20 juice boxes in total.

Question 3.
Six folders are placed on each table. How many folders are
there on 4 tables? Draw and label a tape diagram to solve.

There are 24 folders on 4 tables,

Explanation:
Given Six folders are placed on each table. So number of
folders are there on 4 tables are 4 X 6 = 24,
Drawn and labeled a tape diagram to solve as shown above,
Therefore, there are 24 folders on 4 tables.

Question 4.
Find the total number of corners on 8 squares.

Total number of corners on 8 squares is 32,

Explanation:
We know a square has 4 corners,

So 8 squares will have 8 X 4 = 32 corners,
therefore, total number of corners on 8 squares is 32.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 13 Sprint Answer Key

A
Multiply or Divide by 2

Question 1.
2 × 2 =
2 X 2 = 4,

Explanation:
Given 2 X 2 we multiply 2 with 2,
we get 4 as 2 X 2 = 4.

Question 2.
3 × 2 =
3 X 2 = 6,

Explanation:
Given 3 X 2 we multiply 3 with 2,
we get 6 as 3 X 2 = 6.

Question 3.
4 × 2 =
4 X 2 = 8,

Explanation:
Given 4 X 2 we multiply 4 with 2,
we get 8 as 4 X 2 = 8.

Question 4.
5 × 2 =
5 X 2 = 10,
Explanation:
Given 5 X 2 we multiply 5 with 2,
we get 10 as 5 X 2 = 10.

Question 5.
1 × 2 =
1 X 2 = 2,

Explanation:
Given 1 X 2 we multiply 1 with 2,
we get 2 as 1 X 2 = 2.

Question 6.
4 ÷ 2 =
4 ÷ 2 = 2,

Explanation:
Given 4 ÷ 2 we divide 4 by 2,
we get 2 as 4 ÷ 2 = 2.

Question 7.
6 ÷ 2 =
6 ÷ 2 = 3,
Explanation:
Given 6 ÷ 2 we divide 6 by 2,
we get 3 as 6 ÷ 2 = 3.

Question 8.
10 ÷ 2 =
10 ÷ 2 = 5,

Explanation:
Given 10 ÷ 2 we divide 10 by 2,
we get 5 as 10 ÷ 2 = 5.

Question 9.
2 ÷ 1 =
2 ÷ 1 = 2,

Explanation:
Given 2 ÷ 1 we divide 2 by 1,
we get 2 as 2 ÷ 1 = 2.

Question 10.
8 ÷ 2 =
8 ÷ 2 = 4,

Explanation:
Given 8 ÷ 2 we divide 8 by 2,
we get 4 as 8 ÷ 2 = 4.

Question 11.
6 × 2 =
6 X 2 = 12,

Explanation:
Given 6 X 2 we multiply 6 with 2,
we get 12 as 6 X 2 = 12.

Question 12.
7 × 2 =
7 X 2 = 14,
Explanation:
Given 7 X 2 we multiply 7 with 2,
we get 14 as 7 X 2 = 14.

Question 13.
8 × 2 =
8 X 2 = 16,

Explanation:
Given 8 X 2 we multiply 8 with 2,
we get 16 as 8 X 2 = 16.

Question 14.
9 × 2 =
9 X 2 = 18,

Explanation:
Given 9 X 2 we multiply 9 with 2,
we get 18 as 9 X 2 = 18.

Question 15.
10 × 2 =
10 X 2 = 20,

Explanation:
Given 10 X 2 we multiply 10 with 2,
we get 20 as 10 X 2 = 20.

Question 16.
16 ÷ 2 =
16 ÷ 2 = 8,

Explanation:
Given 16 ÷ 2 we divide 16 by 2,
we get 8 as 16 ÷ 2 = 8.

Question 17.
14 ÷ 2 =
14 ÷ 2 = 7,

Explanation:
Given 14 ÷ 2 we divide 14 by 2,
we get 7 as 14 ÷ 2 = 7.

Question 18.
18 ÷ 2 =
18 ÷ 2 = 9,

Explanation:
Given 18 ÷ 2 we divide 18 by 2,
we get 9 as 18 ÷ 2 = 9.

Question 19.
12 ÷ 2 =
12 ÷ 2 = 6,

Explanation:
Given 12 ÷ 2 we divide 12 by 2,
we get 6 as 12 ÷ 2 = 6.

Question 20.
20 ÷ 2 =
20 ÷ 2 = 10,

Explanation:
Given 20 ÷ 2 we divide 20 by 2,
we get 10 as 20 ÷ 2 = 10.

Question 21.
__ × 2 = 10
5 X 2 = 10,

Explanation:
Given __ X 2 = 10, Let us take missing number
as x, So x X 2 = 10, means x = 10 ÷ 2 = 5,
therefore 5 X 2 = 10.

Question 22.
__ × 2 = 12
6 X 2 = 12,

Explanation:
Given __ X 2 = 12, Let us take missing number
as x, So x X 2 = 12, means x = 12 ÷ 2 = 6,
therefore 6 X 2 = 12.

Question 23.
__ × 2 = 20
10 X 2 = 20,

Explanation:
Given __ X 2 = 20, Let us take missing number
as x, So x X 2 = 20, means x = 20 ÷ 2 = 10,
therefore 10 X 2 = 20.

Question 24.
__ × 2 = 4
2 X 2 = 4,

Explanation:
Given __ X 2 = 4, Let us take missing number
as x, So x X 2 = 4, means x = 4 ÷ 2 = 2,
therefore 2 X 2 = 4.

Question 25.
__ × 2 = 6
3 X 2 = 6,

Explanation:
Given __ X 2 = 6, Let us take missing number
as x, So x X 2 = 6, means x = 6 ÷ 2 = 3,
therefore 3 X 2 = 6.

Question 26.
20 ÷ 2 =
20 ÷ 2 = 10,

Explanation:
Given 20 ÷ 2 we divide 20 by 2,
we get 10 as 20 ÷ 2 = 10.

Question 27.
10 ÷ 2 =
10 ÷ 2 = 5,

Explanation:
Given 10 ÷ 2 we divide 10 by 2,
we get 5 as 10 ÷ 2 = 5.

Question 28.
2 ÷ 1 =
2 ÷ 1 = 2,

Explanation:
Given 2 ÷ 1 we divide 2 by 1,
we get 2 as 2 ÷ 1 = 2.

Question 29.
4 ÷ 2 =
4 ÷ 2 = 2,

Explanation:
Given 4 ÷ 2 we divide 4 by 2,
we get 2 as 4 ÷ 2 = 2.

Question 30.
6 ÷ 2 =
6 ÷ 2 = 3,

Explanation:
Given 6 ÷ 2 we divide 6 by 2,
we get 3 as 6 ÷ 2 = 3.

Question 31.
__ × 2 = 12
6 X 2 = 12,

Explanation:
Given __ X 2 = 12, Let us take missing number
as x, So x X 2 = 12, means x = 12 ÷ 2 = 6,
therefore 6 X 2 = 12.

Question 32.
__ × 2 = 14
7 X 2 = 14,

Explanation:
Given __ X 2 = 14, Let us take missing number
as x, So x X 2 = 14, means x = 14 ÷ 2 = 7,
therefore 7 X 2 = 14.

Question 33.
__ × 2 = 18
9 X 2 = 18,

Explanation:
Given __ X 2 = 18, Let us take missing number
as x, So x X 2 = 18, means x = 18 ÷ 2 = 9,
therefore 9 X 2 = 18.

Question 34.
__ × 2 = 16
8 X 2 = 16,

Explanation:
Given __ X 2 = 16, Let us take missing number
as x, So x X 2 = 16, means x = 16 ÷ 2 = 8,
therefore 8 X 2 = 16.

Question 35.
14 ÷ 2 =
14 ÷ 2 = 7,

Explanation:
Given 14 ÷ 2 we divide 14 by 2,
we get 7 as 14 ÷ 2 = 7.

Question 36.
18 ÷ 2 =
18 ÷ 2 = 9,

Explanation:
Given 18 ÷ 2 we divide 18 by 2,
we get 9 as 18 ÷ 2 = 9.

Question 37.
12 ÷ 2 =
12 ÷ 2 = 6,

Explanation:
Given 12 ÷ 2 we divide 12 by 2,
we get 6 as 12 ÷ 2 = 6.

Question 38.
16 ÷ 2 =
16 ÷ 2 = 8,

Explanation:
Given 16 ÷ 2 we divide 16 by 2,
we get 8 as 16 ÷ 2 = 8.

Question 39.
11 × 2 =
11 X 2 = 22,

Explanation:
Given 11 X 2 we multiply 11 with 2,
we get 22 as 11 X 2 = 22.

Question 40.
22 ÷ 2 =
22 ÷ 2 = 11,

Explanation:
Given 22 ÷ 2 we divide 22 by 2,
we get 11 as 22 ÷ 2 = 11.

Question 41.
12 × 2 =
12 X 2 = 24,

Explanation:
Given 12 X 2 we multiply 12 with 2,
we get 24 as 12 X 2 = 24.

Question 42.
24 ÷ 2 =
24 ÷ 2 = 12,

Explanation:
Given 24 ÷ 2 we divide 24 by 2,
we get 12 as 24 ÷ 2 = 12.

Question 43.
14 × 2 =
14 X 2 = 28,

Explanation:
Given 14 X 2 we multiply 14 with 2,
we get 28 as 14 X 2 = 28.

Question 44.
28 ÷ 2 =
28 ÷ 2 = 14,

Explanation:
Given 28 ÷ 2 we divide 28 by 2,
we get 14 as 28 ÷ 2 = 14.

B
Multiply or Divide by 2

Question 1.
1 × 2 =
1 X 2 = 2,

Explanation:
Given 1 X 2 we multiply 1 with 2,
we get 2 as 1 X 2 = 2.

Question 2.
2 × 2 =
2 X 2 = 4,

Explanation:
Given 2 X 2 we multiply 2 with 2,
we get 4 as 2 X 2 = 4.

Question 3.
3 × 2 =
3 X 2 = 6,

Explanation:
Given 3 X 2 we multiply 3 with 2,
we get 6 as 3 X 2 = 6.

Question 4.
4 × 2 =
4 X 2 = 8,

Explanation:
Given 4 X 2 we multiply 4 with 2,
we get 8 as 4 X 2 = 8.

Question 5.
5 × 2 =
5 X 2 = 10,

Explanation:
Given 5 X 2 we multiply 5 with 2,
we get 10 as 5 X 2 = 10.

Question 6.
6 ÷ 2 =
6 ÷ 2 = 3,

Explanation:
Given 6 ÷ 2 we divide 6 by 2,
we get 3 as 6 ÷ 2 = 3.

Question 7.
4 ÷ 2 =
4 ÷ 2 = 2,

Explanation:
Given 4 ÷ 2 we divide 4 by 2,
we get 2 as 4 ÷ 2 = 2.

Question 8.
8 ÷ 2 =
8 ÷ 2 = 4,

Explanation:
Given 8 ÷ 2 we divide 8 by 2,
we get 4 as 8 ÷ 2 = 4.

Question 9.
2 ÷ 1 =
2 ÷ 1 = 2,

Explanation:
Given 2 ÷ 1 we divide 2 by 1,
we get 2 as 2 ÷ 1 = 2.

Question 10.
10 ÷ 2 =
10 ÷ 2 = 5,

Explanation:
Given 10 ÷ 2 we divide 10 by 2,
we get 5 as 10 ÷ 2 = 5.

Question 11.
10 × 2 =
10 X 2 = 20,

Explanation:
Given 10 X 2 we multiply 10 with 2,
we get 20 as 10 X 2 = 20.

Question 12.
6 × 2 =
6 X 2 = 12,

Explanation:
Given 6 X 2 we multiply 6 with 2,
we get 12 as 6 X 2 = 12.

Question 13.
7 × 2 =
7 X 2 = 14,

Explanation:
Given 7 X 2 we multiply 7 with 2,
we get 14 as 7 X 2 = 14.

Question 14.
8 × 2 =
8 X 2 = 16,

Explanation:
Given 8 X 2 we multiply 8 with 2,
we get 16 as 8 X 2 = 16.

Question 15.
9 × 2 =
9 X 2 = 18,

Explanation:
Given 9 X 2 we multiply 9 with 2,
we get 18 as 9 X 2 = 18.

Question 16.
14 ÷ 2 =
14 ÷ 2 = 7,

Explanation:
Given 14 ÷ 2 we divide 14 by 2,
we get 7 as 14 ÷ 2 = 7.

Question 17.
12 ÷ 2 =
12 ÷ 2 = 6,

Explanation:
Given 12 ÷ 2 we divide 12 by 2,
we get 6 as 12 ÷ 2 = 6.

Question 18.
16 ÷ 2 =
16 ÷ 2 = 8,

Explanation:
Given 16 ÷ 2 we divide 16 by 2,
we get 8 as 16 ÷ 2 = 8.

Question 19.
20 ÷ 2 =
20 ÷ 2 = 10,

Explanation:
Given 20 ÷ 2 we divide 20 by 2,
we get 10 as 20 ÷ 2 = 10.

Question 20.
18 ÷ 2 =
18 ÷ 2 = 9,

Explanation:
Given 18 ÷ 2 we divide 18 by 2,
we get 9 as 18 ÷ 2 = 9.

Question 21.
__ × 2 = 12
6 X 2 = 12,

Explanation:
Given __ X 2 = 12, Let us take missing number
as x, So x X 2 = 12, means x = 12 ÷ 2 = 6,
therefore 6 X 2 = 12.

Question 22.
__ × 2 = 10
5 X 2 = 10,

Explanation:
Given __ X 2 = 10, Let us take missing number
as x, So x X 2 = 10, means x = 10 ÷ 2 = 5,
therefore 5 X 2 = 10.

Question 23.
__ × 2 = 4
2 X 2 = 4,

Explanation:
Given __ X 2 = 4, Let us take missing number
as x, So x X 2 = 4, means x = 4 ÷ 2 = 2,
therefore 2 X 2 = 4.

Question 24.
__ × 2 = 20
10 X 2 = 20,

Explanation:
Given __ X 2 = 20, Let us take missing number
as x, So x X 2 = 20, means x = 20 ÷ 2 = 10,
therefore 10 X 2 = 20.

Question 25.
__ × 2 = 6
3 X 2 = 6,

Explanation:
Given __ X 2 = 6, Let us take missing number
as x, So x X 2 = 6, means x = 6 ÷ 2 = 3,
therefore 3 X 2 = 6.

Question 26.
4 ÷ 2 =
4 ÷ 2 = 2,

Explanation:
Given 4 ÷ 2 we divide 4 by 2,
we get 2 as 4 ÷ 2 = 2.

Question 27.
2 ÷ 1 =
2 ÷ 1 = 2,

Explanation:
Given 2 ÷ 1 we divide 2 by 1,
we get 2 as 2 ÷ 1 = 2.

Question 28.
20 ÷ 2 =
20 ÷ 2 = 10,

Explanation:
Given 20 ÷ 2 we divide 20 by 2,
we get 10 as 20 ÷ 2 = 10.

Question 29.
10 ÷ 2 =
10 ÷ 2 = 5,

Explanation:
Given 10 ÷ 2 we divide 10 by 2,
we get 5 as 10 ÷ 2 = 5.

Question 30.
6 ÷ 2 =
6 ÷ 2 = 3,

Explanation:
Given 6 ÷ 2 we divide 6 by 2,
we get 3 as 6 ÷ 2 = 3.

Question 31.
__ × 2 = 12
6 X 2 = 12,

Explanation:
Given __ X 2 = 12, Let us take missing number
as x, So x X 2 = 12, means x = 12 ÷ 2 = 6,
therefore 6 X 2 = 12.

Question 32.
__ × 2 = 16
8 X 2 = 16,

Explanation:
Given __ X 2 = 16, Let us take missing number
as x, So x X 2 = 16, means x = 16 ÷ 2 = 8,
therefore 8 X 2 = 16.

Question 33.
__ × 2 = 18
9 X 2 = 18,

Explanation:
Given __ X 2 = 18, Let us take missing number
as x, So x X 2 = 18, means x = 18 ÷ 2 = 9,
therefore 9 X 2 = 18.

Question 34.
__ × 2 = 14
7 X 2 = 14,

Explanation:
Given __ X 2 = 14, Let us take missing number
as x, So x X 2 = 14, means x = 14 ÷ 2 = 7,
therefore 7 X 2 = 14.

Question 35.
16 ÷ 2 =
16 ÷ 2 = 8,

Explanation:
Given 16 ÷ 2 we divide 16 by 2,
we get 8 as 16 ÷ 2 = 8.

Question 36.
18 ÷ 2 =
18 ÷ 2 = 9,

Explanation:
Given 18 ÷ 2 we divide 18 by 2,
we get 9 as 18 ÷ 2 = 9.

Question 37.
12 ÷ 2 =
12 ÷ 2 = 6,

Explanation:
Given 12 ÷ 2 we divide 12 by 2,
we get 6 as 12 ÷ 2 = 6.

Question 38.
14 ÷ 2 =
14 ÷ 2 = 7,

Explanation:
Given 14 ÷ 2 we divide 14 by 2,
we get 7 as 14 ÷ 2 = 7.

Question 39.
11 × 2 =
11 X 2 = 22,

Explanation:
Given 11 X 2 we multiply 11 with 2,
we get 22 as 11 X 2 = 22.

Question 40.
22 ÷ 2 =
22 ÷ 2 = 11,

Explanation:
Given 22 ÷ 2 we divide 22 by 2,
we get 11 as 22 ÷ 2 = 11.

Question 41.
12 × 2 =
12 X 2 = 24,

Explanation:
Given 12 X 2 we multiply 12 with 2,
we get 24 as 12 X 2 = 24.

Question 42.
24 ÷ 2 =
24 ÷ 2 = 12,

Explanation:
Given 24 ÷ 2 we divide 24 by 2,
we get 12 as 24 ÷ 2 = 12.

Question 43.
13 × 2 =
13 X 2 = 26,

Explanation:
Given 13 X 2 we multiply 13 with 2,
we get 23 as 13 X 2 = 26.

Question 44.
26 ÷ 2 =
26 ÷ 2 = 13,

Explanation:
Given 26 ÷ 2 we divide 26 by 2,
we get 26 as 26 ÷ 2 = 13.

Eureka Math Grade 3 Module 1 Lesson 13 Problem Set Answer Key

Question 1.
Fill in the blanks to make true number sentences.

Explanation:
Filled the blanks to make true number sentences as
1 X 3 = 3, 3 ÷ 3 = 1,
2 X 3 = 6, 6 ÷ 3 = 2,
3 X 3 = 9, 9 ÷ 3 = 3,
4 X 3 = 12, 12 ÷ 3 = 4,
5 X 3 = 15, 15 ÷ 3 = 5,
6 X 3 = 18, 18 ÷ 3 = 6,
7 X 3 = 21, 21 ÷ 3 = 7,
8 X 3 = 24, 24 ÷ 3 = 8,
9 X 3 = 27, 27 ÷ 3 = 9,
10 x 3 = 30, 30 ÷ 3 = 10.

Question 2.
Mr. Lawton picks tomatoes from his garden.
He divides the tomatoes into bags of 3.

a. Circle to show how many bags he packs.
Then, skip-count to show the total number of tomatoes.


Circled the bags as 4,
The total number of tomatoes are 12,

Explanation:
Given Mr. Lawton picks tomatoes from his garden.
He divides the tomatoes into bags of 3.
a. Circled and showed number of bags he packs
as 12 ÷ 3 = 4 bags,
Then, skipped-count and showed the total number of
tomatoes are 4 X 3 = 12.

b. Draw and label a tape diagram to represent the problem.
____12____ ÷ 3 = ___4 bags__________
Mr. Lawton packs ___4____ bags of tomatoes.

Mr. Lawton packs  4 bags of tomatoes,

Explanation:
Drawn and labeled a tape diagram to represent
the problem as shown above 12 ÷ 3 = 4 bags.

Question 3.
Camille buys a sheet of stamps that measures 15 centimeters long.
Each stamp is 3 centimeters long.
How many stamps does Camille buy?
Draw and label a tape diagram to solve.
Camille buys ____5_____ stamps.

Camille buy’s 5 stamps,

Explanation:
Given Camille buys a sheet of stamps that measures
15 centimeters long and each stamp is 3 centimeters long.
So number of  stamps Camille buy’s is 15 ÷ 3 = 5 stamps,
Drawn and labeled a tape diagram to solve as shown above.

Question 4.
Thirty third-graders go on a field trip. They are equally
divided into 3 vans. How many students are in each van?

In each van there are 11 students,

Explanation:
Given thirty third-graders go on a field trip and they are equally
divided into 3 vans. So number of  students in each van are
33 ÷ 3 = 11, Therefore in each van there are 11 students.

Question 5.
Some friends spend $24 altogether on frozen yogurt.
Each person pays $3. How many people buy frozen yogurt?

8 people buy’s frozen yogurt,

Explanation:
Given some friends spend $24 altogether on frozen yogurt
and each person pays $3, So number of people buy’s frozen
yogurt is $24 ÷ $3 = 8, Therefore 8 people buy’s frozen yogurt.

Eureka Math Grade 3 Module 1 Lesson 13 Exit Ticket Answer Key

Question 1.
Andrea has 21 apple slices. She uses 3 apple slices to
decorate 1 pie. How many pies does Andrea make?
Draw and label a tape diagram to solve.

Andrea makes 7 pies,

Explanation:
Given Andrea has 21 apple slices and she uses 3 apple slices to
decorate 1 pie. So number of pies Andrea makes are 21 ÷ 3 = 7,
Drawn and labeled a tape diagram to solve as shown above.

Question 2.
There are 24 soccer players on the field. They form 3 equal teams.
How many players are on each team?

Number of players in each team are 8,

Explanation:
Given there are 24 soccer players on the field and
they form 3 equal teams, So number of players in
each team are 24 ÷ 3 = 8 players.

Eureka Math Grade 3 Module 1 Lesson 13 Homework Answer Key

Question 1.
Fill in the blanks to make true number sentences.

Explanation:
Filled in the blanks to make true number sentences as
2 X 3 = 6, 6 ÷ 3 = 2, 1 x 3 = 3, 3 ÷ 3 =1,
7 X 3 = 21, 21 ÷ 3 = 7 and 9 X 3 = 27, 27 ÷ 3 = 9.

Question 2.
Ms. Gillette’s pet fish are shown below.
She keeps 3 fish in each tank.

a. Circle to show how many fish tanks she has.
Then, skip-count to find the total number of fish.

Circled the fish tanks as 5,
The total number of fishes are 15,

Explanation:
Given Ms. Gillette’s pet fishes, She keeps 3 fish in each tank,
Circled to show number of fish tanks she has.
Then, skipped-count to find the total number of fishes as
5 X 3 = 15.

b. Draw and label a tape diagram to represent the problem.
_____15______ ÷ 3 = ____5______
Ms. Gillette has ___5____ fish tanks.

Ms. Gillette has 5 fish tanks.

Explanation:
Drawn and labeled a tape diagram to represent
the problem as shown above 15 ÷ 3 = 5 fish tanks.

Question 3.
Juan buys 18 meters of wire. He cuts the wire into
pieces that are each 3 meters long. How many pieces
of wire does he cut?

Juan cuts 6 pieces of wire.

Explanation:
Given Juan buys 18 meters of wire and he cuts the wire into
pieces that are each 3 meters long So number of pieces
of wire he cuts is 18 ÷ 3 = 6 pieces.

Question 4.
A teacher has 24 pencils. They are divided equally
among 3 students. How many pencils does each student get?

Each student will get 8 pencils,

Explanation:
Given a teacher has 24 pencils and they are divided equally
among 3 students, So number of pencils each student gets is
24 ÷ 3 = 8 pencils.

Question 5.
There are 27 third-graders working in groups of 3.
How many groups of third-graders are there?

There are 9 groups of third-graders working,

Explanation:
Given there are 27 third-graders working in groups of 3,
So, number of groups of third-graders working are
27 ÷ 3 = 9 groups.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 12 Pattern Sheet Answer Key

Multiply.

multiply by 3 (6–10)

Multiplied by 3 (6–10) as shown below

Eureka Math Grade 3 Module 1 Lesson 12 Problem Set Answer Key

Question 1.
There are 8 birds at the pet store. Two birds are in each cage.
Circle to show how many cages there are.

8 ÷ 2 = ____4______
There are ___4____ cages of birds.

There are 4 cages of birds,

Explanation:
Given there are 8 birds at the pet store and two
birds are in each cage.
Number of cages are 8 ÷ 2 = 4 cages,
Circled to show 4 number of cages of birds as shown above.

Question 2.
The pet store sells 10 fish. They equally divide the fish into 5 bowls.
Draw fish to find the number in each bowl.

5 × ___2____ = 10
10 ÷ 5 = ___2_____
There are ____2____ fish in each bowl.

There are 2 fish in each bowl,

Explanation:
Given the pet store sells 10 fish and they are equally
divided the fish into 5 bowls.
Means each bowl has 10 ÷ 5 = 2 fish ( 5 X 2 = 10),
Drawn fish and found the number in each bowl as 2 fish,

Question 3.
Match.

Explanation:
Matched expressions as
10 ÷ 2 = 5,
16 ÷ 2 = 8,
18 ÷ 2 = 9,
14 ÷ 2 = 7 and
12 ÷ 2 = 6.

Question 4.
Laina buys 14 meters of ribbon. She cuts her ribbon into
2 equal pieces. How many meters long is each piece?
Label the tape diagram to represent the problem, including the unknown.

Each piece is ____7______ meters long.

Laina’s each piece of ribbon is 7 meters long,

Explanation:
Given Laina buys 14 meters of ribbon and she cuts
her ribbon into 2 equal pieces. So number of meters
long each piece is 14 ÷ 2 = 7 meters long,
Labeled the tape diagram to represent the problem,
including the unknown as shown in the above picture.

Question 5.
Roy eats 2 cereal bars every morning. Each box has a total
of 12 bars. How many days will it take Roy to finish 1 box?

It will take Roy to  finish 1 box in 6 days,

Explanation:
Given Roy eats 2 cereal bars every morning and each
box has a total of 12 bars.
So, Number of days it will take Roy to finish 1 box is
12 ÷ 2 = 6 days.

Question 6.
Sarah and Esther equally share the cost of a present.
The present costs $18. How much does Sarah pay?

Sarah pay’s $9 for the present,

Explanation:
Given Sarah and Esther equally share the cost of a present.
The present costs $18, As 2 persons have equally paid for the
present each paid $18 ÷ 2 = $9,
Therefore  Sarah pay’s $9 for the present.

Eureka Math Grade 3 Module 1 Lesson 12 Exit Ticket Answer Key

There are 14 mints in 1 box. Cecilia eats 2 mints each day.
How many days does it take Cecilia to eat 1 box of mints?
Draw and label a tape diagram to solve.

It takes Cecilia ____7___ days to eat 1 box of mints.

Cecilia eats 1 box of mints in 7 days,

Explanation:
Given there are 14 mints in 1 box and Cecilia eats
2 mints each day. So, number of days it will take Cecilia
to eat 1 box of mints are 14 ÷ 2 = 7 days,
Drawn and labeled a tape diagram to solve as shown above
in the picture.

Eureka Math Grade 3 Module 1 Lesson 12 Homework Answer Key

Question 1.
Ten people wait in line for the roller coaster.
Two people sit in each car. Circle to find the total number of cars needed.

10 ÷ 2 = ____5______
There are ___5____ cars needed.

Number of cars needed are 5,

Explanation:
Given Ten people wait in line for the roller coaster,
Two people sit in each car. So, number of cars needed are
10 ÷ 2 = 5, Circled the total 5 number of cars needed as
shown above in the picture.

Question 2.
Mr. Ramirez divides 12 frogs equally into 6 groups for
students to study. Draw frogs to find the number in each group.
Label known and unknown information on the tape diagram
to help you solve.

6 × ___2____ = 12
12 ÷ 6 = ___2____
There are ____2____ frogs in each group.

The number of frogs in each group are 2,

Explanation:
Given Mr. Ramirez divides 12 frogs equally into 6 groups for
students to study. Drawn frogs to find the number in each group
as 12 ÷ 6 = 2 frogs, Labeled known and unknown information
on the tape diagram and solved as shown above in the picture.

Question 3.
Match.

Explanation:
Matched expressions as
10 ÷ 2 = 5,
16 ÷ 2 = 8,
18 ÷ 2 = 9 and
14 ÷ 2 = 7 respectively.

Question 4.
Betsy pours 16 cups of water to equally fill 2 bottles.
How many cups of water are in each bottle?
Label the tape diagram to represent the problem, including the unknown.
There are ____8_____ cups of water in each bottle.

There are 8 cups of water in each bottle,

Explanation:
Given Betsy pours 16 cups of water to equally fill 2 bottles,
So, number of cups of water in each bottle are 16 ÷ 2 = 8 cups,
Labeled the tape diagram to represent the problem
including the unknown as shown above in the picture.

Question 5.
An earthworm tunnels 2 centimeters into the ground each day.
The earthworm tunnels at about the same pace every day.
How many days will it take the earthworm to tunnel 14 centimeters?

It will take 7 days for the earthworm to tunnel
14 centimeters into the ground,

Explanation:
Given an earthworm tunnels 2 centimeters into the
ground each day and the earthworm tunnels at about
the same pace every day, It will take the earthworm to
tunnel 14 centimeters is 14 ÷ 2 = 7 days.

Question 6.
Sebastian and Teshawn go to the movies.
The tickets cost $16 in total. The boys share the cost equally.
How much does Teshawn pay?

Teshawn pays $8 cost for the ticket,

Explanation:
Given Sebastian and Teshawn go to the movie and
the tickets cost $16 in total. Both the boys share the
cost equally means each had cost of $16 ÷ 2 = $8,
Therefore Teshawn pays $8 cost for the ticket.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 11 Pattern Sheet Answer Key

Multiply.

multiply by 3 (1–5)


Explanation:
Multiplied by 3 (1–5) as shown above.

Eureka Math Grade 3 Module 1 Lesson 11 Problem Set Answer Key

Question 1.
Mrs. Prescott has 12 oranges. She puts 2 oranges in each bag.
How many bags does she have?
a. Draw an array where each column shows a bag of oranges.
___12___ ÷ 2 = ___6_____.

Mrs. Prescott have 6 bags,

Explanation:
Given Mrs. Prescott has 12 oranges and she puts
2 oranges in each bag, So number of bags she have
are 12 ÷ 2 = 6 bags,

a. Drawn an array where each column shows a bag
of oranges as shown above in the picture.

b. Redraw the oranges in each bag as a unit in the tape diagram.
The first unit is done for you. As you draw,
label the diagram with known and unknown information from the problem.

b.

Explanation:
Redrawn the oranges in each bag as a unit in the tape diagram,
labeled the diagram with known and unknown information
from the problem as 6 X 2 = 12 oranges, or 12 ÷ 2 = 6 bags.

Question 2.
Mrs. Prescott arranges 18 plums into 6 bags. How many plums
are in each bag? Model the problem with both an array and
a labeled tape diagram. Show each column as the number
of plums in each bag.
There are ____3_____ plums in each bag.

Mrs. Prescott arranges 3 plums in each bag,

Explanation:
Given Mrs. Prescott arranges 18 plums into 6 bags.
So number of  plums in each bag are 18 ÷ 6 = 3 bags
Modeled the problem with both an array and
labeled tape diagram as shown each column as the
number of plums in each bag.

Question 3.
Fourteen shopping baskets are stacked equally in 7 piles.
How many baskets are in each pile? Model the problem
with both an array and a labeled tape diagram.
Show each column as the number of baskets in each pile.

There are 2 baskets in each pile,

Explanation:
Given Fourteen shopping baskets are stacked equally in 7 piles.
So number of baskets in each pile are 14 ÷ 7 = 2 baskets,
Modeled the problem with both an array and
labeled tape diagram. Shown each column as the
number of baskets in each pile.

Question 4.
In the back of the store, Mr. Prescott packs 24 bell peppers
equally into 8 bags. How many bell peppers are in each bag?
Model the problem with both an array and labeled tape diagram.
Show each column as the number of bell peppers in each bag.

There are 3 bell peppers in each bag,

Explanation:
Given In the back of the store, Mr. Prescott packs 24 bell peppers
equally into 8 bags. So number of  bell peppers in each bag are
24 ÷ 8 = 3 bell peppers,
Modeled the problem with both an array and labeled tape diagram and
shown each column as the number of bell peppers in each bag.

Question 5.
Olga saves $2 a week to buy a toy car. The car costs $16.
How many weeks will it take her to save enough to buy the toy?

It will take 8 weeks to buy a toy car,

Explanation:
Given Olga saves $2 a week to buy a toy car.
The car costs $16. So number of weeks will it take
her to save enough to buy the toy is $16 ÷ $2 = 8 weeks.

Eureka Math Grade 3 Module 1 Lesson 11 Exit Ticket Answer Key

Ms. McCarty has 18 stickers. She puts 2 stickers on
each homework paper and has no more left.
How many homework papers does she have?
Model the problem with both an array and a
labeled tape diagram.

Ms. McCarty has 9 homework papers,

Explanation:
Given Ms. McCarty has 18 stickers and she puts 2 stickers
on each homework paper and has no more left.
So number of homework papers does she have are
18 ÷ 2 = 9 homework papers,
Modeled the problem with both an array and
labeled tape diagram as shown above in the picture.

Eureka Math Grade 3 Module 1 Lesson 11 Homework Answer Key

Question 1.
Fred has 10 pears. He puts 2 pears in each basket.
How many baskets does he have?
a. Draw an array where each column represents the
number of pears in each basket.
___10____ ÷ 2 = ___5_____

Fred has 5 baskets ,

Explanation:
Given Fred has 10 pears and he puts 2 pears in each basket.
So number of baskets does he have are 10 ÷ 2 = 5 baskets,

a. Drawn an array where each column represents the
number of pears in each basket as shown in the picture above.

b. Redraw the pears in each basket as a unit in the tape diagram.
Label the diagram with known and unknown information from the problem.

Redrawn the pears in each basket as a unit in the tape diagram,

Explanation:
Redrawn the pears in each basket as a unit in the tape diagram.
Labeled the diagram with known and unknown information
from the problem as 10 ÷ 2 = 5 baskets or 5 X 2 = 10 pears.

Question 2.
Ms. Meyer organizes 15 clipboards equally into 3 boxes.
How many clipboards are in each box? Model the problem
with both an array and a labeled tape diagram. Show each
column as the number of clipboards in each box.
There are ____5_____ clipboards in each box.

Ms. Meyer organizes 5 clipboards in each box,

Explanation:
Given Ms. Meyer organizes 15 clipboards equally into 3 boxes.
So, Number of clipboards in each box are 15 ÷ 3 = 5,
Modeled the problem with both an array and
labeled tape diagram as shown above each
column has 5 number of clipboards in each box.

Question 3.
Sixteen action figures are arranged equally on 2 shelves.
How many action figures are on each shelf?
Model the problem with both an array and a
labeled tape diagram. Show each column as the number
of action figures on each shelf.

There are 8 action figures on each shelf,

Explanation:
Given Sixteen action figures are arranged equally on 2 shelves.
So number of action figures on each shelf are 16 ÷ 2 = 8,
Modeled the problem with both an array and
labeled tape diagram as show each column has 8 number
of action figures on each shelf.

Question 4.
Jasmine puts 18 hats away. She puts an equal number of
hats on 3 shelves. How many hats are on each shelf?
Model the problem with both an array and a labeled
tape diagram. Show each column as the number of
hats on each shelf.

On each shelf there are 6 hats,

Explanation:
Given Jasmine puts 18 hats away and she puts an equal
number of hats on 3 shelves. So number of hats on each
shelf are 18 ÷ 3 = 6 hats,
Modeled the problem with both an array and labeled
tape diagram as shown each column has 6 number of
hats on each shelf.

Question 5.
Corey checks out 2 books a week from the library.
How many weeks will it take him to check out a
total of 14 books?

Corey will take 7 weeks to check out total 14 books,

Explanation:
Given Corey checks out 2 books a week from the library.
So, number of weeks it will take Corey to check out a
total of 14 books are 14 ÷ 2 = 7 weeks.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 10 Pattern Sheet Answer Key

Multiply.

multiply by 2 (6–10)


Explanation:
Multiplied  by 2 (6–10) as shown above.

Eureka Math Grade 3 Module 1 Lesson 10 Problem Set Answer Key

Question 1.
7 × 3 = (5 × 3) + (2 × 3) = ___21_______

(5 × 3) + (2 × 3) = 15 + ___6___
15 + ___6___ = _____21________

7 × 3 = (5 × 3) + (2 × 3) =
15 + 6 = 21 or 7 X 3 = 21.

Explanation:
Given 7 X 3 wrote 7 as (5 + 2) X 3 =
(5 × 3) + (2 × 3) =
15 + 6 = 21 or 7 X 3 = 21.

Question 2.
8 × 3 = (4 × 3) + (4 × 3) = __24____

(4 × 3) + (4 × 3) = ____12_____ + _____12____ = 24,
____8_____ × 3 = ____24______

8 × 3 = (4 × 3) + (4 × 3) =
12 + 12 = 24 or 8 X 3 = 24,

Explanation:
Given 8 X 3 wrote 8 as (4 + 4) X 3 =
(4 × 3) + (4 × 3) =
12 + 12 = 24 or 8 X 3 = 24.

Question 3.
Ruby makes a photo album. One page is shown below.
Ruby puts 3 photos in each row.
a. Fill in the equations on the right.
Use them to help you draw arrays that show the photos
on the top and bottom parts of the page.


Explanation:
Filled in the equations on the right as 2 X 3 = 6, 3 X 3 =9,
Used them to help to draw arrays that showed the photos
on the top and bottom parts of the page as shown above
in the picture.

b. Ruby calculates the total number of photos as shown below.
Use the array you drew to help explain Ruby’s calculation.

Explanation:
Ruby calculates the total 15 number of photos as shown above,
Used the array to drew to help explain Ruby’s calculation as
(2 X 3) + (3 X 3) = 6 + 9 = 15.

Eureka Math Grade 3 Module 1 Lesson 10 Exit Ticket Answer Key

Question 1.
6 × 3 = ___18___

(4 × 3) + (2 × 3) = __12__ + ___6___
6 × 3 = _12__ + _6__
_6_ × 3 = _18__

6 X 3  = (4 × 3) + (2 × 3) = 12 + 6 = 18 or 6 X 3 = 18,

Explanation:
Given 6 X 3 wrote 6 as (4 + 2) X 3 =
(4 × 3) + (2 × 3) =
12 + 6 = 18 or 6 X 3 = 18.

Question 2.
7 × 3 = _21_

(5 × 3) + (2 × 3) = __ + __
7 × 3 = __ + __
__ × 3 = ___

7 X 3  = (5 × 3) + (2 × 3) = 15 + 6 = 21 or 7 X 3 = 21,

Explanation:
Given 7 X 3 wrote 7 as (5 + 2) X 3 =
(5 × 3) + (2 × 3) =
15 + 6 = 21 or 7 X 3 = 21.

Eureka Math Grade 3 Module 1 Lesson 10 Homework Answer Key

Question 1.
6 × 3 = ____18______

6 X 3 = (4 × 3) + (2 × 3) = 12 + 6 = 18 or 6 X 3 = 18,

Explanation:
Given 6 X 3 wrote 6 as (4 + 2) X 3 =
(4 × 3) + (2 × 3) =
12 + 6 = 18 or 6 X 3 = 18.

Question 2.
8 × 2 = _16_

8 X 2 = (4 × 2) + (4 × 2) = 8 + 8 = 16 or 8 X 2 = 16,

Explanation:
Given 8 X 2 wrote 8 as (4 + 4) X 2 =
(4 × 2) + (4 × 2) =
8 + 8 = 16 or 8 X 2 = 16.

Question 3.
Adriana organizes her books on shelves. She puts 3 books in each row.
a. Fill in the equations on the right. Use them to draw arrays
that show the books on Adriana’s top and bottom shelves.


Explanation:
Given Adriana organizes her books on shelves.
She puts 3 books in each row.
a. Filled in the equations on the right as (5 X 3), (1 X 3)
Used them to draw arrays that show the books on
Adriana’s top and bottom shelves as shown above.

b. Adriana calculates the total number of books as shown below.
Use the array you drew to help explain Adriana’s calculation.


Explanation:
Adriana calculates the total 18 number of books as shown above,
Used the array to drew to help explain Adriana’s calculation as
6 X 3 = (5 X 3) + (1 X 3) = 15 + 3 = 18 or 6 X 3 = 18.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 9 Pattern Sheet Answer Key

multiply by 2 (1–5)


Explanation:
Multiply by 2 (1–5) as shown above.

Eureka Math Grade 3 Module 1 Lesson 9 Problem Set Answer Key

Question 1.
The team organizes soccer balls into 2 rows of 5.
The coach adds 3 rows of 5 soccer balls.
Complete the equations to describe the total array.


Explanation:
Given the team organizes soccer balls into 2 rows of 5 as
2 X 5 = 10 and the coach adds 3 rows of 5 soccer balls as
3 X 5 = 15, Completed the equations to described the
total array as 5 x 5 = (2 + 3) X 5 = (2 X 5) + (3 X 5) =
10 + 15 = 25 or 5 X 5 = 25.

Question 2.
7 × 2 = __14___

7 X 2 = 14,

Explanation:
Given 7 X 2, we wrote 7 X 2 as (5 + 2) X 2 =
(5 X 2) + ( 2 x 2) = 10 + 4 = 14 or
7 X 2 = 14.

Question 3.
9 × 2 = __18___

9 X 2 = 18,

Explanation:
Given 9 X 2  we wrote 9 X 2 as
(10 – 1) X 2 = (10 X 2) – (1 X 2) =
20 – 2 = 18 or 9 X 2 = 18.

Question 4.
Matthew organizes his baseball cards in 4 rows of 3.
a. Draw an array that represents Matthew’s cards using
an x to show each card.
b. Solve the equation to find Matthew’s total number of cards.
4 × 3 = __12__,
a.

Explanation:
Given Matthew organizes his baseball cards in 4 rows of 3,
So array shown as 4 X 3,
Drawn an array that represents Matthew’s cards using
an x to show each card as shown above.

b. Total number of  Matthew’s cards are 12,

Explanation:
Solved the equation to find Matthew’s total number of
cards as 4 X 3 = 12.

Question 5.
Matthew adds 2 more rows. Use circles to show his new
cards on the array in Problem 4(a).
a. Write and solve a multiplication equation to represent
the circles you added to the array.
___2___ × 3 = __6____

Explanation:
Given Matthew adds 2 more rows.
Used circles to show his new cards on the array in
Problem 4(a) as shown above.

b. Add the totals from the equations in Problems 4(b)
and 5(a) to find Matthew’s total cards.
__12____ + ___6___ = 18

Explanation:
Added the totals from the equations in Problems 4(b)
and 5(a) to find Matthew’s total cards as
(4 X 3) + (2 X 3) = 12 + 6 = 18.

c. Write the multiplication equation that shows Matthew’s
total number of cards.
___6___ × ___3___ = 18,

The multiplication equation to show total number of cards
is 6 X 3 = 18,

Explanation:
The multiplication equation that shows Matthew’s
total number of cards is 6 X 3 = (4 X 3) + (2 X 3) =
12 + 6 = 18 or 6 X 3 = 18.

Eureka Math Grade 3 Module 1 Lesson 9 Exit Ticket Answer Key

Question 1.
Mrs. Stern roasts cloves of garlic. She places 10 rows of
two cloves on a baking sheet. Write an equation to describe
the number of cloves Mrs. Stern bakes.
___10____ × ___2____ = __20____ cloves

The number of cloves Mrs. Stern bakes is 20 cloves,

Explanation:
Given Mrs. Stern roasts cloves of garlic. She places 10 rows of
two cloves on a baking sheet. The equation to describe
the number of cloves Mrs. Stern bakes is 10 X 2 = 20 cloves.

Question 2.
When the garlic is roasted, Mrs. Stern uses some for a recipe.
There are 2 rows of two garlic cloves left on the pan.
a. Complete the equation below to show how many garlic cloves Mrs. Stern uses.
____10____ twos – ____2____ twos = ____8___twos,

10 twos – 2 twos = 8 twos,

Explanation:
Completed the equation below to show how many
garlic cloves Mrs. Stern uses as 10 twos – 2 twos = 8 twos.

b. 20 – ________ = 16
20 – 4 = 16,

Explanation:
Subtracted 4 from 20 we get 16 as 20 – 4 =16 cloves.

c. Write an equation to describe the number of garlic cloves
Mrs. Stern uses. ___8____ × 2 = ___16_____,

The number of garlic cloves Mrs. Stern uses are 16 cloves,

Explanation:
Given Mrs. Stern roasts cloves of garlic,
She places 10 rows of two cloves on a baking sheet and
Mrs. Stern uses some for a recipe there are 2 rows of
two garlic cloves left on the pan, 10 x 2 = 20 cloves and left are
2 X 2 = 4 cloves, Means used cloves are ( 10 X 2) – (2 X 2) =
20 – 4 = 16 cloves or (10 – 2) X 2 = 8 X 2= 16 cloves.
Therefore, the equation for number of garlic cloves Mrs. Stern
uses are 8 X 2 = 16 cloves.

Eureka Math Grade 3 Module 1 Lesson 9 Homework Answer Key

Question 1.
Dan organizes his stickers into 3 rows of four.
Irene adds 2 more rows of stickers. Complete the
equations to describe the total number of stickers in the array.

a. (4 + 4 + 4) + (4 + 4) = __12 + 8 = ____20_____
b. 3 fours + ___2___ fours = _____5______ fours
c. ___5_____ × 4 = ____20____

a. (4 + 4 + 4) + (4 + 4) = 12 + 8 = 20,
b. 3 fours + 2 fours = 5 fours,
c. 5 X 4 = 20,

Explanation:
Given Dan organizes his stickers into 3 rows of four.
Irene adds 2 more rows of stickers.
Completed the equations to describe the
total number of stickers in the array as 5 X 5 =
(3 X 5) + (2 X 5) = 15 + 10 = 25 or 5 X 5 = 25,
a. We wrote 5 X 5 as (4 + 4 + 4) + (4 + 4) = 12 + 8 = 20,
b. We wrote 5 X 5 as 3 fours + 2 fours = 5 fours,
c. We wrote 5 x 4 as 20, 5 X 4 = 20.

Question 2.
7 × 2 = __14____

7 x 2 = 14,

Explanation:
Given 7 X 2 we wrote 7 x 2 as (6 + 1) X 2 =
(6 x 2) + (1 x 2) = 12 + 2 = 14 or 7 x 2 = 14.

Question 3.
9 × 3 = __27___

9 X 3 = 27,

Explanation:
Given 9 X 3 we wrote 9 x 3 as (10 – 1) X 3 =
(10 x 3) – (1 x 3) = 30 – 3 = 27 or 9 x 2 = 27.

Question 4.
Franklin collects stickers. He organizes his stickers in 5 rows of four.
a. Draw an array to represent Franklin’s stickers.
Use an x to show each sticker.
b. Solve the equation to find Franklin’s total number of
stickers. 5 × 4 = ___20___
a.

b. Franklin’s total number of stickers are 20.

Explanation:
Given Franklin collects stickers. He organizes his
stickers in 5 rows of four.
a. Drawn an array to represent Franklin’s stickers,
Used an x to show each sticker as shown above.
b. Solved the equation to find Franklin’s total number of
stickers as 5 × 4 = 20.

Question 5.
Franklin adds 2 more rows. Use circles to show his new stickers
on the array in Problem 4(a).
a. Write and solve an equation to represent the circles you added to the array.
___2___ × 4 = ___8___

Explanation:
Given Franklin adds 2 more rows. Used circles to show
his new stickers on the array in Problem 4(a).
a. Wrote and solved an equation to represent the
circles I added to the array as 2 X 4 = 8.

b. Complete the equation to show how you add the
totals of 2 multiplication facts to find Franklin’s
total number of stickers. __20____ + ___8___ = 28,

Equation of totals of 2 multiplication facts to find Franklin’s
total number of stickers are 20 + 8 = 28,

Explanation:
Completed the equation to show how I added the
totals of 2 multiplication facts to find Franklin’s
total number of stickers as (5 X 4)  + (2 X 4) = 20 + 8 = 28.

c. Complete the unknown to show Franklin’s total number of stickers.
__5___ × 4 = 20,

The unknown Franklin’s total number of stickers are 20,

Explanation:
To show unknown Franklin’s total number of stickers
as given Franklin collects stickers. He organizes his
stickers in 5 rows of four, So, Franklin’s total number
of stickers are 5 X 4 = 20.

Eureka Math Grade 3 Module 1 Answer Key

Eureka Math Grade 3 Module 1 Lesson 4 Sprint Answer Key

A
Repeated Addition as Multiplication

Question 1.
5 + 5 + 5 =
5 + 5 + 5 = 15,

Explanation:
Given 5 + 5 + 5 we add 5 by 3 times
we get 15, So 5 + 5 + 5 = 15.

Question 2.
3 × 5 =
3 X 5 = 15,

Explanation:
Given 3 X 5 we multiply 3 with 5,
we get 15 as 3 X 5 = 15.

Question 3.
5 × 3 =
5 X 3 = 15,

Explanation:
Given 5 X 3 we multiply 5 with 3,
we get 15 as 5 X 3 = 15.

Question 4.
2 + 2 + 2 =
2 + 2 + 2 = 6,

Explanation:
Given 2 + 2 + 2 we add 2 by 3 times
we get 6, So 2 + 2 + 2 = 6.

Question 5.
3 × 2 =
3 X 2 = 6,

Explanation:
Given 3 X 2 we multiply 3 with 2,
we get 6 as 3 X 2 = 6.

Question 6.
2 × 3 =
2 X 3 = 6,

Explanation:
Given 2 X 3 we multiply 2 with 3,
we get 6 as 2 X 3 = 6.

Question 7.
5 + 5 =
5 + 5 = 10,

Explanation:
Given 5 + 5 we add 5 by 2 times
we get 10, So 5 + 5 = 10.

Question 8.
2 × 5 =
2 X 5 = 10,

Explanation:
Given 2 X 5 we multiply 2 with 5,
we get 10 as 2 X 5 = 10.

Question 9.
5 × 2 =
5 X 2 = 10,

Explanation:
Given 5 X 2 we multiply 5 with 2,
we get 10 as 5 X 2 = 10.

Question 10.
2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 = 8,

Explanation:
Given 2 + 2 + 2 + 2 we add 2 by 4 times
we get 8, So 2 + 2 + 2 + 2= 8.

Question 11.
4 × 2 =
4 X 2 = 8,

Explanation:
Given 4 X 2 we multiply 4 with 2,
we get 8 as 4 X 2 = 8.

Question 12.
2 × 4 =
2 X 4 = 8,

Explanation:
Given 2 X 4 we multiply 2 with 4,
we get 8 as 2 X 4 = 8.

Question 13.
2 + 2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 + 2 = 10,

Explanation:
Given 2 + 2 + 2 + 2 + 2 we add 2 by 5 times
we get 10, So 2+ 2 + 2 + 2 + 2= 10.

Question 14.
5 × 2 =
5 X 2 = 10,

Explanation:
Given 5 X 2 we multiply 5 with 2,
we get 10 as 5 X 2 = 10.

Question 15.
2 × 5 =
2 X 5 = 10,

Explanation:
Given 2 X 5 we multiply 2 with 5,
we get 10 as 2 X 5 = 10.

Question 16.
3 + 3 =
3 + 3 = 6,

Explanation:
Given 3 + 3 we add 3 by 2 times
we get 6, So 3 + 3 = 6.

Question 17.
2 × 3 =
2 X 3 = 6,

Explanation:
Given 2 X 3 we multiply 2 with 3,
we get 6 as 2 X 3 = 6.

Question 18.
3 × 2 =
3 X 2 = 6,

Explanation:
Given 3 X 2 we multiply 3 with 2,
we get 6 as 3 X 2 = 6.

Question 19.
5 + 5 + 5+ 5 =
5 + 5 + 5 + 5 = 20,

Explanation:
Given 5 + 5 + 5 + 5 we add 5 by 4 times
we get 20, So 5 + 5 + 5 + 5 = 20.

Question 20.
4 × 5 =
4 X 5 = 20,

Explanation:
Given 4 X 5 we multiply 4 with 5,
we get 20 as 4 X 5 = 20.

Question 21.
5 × 4 =
5 X 4 = 20,

Explanation:
Given 5 X 4 we multiply 5 with 4,
we get 20 as 5 X 4 = 20.

Question 22.
2 × 2 =
2 X 2 = 4,

Explanation:
Given 2 X 2 we multiply 2 with 2,
we get 4 as 2 X 2 = 4.

Question 23.
3 + 3 + 3 + 3 =
3 + 3 + 3 + 3 = 12,

Explanation:
Given 3 + 3 + 3 + 3 we add 3 by 4 times
we get 12, So 3 + 3 + 3 + 3 = 12.

Question 24.
4 × 3 =
4 X 3 = 12,

Explanation:
Given 4 X 3 we multiply 4 with 3,
we get 12 as 4 X 3 = 12.

Question 25.
3 × 4 =
3 X 4 = 12,

Explanation:
Given 3 X 4 we multiply 3 with 4,
we get 12 as 3 X 4 = 12.

Question 26.
3 + 3 + 3 =
3 + 3 + 3 = 9,

Explanation:
Given 3 + 3 + 3 we add 3 by 3 times
we get 9, So 3 + 3 + 3 = 9.

Question 27.
3 × 3 =
3 X 3 = 9,

Explanation:
Given 3 X 3 we multiply 3 with 3,
we get 9 as 3 X 3 = 9.

Question 28.
3 + 3 + 3 + 3 + 3 =
3 + 3 + 3 + 3 + 3 = 15,

Explanation:
Given 3 + 3 + 3 + 3 + 3 we add 3 by 5 times
we get 15, So 3 + 3 + 3 + 3 + 3 = 15.

Question 29.
5 × 3 =
5 X 3 = 15,

Explanation:
Given 5 X 3 we multiply 5 with 3,
we get 15 as 5 X 3 = 15.

Question 30.
3 × 5 =
3 X 5 = 15,

Explanation:
Given 3 X 5 we multiply 3 with 5,
we get 15 as 3 X 5 = 15.

Question 31.
7 + 7 =
7 + 7 = 14,

Explanation:
Given 7 + 7 we add 7 by 2 times
we get 14, So 7 + 7 = 14.

Question 32.
2 × 7 =
2 X 7 = 14,

Explanation:
Given 2 X 7 we multiply 2 with 7,
we get 14 as 2 X 7 = 14.

Question 33.
7 × 2 =
7 X 2 = 14,

Explanation:
Given 7 X 2 we multiply 7 with 2,
we get 14 as 7 X 2 = 14.

Question 34.
9 + 9 =
9 + 9 = 18,

Explanation:
Given 9 + 9 we add 9 by 2 times
we get 18, So 9 + 9 = 18.

Question 35.
2 × 9 =
2 X 9 = 18,

Explanation:
Given 2 X 9 we multiply 2 with 9,
we get 18 as 2 X 9 = 18.

Question 36.
9 × 2 =
9 X 2 = 18,

Explanation:
Given 9 X 2 we multiply 9 with 2,
we get 18 as 9 X 2 = 18.

Question 37.
6 + 6 =
6 + 6 = 12,

Explanation:
Given 6 + 6 we add 6 by 2 times
we get 12, So 6 + 6 = 12.

Question 38.
6 × 2 =
6 X 2 = 12,

Explanation:
Given 6 X 2 we multiply 6 with 2,
we get 12 as 6 X 2 = 12.

Question 39.
2 × 6 =
2 X 6 = 12,

Explanation:
Given 2 X 6 we multiply 2 with 6,
we get 12 as 2 X 6 = 12.

Question 40.
8 + 8 =
8 + 8 = 16,

Explanation:
Given 8 + 8 we add 8 by 2 times
we get 16, So 8 + 8 = 16.

Question 41.
2 × 8 =
2 X 8 = 16,

Explanation:
Given 2 X 8 we multiply 2 with 8,
we get 16 as 2 X 8 = 16.

Question 42.
8 × 2 =
8 X 2 = 16,

Explanation:
Given 8 X 2 we multiply 8 with 2,
we get 16 as 8 X 2 = 16.

Question 43.
7 + 7 + 7 + 7 =
7 + 7 + 7 + 7 = 28,

Explanation:
Given 7 + 7 + 7 + 7 we add 7 by 4 times
we get 28, So 7 + 7 + 7 + 7 = 28.

Question 44.
4 × 7 =
4 X 7 = 28,

Explanation:
Given 4 X 7 we multiply 4 with 7,
we get 28 as 4 X 7 = 28.

B
Repeated Addition as Multiplication

Question 1.
2 + 2 + 2 =
2 + 2 + 2 = 6,

Explanation:
Given 2 + 2 + 2 we add 2 by 3 times
we get 6, So 2 + 2 + 2 = 6.

Question 2.
3 × 2 =
3 X 2 = 6,
Explanation:
Given 3 X 2 we multiply 3 with 2,
we get 6 as 3 X 2 = 6.

Question 3.
2 × 3 =
2 X 3 = 6,
Explanation:
Given 2 X 3 we multiply 2 with 3,
we get 6 as 2 X 3 = 6.

Question 4.
5 + 5 + 5 =
5 + 5 + 5 = 15,
Explanation:
Given 5 + 5 + 5 we add 5 by 3 times
we get 15, So 5 + 5 + 5 = 15.

Question 5.
3 × 5 =
3 X 5 = 15,
Explanation:
Given 3 X 5 we multiply 3 with 5,
we get 15 as 3 X 5 = 15.

Question 6.
5 × 3 =
5 X 3 = 15,
Explanation:
Given 5 X 3 we multiply 5 with 3,
we get 15 as 5 X 3 = 15.

Question 7.
2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 = 8,

Explanation:
Given 2 + 2 + 2 + 2 we add 2 by 4 times
we get 8, So 2 + 2 + 2 + 2= 8.

Question 8.
4 × 2 =
4 X 2 = 8,
Explanation:
Given 4 X 2 we multiply 4 with 2,
we get 8 as 4 X 2 = 8.

Question 9.
2 × 4 =
2 X 4 = 8,
Explanation:
Given 2 X 4 we multiply 2 with 4,
we get 8 as 2 X 4 = 8.

Question 10.
5 + 5 =
5 + 5 = 10,
Explanation:
Given 5 + 5 we add 5 by 2 times
we get 10, So 5 + 5 = 10.

Question 11.
2 × 5 =
2 X 5 = 10,
Explanation:
Given 2 X 5 we multiply 2 with 5,
we get 10 as 2 X 5 = 10.

Question 12.
5 × 2 =
5 X 2 = 10,
Explanation:
Given 5 X 2 we multiply 5 with 2,
we get 10 as 5 X 2 = 10.

Question 13.
3 + 3 =
3 + 3 = 6,

Explanation:
Given 3 + 3 we add 3 by 2 times
we get 6, So 3 + 3 = 6.

Question 14.
2 × 3 =
2 X 3 = 6,

Explanation:
Given 2 X 3 we multiply 2 with 3,
we get 6 as 2 X 3 = 6.

Question 15.
3 × 2 =
3 X 2 = 6,

Explanation:
Given 3 X 2 we multiply 3 with 2,
we get 6 as 3 X 2 = 6.

Question 16.
2 + 2 + 2 + 2 + 2 =
2 + 2 + 2 + 2 + 2 = 10,
Explanation:
Given 2 + 2 + 2 + 2 + 2 we add 2 by 5 times
we get 10, So 2+ 2 + 2 + 2 + 2= 10.

Question 17.
5 × 2 =
5 X 2 = 10,

Explanation:
Given 5 X 2 we multiply 5 with 2,
we get 10 as 5 X 2 = 10.

Question 18.
2 × 5 =
2 X 5 = 10,
Explanation:
Given 2 X 5 we multiply 2 with 5,
we get 10 as 2 X 5 = 10.

Question 19.
5 + 5 + 5 + 5 =
5 + 5 + 5 + 5 = 20,

Explanation:
Given 5 + 5 + 5 + 5 we add 5 by 4 times
we get 20, So 5 + 5 + 5 + 5 = 20.

Question 20.
4 × 5 =
4 X 5 = 20,
Explanation:
Given 4 X 5 we multiply 4 with 5,
we get 20 as 4 X 5 = 20.

Question 21.
5 × 4 =
5 X 4 = 20,

Explanation:
Given 5 X 4 we multiply 5 with 4,
we get 20 as 5 X 4 = 20.

Question 22.
2 × 2 =
2 X 2 = 4,
Explanation:
Given 2 X 2 we multiply 2 with 2,
we get 4 as 2 X 2 = 4.

Question 23.
4 + 4 + 4 =
4 + 4 + 4 = 12,

Explanation:
Given 4 + 4 + 4 we add 4 by 3 times
we get 12, So 4 + 4 + 4 = 12.

Question 24.
3 × 4 =
3 X 4 = 12,

Explanation:
Given 3 X 4 we multiply 3 with 4,
we get 12 as 3 X 4 = 12.

Question 25.
4 × 3 =
4 X 3 = 12,

Explanation:
Given 4 X 3 we multiply 4 with 3,
we get 12 as 4 X 3 = 12.

Question 26.
4 + 4 + 4 + 4 =
4 + 4 + 4 + 4 = 16,

Explanation:
Given 4 + 4 + 4 + 4 we add 4 by 4 times
we get 16, So 4 + 4 + 4 +4 = 16.

Question 27.
4 × 4 =
4 X 4 = 16,

Explanation:
Given 4 X 4 we multiply 4 with 4,
we get 14 as 4 X 4 = 16.

Question 28.
4 + 4 + 4 + 4 + 4 =
4 + 4 + 4 + 4 + 4 = 20,

Explanation:
Given 4 + 4 + 4 + 4 + 4 we add 4 by 5 times
we get 20, So 4 + 4 + 4 + 4 + 4 = 20.

Question 29.
4 × 5 =
4 X 5 = 20,

Explanation:
Given 4 X 5 we multiply 4 with 5,
we get 20 as 4 X 5 = 20.

Question 30.
5 × 4 =
5 X 4 = 20,

Explanation:
Given 5 X 4 we multiply 5 with 4,
we get 20 as 5 X 4 = 20.

Question 31.
6 + 6 =
6 + 6 = 12,

Explanation:
Given 6 + 6 we add 6 by 2 times
we get 12, So 6 + 6 = 12.

Question 32.
6 × 2 =
6 X 2 = 12,

Explanation:
Given 6 X 2 we multiply 6 with 2,
we get 12 as 6 X 2 = 12.

Question 33.
2 × 6 =
2 X 6 = 12,

Explanation:
Given 2 X 6 we multiply 2 with 6,
we get 12 as 2 X 6 = 12.

Question 34.
8 + 8 =
8 + 8 = 16,

Explanation:
Given 8 + 8 we add 8 by 2 times
we get 16, So 8 + 8 = 16.

Question 35.
2 × 8 =
2 X 8 = 16,

Explanation:
Given 2 X 8 we multiply 2 with 8,
we get 16 as 2 X 8 = 16.

Question 36.
8 × 2 =
8 X 2 = 16,

Explanation:
Given 8 X 2 we multiply 8 with 2,
we get 16 as 8 X 2 = 16.

Question 37.
7 + 7 =
7 + 7 = 14,

Explanation:
Given 7 + 7 we add 7 by 2 times
we get 14, So 7 + 7 = 14.

Question 38.
2 × 7 =
2 X 7 = 14,

Explanation:
Given 2 X 7 we multiply 2 with 7,
we get 14 as 2 X 7 = 14.

Question 39.
7 × 2 =
7 X 2 = 14,

Explanation:
Given 7 X 2 we multiply 7 with 2,
we get 14 as 7 X 2 = 14.

Question 40.
9 + 9 =
9 + 9 = 18,

Explanation:
Given 9 + 9 we add 9 by 2 times
we get 18, So 9 + 9 = 18.