HMH Go Math

Access Go Math Grade 3 Answer Key Chapter 5 Use Multiplication Facts here for quick reference. Solve various questions from Go Math Grade 3 Answer Key Chapter 5 and get basics of multiplication easily. Resolve your queries and practice on your own to understand where you stand in your preparation. Attain the logic behind each problem in the exercise questions from 3rd Grade Go Math Answer Key Ch 5 USe Multiplication Facts and clear the exam with better grades.

Go Math Grade 3 Answer Key Chapter 5 Use Multiplication Facts

Step by Step Solution is given in the HMH Go Math Grade 3 Answer Key by subject experts keeping in mind the student’s level of understanding. Have an overview of the concepts present in Grade 3 Chapter 5 through the quick links available. Utilize the Grade 3 HMH Go Math Answer Key Chapter 5 Use Multiplication Facts and clear your queries regarding the topics instantly. You just need to click on the below mentioned Go Math 3rd standard Grade 3 Chapter Key links and take your preparation to the next level.

Lesson 1: Algebra • Describe Patterns

• Describe Patterns Page No 265
• Describe Patterns Lesson Check Page No 266

Lesson 2: Algebra • Find Unknown Numbers

• Find Unknown Numbers Page No 271
• Find Unknown Numbers Lesson Check Page No 272

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint Page No 273
• Mid-Chapter Checkpoint Lesson Check Page No 274

Lesson 3: Problem Solving • Use the Distributive Property

• Use the Distributive Property Page No 279
• Use the Distributive Property Lesson Check Page No 280

Lesson 4: Multiplication Strategies with Multiples of 10

• Multiplication Strategies with Multiples of 10 Page No 285
• Multiplication Strategies with Multiples of 10 Lesson Check Page No 286

Lesson 5: Multiply 1-Digit Numbers by Multiplies of 10

• Multiply 1-Digit Numbers by Multiplies of 10 Page No 291
• Multiply 1-Digit Numbers by Multiplies of 10 Lesson Check Page No 292

Chapter 5 Review/Test

• Review/Test Page No 293
• Review/Test Page No 294
• Review/Test Page No 295
• Review/Test Page No 296
• Review/Test Page No 297
• Review/Test Page No 298

Describe Patterns Page No 265

Describe a pattern for the table. Then complete the table.

Question 1.

Answer: Add 6 muffins for each pan; Multiply the number of pans by 6.

Explanation:

Now we have to multiple no. of pans by 6
4 × 6 = 24; 5 × 6 = 30

Question 2.

Wagons	2	3	4	5	6
Wheels	8	12	16	_______	_______

Answer:

Wagons	2	3	4	5	6
Wheels	8	12	16	20	24

Explanation:

Add 4 wheels for each Wagons; Multiply the number of Wagons by 4
5 × 4 = 20; 6 × 4 = 24

Question 3.

Vases	Flowers
2	14
3	_______
4	28
5	_______
6	42

Answer:

Vases	Flowers
2	14
3	21
4	28
5	35
6	42

Explanation:

Add 7 flowers for each vase; Multiply the number of flowers by 7
3 × 7 = 21; 5 × 7 = 35

Question 4.

Spiders	Legs
1	8
2	_______
3	24
4	_______
5	40

Answer:

Spiders	Legs
1	8
2	16
3	24
4	32
5	40

Explanation:

Add 8 legs for each spider and then multiply the number of spiders by 8
i.e., 8 × 2 = 16; 8 × 4 = 32

Problem Solving

Describe Patterns Lesson Check Page No 266

Question 1.
Which of the following describes a pattern in the table?

Options:
a. Multiply by 3.
b. Multiply by 5.
c. Add 1.
d. Add 4.

Answer: Multiply by 5

Explanation:

From the above table, we can see that each chair is added by 5 for each table.
So, multiply the number of tables by 5
The correct answer is option B

Question 2.
Which number completes this table?

Options:
a. 30
b. 20
c. 24
d. 22

Answer: 24

Explanation:

Each butterfly is added by 4
Multiply the number of butterflies by 4
4 × 6 = 24 wings
So, the correct answer is option C

Spiral Review

Question 3.
Jennilee buys 7 packs of crayons. There are 6 crayons in each pack. How many crayons does Jennilee buy in all?
Options:
a. 13
b. 36
c. 42
d. 48

Answer: 42

Explanation:

Given that, Jennilee buys 7 packs of crayons
There are 6 crayons in each pack
1 pack = 6 crayons
7 packs = x
x × 1 = 6 × 7
x = 42

Question 4.
Maverick has 5 books of circus tickets. Each book has 5 tickets. How many tickets does Maverick have in all?
Options:
a. 10
b. 15
c. 20
d. 25

Answer: 25

Explanation:

Maverick has 5 books on circus tickets
Each book has 5 tickets
1 book =5 tickets
5 books = x tickets
x × 1 = 5 × 5
x = 25
Thus the correct answer is option D

Question 5.
Bailey walked his dog 2 times each day for 9 days. How many times did Bailey walk his dog in all?
Options:
a. 9
b. 11
c. 18
d. 27

Answer: 18

Explanation:

Given, Bailey walked his dog 2 times each day for 9 days
Number of times Bailey walk his dog in all = x
x = 9 × 2
x = 18
Thus the correct answer is option C

Question 6.
Drew’s Tree Company delivers pear trees in groups of 4. Yesterday, the company delivered 8 groups of pear trees. How many pear trees were delivered in all?
Options:
a. 12
b. 16
c. 24
d. 32

Answer: 32

Explanation:

Given,

Drew’s Tree Company delivers pear trees in groups of 4
Yesterday, the company delivered 8 groups of pear trees
How many pear trees were delivered in all = x
x = 4 × 8
x = 32
Thus the correct answer is option D

Find Unknown Numbers Page No 271

Find the unknown factor.

Question 1.
n × 3 = 12
Think: How many groups of 3 equal 12?
n = 4

Answer: 4

Explanation:

n × 3 = 12
n = 12/4
n = 3

Question 2.
s × 8 = 64
s = ________

Answer: 8

Explanation:

How many groups of 8 equals 64?

s × 8 = 64
s = 64/8
s = 8

Question 3.
21 = 7 × n
n = ________

Answer: 3

Explanation:

Number of groups 7 equals 21

21 = 7 × n
n = 21/7
n = 3

Question 4.
y × 2 = 18
y = ________

Answer: 9

Explanation:

y × 2 = 18
y = 18/2
y = 9

Question 7.
m × 4 = 28
m = ________

Answer: 7

Explanation:

Here m is the unknown product
4 × m = 28
4m = 28
m = 28/4
m = 7

Question 8.
★ × 1 = 9
★ = ________

Answer: 9

Explanation:

Here the symbol ★ is the unknown product
★ = 9/1
★ = 9

Question 9.
18 = 6 × r
r = ________

Answer: 3

Explanation:

r is the unknown product
6 × r = 18
r = 18/6
r = 3

Question 10.
u × 5 = 30
u = ________

Answer: 6

Explanation:

u is the unknown product
u × 5 = 30
5u = 30
u = 30/5
u = 6

Question 11.
4 × ■ = 24
■ = ________

Answer: 6

Explanation:

■ is the unknown product
4 × ■ = 24
■ = 24/4
■ = 6
Therefore the answer is 6

Question 14.
5 × ▲ = 40
▲ = ________

Answer: 8

Explanation:

Here the symbol ▲ is the unknown product
▲ × 5 = 40
▲ = 40/5
▲ = 8

Question 15.
30 = d × 3
d = ________

Answer: 10

Explanation:

d is the unknown product
30 = d × 3
30/3 = d
d = 30/3
d = 10
Therefore the answer is 10

Question 16.
7 × k = 42
k = ________

Answer: 6

Explanation:

k is the unknown product
7 × k = 42
k = 42/7
k = 6

Problem Solving

Find Unknown Numbers Lesson Check Page No 272

Question 1.
What is the unknown factor?
b × 7 = 56
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

b × 7 = 56
b = 56/7
Now we have to check how many groups of 7 equals 56
7 × 8 = 56
b = 8
Thus the answer is option C

Question 2.
What is the unknown factor shown by this array?

3 × ■ = 24
Options:
a. 3
b. 6
c. 8
d. 9

Answer: 8

Explanation:

The unknown product is ■
Here we have to find the product of 3 × ■  which equals 24
3 × ■ = 24
■ = 24/3
■ = 8
Therefore the unknown factor shown by this array is 8

Spiral Review

Question 3.
Which is an example of the Commutative Property of Multiplication?
Options:
a. 6 + 4 = 4 + 6
b. 4 × 6 = 6 × 4
c. 4 × 3 = 4 + 8
d. 3 × 6 = 9 × 2

Answer: 4 × 6 = 6 × 4

Explanation:

According to the commutative property of multiplication, changing the order of the numbers we are multiplying, does not change the product.
a × b = b × a
So, the answer is 4 × 6 = 6 × 4

Question 4.
Find the product.
5 × (4 × 2)
Options:
a. 13
b. 22
c. 40
d. 80

Answer: 40

Explanation:

This is in the form of a × (b × c)
First, multiply 4 and 2
5 × (4 × 2) = 5 × 8
5 × 8 = 40
Therefore the correct answer is option D

Question 5.
Which number sentence is an example of the Distributive Property?
Options:
a. 4 × 7 = (4 × 3) + (4 × 4)
b. 4 × 7 = 7 × 4
c. 4 × 7 = 28
d. 7 × 4 = 15 + 13

Answer: 4 × 7 = (4 × 3) + (4 × 4)

Example:

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
The example of Distributive Property is 4 × 7 = (4 × 3) + (4 × 4)

Question 6.
In a group of 10 boys, each boy had 2 hats. How many hats did they have in all?
Options:
a. 5
b. 12
c. 20
d. 40

Answer: 20

Explanation:

Given that,
Each boy has 2 hats
A group of 10 boys has x hats
x × 1 = 2 × 10
x = 20

Mid-Chapter Checkpoint Page No 273

Vocabulary
Choose the best term from the box.

Question 1.
An __________ is a number sentence that uses the equal sign to show that two amounts are equal.
__________

Answer: Equation

Explanation:

The definition of the Equation is the number sentence that uses an equal sign to show that two amounts are equal.

Concepts and Skills

Describe a pattern in the table. Then complete the table.

Question 2.

Type below:
__________

Answer:

Weeks	1	2	3	4	5
Days	7	14	21	28	35

Explanation:

First of all look for the pattern to complete the table.
As you look across the rows you can find the days are increased by 7 for each week.
Now use the pattern to find the number of days in 4 and 5 weeks.
7 × 4 = 28; 7 × 5 = 35

Question 3.

Type below:
__________

Answer:

Tickets	2	3	4	5	6
Cost	$8	$12	$16	$20	$24

Explanation:

Look for the pattern to complete the table.
As you look across the rows you can find the cost increased by $4 for each ticket.
Now use the pattern to find the cost for 5 and 6 tickets
4 × 5 = 20; 4 × 6 = 24

Question 4.

Type below:
__________

Answer:

Project Teams	Members
3	9
4	12
5	15
6	18
7	21

Explanation:

Look for the pattern by comparing the columns in the table. You can multiply number of project teams by 3 to find the members.
3 × 5 = 15; 3 × 7 = 21

Question 5.

Type below:
__________

Answer:

Tables	Chairs
1	8
2	16
3	24
4	32
5	40

Explanation:

Look for the pattern by comparing the rows in the table.
Now multiply the number of tables by 8 so that you can find the number of chairs for 3 and 5 tables.
3 × 8 = 24; 5 × 8 = 40

Find the unknown number.

Question 6.
m × 5 = 30
m = _______

Answer: 6

Explanation:

m is the unknown product
m × 5 = 30
m = 30/5
m = 6
Therefore the value of m is 6

Question 7.
■ × 6 = 48
■ = _______

Answer: 8

Explanation:

■ is the symbol of the unknown product
■ × 6 = 48
■ = 48/6
■ = 8

Question 11.
★ × 10 = 10
★ = _______

Answer: 1

Explanation:

★ is the symbol of the unknown product
★ × 10 = 10
★ = 10/10
★ = 1

Mid-Chapter Checkpoint Lesson Check Page No 274

Question 12.
Describe a pattern in the table.

Type below:
__________

Answer: Multiply by 6

Explanation:

As you look across the rows, you can see that the number of stickers increases by 6 for each package.

Question 15.
Kyle saves $10 every week for 6 weeks. How much money will Kyle have in Week 6?

a. 60

Answer:

Weeks	1	2	3	4	5	6
Amount	$10	$20	$30	$40	$50	$60

Explanation:

Look for the pattern to complete the table.
As you look across the rows you can find the amount increased for each week.
You can multiply 10 by weeks 4, 5 and 6
i.e., 10 × 4 = 40; 10 × 5 = 50; 10 × 6 = 60

Question 16.
Tennis balls cost $7 for a can of 3. Steve gives the cashier $40 to buy balls and receives $12 in change. How many tennis balls did Steve buy?
_______ tennis balls

Answer: 12 tennis balls

Explanation:

Steve spent $40 – $12 = $28
Let y represent the number of cans.
Tennis balls cost $7 for a can of 3
7 × y = 28
y = 28/7
y = 4 cans
So, Steve buys 4 cans of 3 tennis balls
Then, we need to multiply the no. of cans, 4, by the number of tennis balls in each can, 3
4 × 3 = 12 tennis balls

Use the Distributive Property Page No 279

Read each problem and solve.

Question 1.
Each time a student turns in a perfect spelling test, Ms. Ricks puts an achievement square on the bulletin board. There are 6 rows of squares on the bulletin board. Each row has 30 squares. How many perfect spelling tests have been turned in?
Think: 6 × 30 = 6 × (10 + 10 + 10)
= 60 + 60 + 60 = 180
180 spelling tests

Answer: 180 spelling test

Explanation:

There are 6 rows of squares on the bulletin board
Each row has 30 squares
We can use the distributive property to find the number of perfect spelling tests have been turned in
6 × 30 = 6 × (10+10+10)
6 × 10 + 6 × 10 + 6 × 10
60 + 60 + 60 = 180 spelling test

Question 2.
Norma practices violin for 50 minutes every day. How many minutes does Norma practice violin in 7 days?
_______ minutes

Answer: 350 minutes

Explanation:

Given,
Norma practices violin for 50 minutes every day
To find:
How many minutes does Norma practice violin in 7 days?
We can solve this problem by using the distributive property
7 × 50 = 7 × (20 + 30) = (7 × 20) + (7 × 30)
= 350 minutes

Use the Distributive Property Lesson Check Page No 280

Question 1.
Each snack pack holds 20 crackers. How many crackers in all are there in 4 snack packs?
Options:
a. 60
b. 80
c. 100
d. 800

Answer: 80

Explanation:

Given:
Each snack pack holds 20 crackers
To find:
How many crackers in all are there in 4 snack packs
By using the Distributive property we can find the crackers in 4 snack packs
4 × 20 = 4 × (10 + 10)
4 × 10 + 4 × 10 = 40 + 40 = 80
Thus the correct answer is option B

Question 2.
A machine makes 70 springs each hour. How many springs will the machine make in 8 hours?
Options:
a. 500
b. 520
c. 540
d. 560

Answer: 560

Explanation:

Given,
A machine makes 70 springs each hour
To find:
How many springs will the machine make in 8 hours
8 × 70 = 8 × (35 + 35)
= (8 × 35) + (8 × 35)
= 280 + 280
= 560
Thus option D is the correct answer

Spiral Review

Question 3.
Lila read 142 pages on Friday and 168 pages on Saturday. Which is the best estimate of how many pages Lila read on Friday and Saturday combined?
Options:
a. 100
b. 200
c. 300
d. 400

Answer: 300

Explanation:

Lila read 142 pages on Friday and 168 pages on Saturday
We can estimate the number of pages Lila read on Friday and Saturday combined by using the Distributive property
142 + 168 = (2 × 71) + (2 × 84) = 300
So, the correct answer is option C

Question 4.
Jessica wrote 6 + 6 + 6 + 6 on the board. Which is another way to show 6 + 6 + 6 + 6?
Options:
a. 4 × 4
b. 4 × 6
c. 4 × 4 × 6
d. 6 × 6

Answer: 4 × 6

Explanation:
Jessica wrote 6 + 6 + 6 + 6 on the board
The another way to write 6 + 6 + 6 + 6 is 4 × 6
Because here 6 is added 4 times. So the multiplication form of 6 + 6 + 6 + 6 is 4 × 6
So, the correct answer is option B

Use the line plot for 5–6.

Question 5.
Eliot made a line plot to record the number of birds he saw at his bird feeder. How many more sparrows than blue jays did he see?
Options:
a. 2
b. 3
c. 4
d. 5

Answer: 4

Explanation:

Number of sparrows = 5
Number of Blue Jays = 1
To know how many more sparrows than blue jays we have to subtract number of blue jay from number of sparrows
= 5 – 1 = 4
So, the correct answer is option C

Question 6.
How many robins and cardinals combined did Eliot see?
Options:
a. 2
b. 3
c. 4
d. 5

Answer: 5

Explanation:

Number of robins = 3
Number of Cardinals = 2
Total Number of robins and cardinals = 3 + 2 = 5
So, the answer is option D

Multiplication Strategies with Multiples of 10 Page No 285

Use a number line to find the product.

Question 1.
2 × 40 = 80

Answer: 80

Explanation:

The number line given above shows that there are 2 groups of 4 tens
So, 2 × 4 tens
2 × 40 = 80

Question 2.

4 × 30 = _______

Answer: 120

Explanation:

There are 4 groups of 3 tens
So, the number jumps from 0 to 30, 30 to 60, 60 to 90, and from 90 to 120.
4 × 3 tens = 4 × 30 = 120

Use place value to find the product.

Question 3.
5 × 70 = 5 × _______ tens
= _______ tens = _______

Answer:

i. 7 tens
ii. 35 tens
iii. 350

Explanation:

70 = 7 × 10 = 7 tens
5 × 70 = 35 × 10 = 35 tens = 350

Question 4.
60 × 4 = _______ tens × 4
= _______ tens = _______

Answer:

i. 6 tens
ii. 24 tens
iii. 240

Explanation:

Here 60 is multiplied with 4
60 = 6 × 10 = 6 tens
60 × 4 = 6 tens × 4
24 tens = 24 × 10 = 240

Question 5.
7 × 30 = 7 × _______ tens
= _______ tens = _______

Answer:

i. 3 tens
ii. 21 tens
iii. 210

Explanation:

30 = 3 × 10 = 3 × 1 ten = 3 tens
7 × 30 = 7 × 3 tens
= 21 tens
= 21 × 10 = 210

Question 6.
90 × 3 = _______ tens × 3
= tens = _______

Answer:

i. 9 tens
ii. 27 tens
iii. 270

Explanation:

90 = 9 × 1 ten = 9 × 10 = 9 tens
9 tens × 3 = 27 tens
27 tens = 27 × 1 ten
= 27 × 10 = 270

Problem Solving

Multiplication Strategies with Multiples of 10 Lesson Check Page No 286

Question 1.
Each bag of pattern blocks contains 50 blocks. To make a class pattern, the teacher combines 4 bags of blocks. How many pattern blocks are there in all?
Options:
a. 20
b. 200
c. 240
d. 250

Answer: 200

Explanation:

Given,
Each bag of pattern blocks contains 50 blocks
To make a class pattern, the teacher combines 4 bags of blocks
Here we make use of multiplication strategies to know the number of pattern blocks
50 × 4 = 5 tens × 4
= 20 tens = 20 × 10 = 200
Therefore the correct answer is option B

Question 2.
A deli received 8 blocks of cheese. Each block of cheese weighs 60 ounces. What is the total weight of the cheeses?
Options:
a. 420 ounces
b. 460 ounces
c. 480 ounces
d. 560 ounces

Answer: 480 ounces

Explanation:

A deli received 8 blocks of cheese
Each block of cheese weighs 60 ounces
60 × 8 = 6 tens × 8
48 tens = 48 × 10 = 480 ounces
So, the correct answer is option C

Spiral Review

Question 3.
Alan and Betty collected cans for recycling. Alan collected 154 cans. Betty collected 215 cans. How many cans did they collect in all?
Options:
a. 369
b. 379
c. 469
d. 479

Answer: 369

Explanation:

Given, Alan and Betty collected cans for recycling
Alan collected 154 cans
Betty collected 215 cans
To know total cans they collected in all, we have to add both the cans of Alan and Betty
154 + 215 = 369 cans
Therefore the correct answer is option A

Question 4.
The third graders collected 754 cans. The fourth graders collected 592 cans. Which is the best estimate of how many more cans the third graders collected?
Options:
a. 50
b. 100
c. 200
d. 300

Answer: 200

Explanation:

Given,
The third graders collected 754 cans
The fourth graders collected 592 cans
To find the best estimate of how many more cans the third graders collected
We have to subtract fourth graders cans from third graders can
Here they are asking the estimated number of cans the third graders collected
754 rounded to the nearest hundred is 800 and
592 rounded to the nearest hundred is 600
800 – 600 = 200
Therefore the correct answer is 200

Use the bar graph for 5–6.

Question 5.
How many more books did Ed read than Bob?
Options:
a. 2
b. 3
c. 4
d. 5

Answer: 3

Explanation:

The bar graph shows that Ed read 8 books in June
Bob read 5 books in June
To know the number of books Ed read than Bob
We have to subtract the no. of books Bob read from Ed
= 8 – 5 = 3 books
So, the correct answer is option B

Question 6.
How many books in all did the four students read in June?
Options:
a. 22
b. 24
c. 26
d. 36

Answer: 26

Explanation:

Bob read 5 books in June
Ed read 8 books in June
Eve read 7 books in June
Ann read 6 books in June
Total = 5 + 8 + 7 + 6 = 26 books
So, the answer is option C

Multiply 1-Digit Numbers by Multiplies of 10 Page No 291

Find the product. Use base-ten blocks or draw a quick picture.

Question 1.
4 × 50 = 200

Answer: 200

Explanation:

First, multiply the ones
4 × o ones = 0
Next, multiply the tens
4 × 5 tens = 200

Question 2.
60 × 3 = _______

Answer: 180

Explanation:

Mutliply the ones
3 × o ones = 0
Now multiply the tens
3 × 6 tens = 18 tens = 180

Question 5.
5 0
× 2
—–
_______

Answer: 100

Explanation:

Multiply the ones
2 × 0 ones = 0
Multiply the tens
2 × 5 tens = 10 tens = 100

Question 6.
6 0
× 7
—–
_______

Answer: 420

Explanation:

Multiply the ones
7 × 0 ones = 0
Multiply the tens
7 × 6 tens = 42 tens = 420

Question 7.
70
× 4
—–
_______

Answer: 280

Explanation:

Multiply the ones
4× 0 ones = 0
Multiply the tens
4 × 7 tens = 28 tens = 280

Question 8.
6 × 90 = _______

Answer: 540

Explanation:

Multiply the ones
6 × 0 ones = 0
Multiply the tens
6 × 9 tens = 54 tens = 540

Question 9.
9 × 70 = _______

Answer: 630

Explanation:

Multiply the ones
9 × 0 ones = 0
Multiply the tens
9 × 7 tens = 63 tens = 630

Question 10.
8 × 90 = _______

Answer: 720

Explanation:

Multiply the ones
8 × 0 ones = 0
Multiply the tens
8 × 9 tens = 72 tens = 720

Question 11.
_______ = 6 × 80

Answer: 480

Explanation:

Multiply the ones
6 × 0 ones = 0
Multiply the tens
6 × 8 tens = 48 tens = 480

Problem Solving

Multiply 1-Digit Numbers by Multiplies of 10 Lesson Check Page No 292

Question 1.
Each shelf in one section of the library holds 30 books. There are 9 shelves in that section. How many books will these shelves hold?
Options:
a. 220
b. 260
c. 270
d. 280

Answer: 270

Explanation:

Given,

Each shelf in one section of the library holds 30 books
There are 9 shelves in that section
30 × 9 = 3 tens × 9
= 27 tens = 270
Therefore the correct answer is option C

Question 2.
One can of juice mix makes 60 ounces of juice. How many ounces of juice can be made from 6 cans of juice mix?
Options:
a. 300 ounces
b. 360 ounces
c. 390 ounces
d. 600 ounces

Answer: 360 ounces

Explanation:

Given,
One can of juice mix makes 60 ounces of juice
Number of ounces of juice can be made from 6 cans of juice mix
60 ounces × 6 = 6 tens × 6
= 36 tens = 360 ounces
Thus the answer is option B

Spiral Review

Question 3.
Sue bought 7 cans of tennis balls. There are 3 balls in each can. How many balls did Sue buy?
Options:
a. 10
b. 21
c. 28
d. 37

Answer: 21

Explanation:

Sue bought 7 cans of tennis balls
There are 3 balls in each can
To know the number of balls Sue buy
We have multiply number of cans and number of balls
= 7 × 3 = 21 balls

Question 4.
Which is an example of the Commutative Property of Multiplication?
Options:
a. 3 + 4 = 4 + 3
b. 5 × 0 = 0
c. 1 × 7 = 7
d. 3 × 4 = 4 × 3

Answer: 3 × 4 = 4 × 3

Explanation:

According to the commutative property of multiplication, changing the order of the numbers we are multiplying, does not change the product.
a × b = b × a
3 × 4 = 4 × 3
Option D is the correct example of the Commutative property

Question 5.
Lyn drew this bar model to solve a problem. Which operation should she use to find the unknown number?

Options:
a. addition
b. division
c. multiplication
d. subtraction

Answer: addition

Explanation:

To know the unknown number we have to add both the number of flowers
90 + 54 = 144

Question 6.
Joe drew this bar model to find the unknown number of balls. Which is the correct answer?

Options:
a. 356
b. 256
c. 144
d. 124

Answer: 144

Explanation:

Given that
Joe drew this bar model to find the unknown number of balls
106 balls + ___ = 250 balls
let the unknown number be x
106 + x = 250
x = 250 – 106
x = 144 balls

Review/Test Page No 293

Question 1.
The camping club wants to rent rafts. Each raft can hold 8 people. Which equation could be used to find how many rafts are needed for 32 people?
Options:
a. 8 × 32 = ■
b. 32 × ■ = 8
c. ■ × 8 = 32
d. 32 × 8 = ■

Answer: ■ × 8 = 32

Explanation:

Each raft can hold 8 people
■ represents raft that can hold 32 people
Now we have to multiple number of people with rafts for 32 people
■ × 8 = 32
■ = 32/8
■ = 4
Therefore 4 rafts are needed for 32 people

Question 2.
Select the equations that show the Distributive Property. Mark all that apply.
Options:
a. 8 × 20 = 8 × (10 + 10)
b. 5 × 60 = 5 × (20 + 40)
c. 30 × 6 = 6 × 30
d. 9 × (4 + 3) = 9 × 7

Answer: a, b, d

Explanation:

The sum of two numbers times a third number is equal to the sum of each addend times the third number.
The above 3 options satisfy the law of Distributive Property

Question 3.
Choose the number from the box that makes the sentence true.
A library has 48 shelves of fiction books. There are 6 shelves in each cabinet.
There are cabinets of fiction books in the library.
_________

Answer: 8

Explanation:

Let x represents cabinets of fiction in the library
x × 6 = 48
x = 48/6
x = 8
Therefore the answer is 8

Review/Test Page No 294

Question 4.
For numbers 4a–4d, choose True or False for each equation.
a. 5 × (4 + 4) = 8 × 5
i. True
ii. False

Answer: True

Explanation:

The above question satisfies the distributive property
5 × (4 + 4) = 5 × 8 = 40
8 × 5 = 40
Therefore LHS = RHS
So, the equation is true

Question 4.
b. 8 × (3 + 3) = 8 × 5
i. True
ii. False

Answer: False

Explanation:

8 × (3 + 3) = 8 × 6 = 48
8 × 5 = 40
So, the equation is false

Question 4.
c. (3 × 5) + (5 × 5) = 8 × 5
i. True
ii. False

Answer: True

Explanation:

(3 × 5) + (5 × 5) = 8 × 5
The above question satisfies the distributive property
8 × 5 = 40
(3 × 5) + (5 × 5) = 15 + 25 = 40
Both LHS and RHS are equal
So, the answer is true

Question 4.
d. (3 × 2) + (8 × 3) = 8 × 5
i. True
ii. False

Answer: False

Explanation:

(3 × 2) + (8 × 3)
3 × 2 = 6; 8 × 3 = 24
= (3 × 2) + (8 × 3) = 6 + 24
But it is given as 8 × 5
So, the answer is false

Question 5.
Alya planted 30 trays of flowers. Each tray held 8 flowers. Javon planted 230 flowers. Did Alya plant more flowers than Javon, the same number of flowers as Javon, or fewer flowers than Javon?
Options:
a. She planted more flowers than Javon.
b. She planted the same number of flowers as Javon.
c. She planted fewer flowers than Javon. 6.

Answer: She planted more flowers than Javon.

Explanation:

Given that, Alya planted 30 trays of flowers and each tray held 8 flowers
30 × 8 = 240 flowers
So, Alya planted 240 flowers
Javon planted 230 flowers
To know whether Alya plant more flowers than Javon, the same number of flowers as Javon, or fewer flowers than Javon
We have to subtract Number of flowers planted by Javon from Alya
240 – 230 = 10
So, Alya planted more flowers than Javon

Question 6.
For numbers, 6a–6d, choose Yes or No to show whether the unknown number is 6.

a. 4 × ■ = 32

i. Yes
ii. No

Answer: No

Explanation:

■ = 6
Now we have to substitute ■ = 6 in the above question
4 × 6 = 24
So, the answer is No

b. ■ × 6 = 36

i. Yes
ii. No

Answer: Yes

Explanation:

■ = 6
6 × 6 = 36
It satisfies the above equation
So, the answer is Yes

c. 8 × ■ = 49

i. Yes
ii. No

Answer: No

Explanation:

■ = 6
8 × 6 = 48 but not 49
So, the answer is No

d. ■ × 30 = 180

i. Yes
ii. No

Answer:

Explanation:

■ = 6
6 × 30 = 180
It satisfies the above equation
So, the answer is yes

Question 7.

Each train can carry 20 cars. Use the number line to find how many cars 6 trains can carry.

Answer: 120 cars

Explanation:

Each train can carry 20 cars
6 trains can carry x cars
x × 1 = 20 × 6
x = 120 cars

Review/Test Page No 295

Question 8.
Samantha made this multiplication model. Complete the equation that represents the model.

_____ × _____ = _____
Type below:
__________

Answer: 90

Explanation:

Each vertical bar represents a ten. Each group of 3 vertical bars represents 30
We have 3 groups of 30, therefore the equation that represents the model is
3 × 30 = 90 models

Question 9.
A printer prints newsletters for many groups every month. Which group uses the greatest number of pieces of paper?

__________

Answer: Book Lovers Club

Explanation:

From the above table, we can say that Book Lovers Club group uses the greatest number of pieces of paper

Question 10.
A store has 30 boxes of melons. Each box holds 4 bags. Each bag holds 2 melons. What is the total number of melons in the store?
__________ melons

Answer: 240 melons

Explanation:

Given,
A store has 30 boxes of melons
Each box holds 4 bags
Each bag holds 2 melons
1 box holds 4 bags
30 × 4 = 120 bags
1 bag = 2 melons
120 bags = x
x = 120 × 2
x = 240 melons
Therefore total number of melons in the store = 240 melons

Review/Test Page No 296

Question 12.
Tim describes a pattern. He says the pattern shown in the table is “Add 3.” Is Tim correct? Explain how you know.

Type below:
__________

Answer:

No, Tim is not correct
The pattern works for the first pair of numbers 1 + 3 = 4
But it doesn’t work for any of the other pairs. The pattern should be to Multiply the number of packages by 4

Question 13.
This shows a part of a multiplication table. Find the missing numbers. Explain how you found the numbers.

Type below:
__________

Answer:

Explanation:

The only numbers that have a product of 35 are 5 and 7. The only numbers that have a product of 40 are 5 and 8.
This tells us that 5 is the number for the row. That means 6 is the next row down, and 7 is the row after that. The factors of 7 and 8 are the columns, so we can multiply to find the missing numbers

Question 14.
Describe a pattern for this table.

Pattern: _____
How would the table change if the pattern was “Multiply the number of tanks by 8”? Explain.
Type below:
__________

Answer: Multiply the number of tanks by 80
The table would change by taking a zero off each number of fish in the second row because you would be multiplying by ones, not tens.

Review/Test Page No 297

Question 16.
The bookstore has 6 shelves of books about animals. There are 30 books on each shelf. How many books about animals does the bookstore have?
Shade squares to make a diagram to show how you can use the Distributive Property to find the number of books about animals in the bookstore.

__________ animal books

Answer:

6 × (10 + 10 + 10) = (6 × 10) + (6 × 10) + (6 × 10)
= 60 + 60 + 60
= 180 animal books

Review/Test Page No 298

Question 17.
Cody saves all his nickels. Today he is getting them out of his piggy bank and wrapping them to take to the bank. He finds he has 360 nickels. It takes 40 nickels to fill each paper wrapper and make a roll. How many wrappers does he need?
Part A
Write an equation using n for the unknown number. Find the number of wrappers needed.
______ × ______ = ______

Answer: n × 40 = 360

Explanation:

n represents no. of wrappers need
Each paper wrapper needs 40 nickels
Cody has 360 nickels
n × 40 = 360

Question 17.
Part B
Explain how you solved this problem and how you know your answer is correct.
Type below:
__________

Answer:

Explanation:

Given that Cony has 360 nickels
Each paper wrapper needs 40 nickels
Let n be the number of wrappers needed
That means n × 40 = 360
n = 360/40
n = 9
So, n wrappers are needed to make the rolls

Question 18.
Ruben is collecting cans for the recycling contest at school. He makes two plans to try to collect the most cans.
Plan A: Collect 20 cans each week for 9 weeks.
Plan B: Collect 30 cans each week for 7 weeks.
Part A
Which plan should Ruben choose?
__________

Answer: Plan B

Collect 30 cans each week for 7 weeks.

Question 18.
Part B
Explain how you made your choice.
Type below:
__________

Answer:

Given that Ruben is collecting cans for the recycling contest at school
His plan is to collect more cans
That means he has to collect more number of cans in less number of weeks
So, Plan B is perfect to win the recycling contest at school

We hope the info shared regarding the Go Math Grade 3 Chapter 5 Answer Key has been beneficial to you. Refer to Go Math Grade 3 Answer Key Chapter 5 Use Multiplication Facts Extra Practice. Practice is the only key to success and make the most out of the Answer Key available and achieve success in your assessments or tests.

Are you looking everywhere to learn about Go Math Grade 3 Answer Key Chapter 6 Understand Division? This Answer Key includes topics like related multiplication and division facts, repeated subtraction, number of equal groups, and so on. Those who are preparing for the Grade 3 Ch 6 will find the HMH Go Math Grade 3 Answer Key Chapter 6 Understand Division extremely helpful. You can identify your knowledge gap by solving the Questions from 3rd Grade Go Math Answer Key Chapter 6 Understand Division.

Go Math Grade 3 Answer Key Chapter 6 Understand Division

Before you begin your preparation learn the topics included in Grade 3 Go Math Answer Key Chapter Understand Division. You can always look up to Go Math Grade 3 Chapter 6 Key as a reference to clear all your queries. Practice the problems in 3rd Grade Go Math Answer Key Ch 6 Understand Division and understand the concepts easily.

Lesson 1: Problem Solving • Model Division

• Model Division Page No 305
• Model Division Page No 306

Lesson 2: Size of Equal Groups

• Size of Equal Groups Page No 311
• Size of Equal Groups Page No 312

Lesson 3: Number of Equal Groups

• Number of Equal Groups Page No 317
• Number of Equal Groups Page No 318

Lesson 4: Model with Bar Models

• Model with Bar Models Page No 323
• Model with Bar Models Page No 324

Lesson 5: Algebra • Relate Subtraction and Division

• Relate Subtraction and Division Page No 329
• Relate Subtraction and Division Page No 330

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint Page No 331
• Mid-Chapter Checkpoint Page No 332

Lesson 6: Investigate • Model with Arrays

• Model with Arrays Page No 337
• Model with Arrays Page No 338

Lesson 7: Algebra • Relate Multiplication and Division

• Relate Multiplication and Division Page No 343
• Relate Multiplication and Division Page No 344

Lesson 8: Algebra • Write Related Facts

• Write Related Facts Page No 349
• Write Related Facts Page No 350

Lesson 9: Algebra • Division Rules for 1 and 0

• Division Rules for 1 and 0 Page No 355
• Division Rules for 1 and 0 Page No 356

Chapter 6 Review/Test

• Review/Test Page No 361
• Review/Test Page No 362

Model Division Page No 305

Question 1.
Six customers at a toy store bought 18 jump ropes. Each customer bought the same number of jump ropes. How many jump ropes did each customer buy?
__________

Answer: 3 jump ropes

Explanation:

Given that there are Six customers at a toy store bought 18 jump ropes
Each customer bought the same number of jump ropes
To know the number of jump roses that each customer bought
You must place each jump ropes until all the jump ropes are used.
That means 18 jump ropes to all 6 customers
= 18 ÷ 6 = 3
Therefore each customer bought 3 jump ropes

Question 2.
Hiro has 36 pictures of his summer trip. He wants to put them in an album. Each page of the album holds 4 pictures. How many pages will Hiro need for his pictures?
__________

Answer: 9 pages

Explanation:

Hiro has 36 pictures of his summer trip. He wants to put them in an album
Each page of the album holds 4 pictures
Make it into equal groups and put 4 pictures in each page
= 36 ÷ 4 = 9
Thus Hiro need 9 pages for his pictures

Question 3.
Katia has 42 crayons in a box. She buys a storage bin that has 6 sections. She puts the same number of crayons in each section. How many crayons does Katia put in each section of the storage bin?
__________

Answer: 7 crayons

Explanation:

Katia has 42 crayons in a box
She buys a storage bin that has 6 sections
Make 42 crayons as a group and place 1 crayon in each section. Then you get 7 crayons in each section
42 ÷ 6 = 42/6 = 7
Therefore 7 crayons do Katia put in each section of the storage bin

Model Division Page No 306

Question 1.
Maria buys 15 apples at the store and places them into bags. She puts 5 apples into each bag. How many bags does Maria use for all the apples?
Options:
a. 2
b. 3
c. 4
d. 10

Answer: 3

Explanation:

Maria buys 15 apples at the store and places them into bags
She puts 5 apples into each bag
That means each bag contains 5 apples
Now, Divide the apples into equal groups and place them in each bag
15 ÷ 5 = 3
Therefore Maria uses 3 bags to put 15 apples.

Question 2.
Tom’s neighbor is fixing a section of his walkway. He has 32 bricks that he is placing in 8 equal rows. How many bricks will Tom’s neighbor place in each row?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given: Tom’s neighbor is fixing a section of his walkway
He has 32 bricks that he is placing in 8 equal rows
Now place each brick in all 8 rows  equally and repeat until the bricks are over
32 ÷ 8 = 4
So, you get 4 bricks in each row
Thus the correct answer is option B

Question 3.
Find the unknown factor.
7 × _ = 56
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

Let the unknown factor be x
7 × x = 56

So, the correct answer is option C

Question 4.
How many students practiced the piano more than 3 hours a week?

Options:
a. 2
b. 6
c. 8
d. 10

Answer: 6

Explanation:

3 students practiced the piano for 4 hours
2 students practiced the piano for 5 hours and
1 student practiced the piano for 6 hours
= 3 + 2 + 1 = 6
The above line plot shows that 6 students practiced the piano for more than 3 hours

Question 5.
Count equal groups to find how many there are.

Options:
a. 3
b. 4
c. 12
d. 16

Answer: 12

Explanation:

The above figure shows that there are 4 circles and each circle is divided into 3 equal groups
So, multiply number of circles with equal groups
= 4 × 3 = 12
Thus the correct answer is option C

Question 6.
Which is another way to group the factors?
(3 × 2) × 5
Options:
a. (3 + 2) + 5
b. (3 × 2) + 5
c. 3 × (2 + 5)
d. 3 × (2 × 5)

Answer: 3 × (2 × 5)

Explanation:

The another way to group (3 × 2) × 5 is 3 × (2 × 5)
Because there is no change in the symbol and number
So, the correct answer is option D

Size of Equal Groups Page No 311

Use counters or draw a quick picture. Make equal groups. Complete the table.

Question 1.

	Counters	Number of Equal Groups	Number in Each Group
1.	15	3	__________
2.	21	7	__________
3.	28	7	__________
4.	32	4	__________
5.	9	3	__________
6.	18	3	__________
7.	20	5	__________
8.	16	8	__________
9.	35	5	__________
10.	24	3	__________

Answer:

	Counters	Number of Equal Groups	Number in Each Group
1.	15	3	5
2.	21	7	3
3.	28	7	4
4.	32	4	8
5.	9	3	3
6.	18	3	6
7.	20	5	4
8.	16	8	2
9.	35	5	7
10.	24	3	8

Explanation:

1. No. of counters = 15
Number of equal groups = 3
Place 1 counter to each group, you get 5 in each group

2. No. of counters = 21
Number of equal groups = 7
Place 1 counter to each group, you get 3 in each group

3. No. of counters = 28
Number of equal groups = 7
Place 1 counter to each group, you get 4 in each group

4. No. of counters = 32
Number of equal groups = 4
Place 1 counter to each group, you get 8 in each group

5. No. of counters = 9
Number of equal groups = 3
Place 1 counter to each group, you get 3 in each group

6. No. of counters = 18
Number of equal groups = 3
Place 1 counter to each group, you get 6 in each group

7. No. of counters = 20
Number of equal groups = 5
Place 1 counter to each group, you get 4 in each group

8. No. of counters = 16
Number of equal groups = 8
Place 1 counter to each group, you get 2 in each group

9. No. of counters = 35
Number of equal groups = 5
Place 1 counter to each group, you get 7 in each group

10. No. of counters = 24
Number of equal groups = 3
Place 1 counter to each group, you get 8 in each group

Size of Equal Groups Page No 312

Question 1.
Ryan has 21 pencils. He wants to put the same number of pencils in each of 3 pencil holders. How many pencils will he put in each pencil holder?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 7

Explanation:

Ryan has 21 pencils
He wants to put the same number of pencils in each of 3 pencil holders
Split it into 3 groups and share each pencil to each group
You get 7 pencils for each of 3 groups
21/3 = 7
Thus the correct answer is option B

Question 2.
Corrine is setting out 24 plates on 6 tables for a dinner. She sets the same number of plates on each table. How many plates does Corrine set on each table?
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

Given,
Corrine is setting out 24 plates on 6 tables for a dinner
She sets the same number of plates on each table
Make a group of 6 tables and place 1 plate for each group
You get 4 plates for each table
24/6 = 4 plates
So, the correct answer is Option B

Question 3.
Each table has 4 legs. How many legs do 4 tables have?
Options:
a. 1
b. 8
c. 16
d. 20

Answer: 16

Explanation:

Given that Each table has 4 legs
4 tables have x number of legs
x = 4 × 4 = 16
Therefore 4 tables have 16 legs

Question 4.
Tina has 3 stacks of 5 CDs on each of 3 shelves. How many CDs does she have in all?
Options:
a. 14
b. 30
c. 35
d. 45

Answer: 45

Given,
Tina has 3 stacks of 5 CDs on each of 3 shelves
How many CDs does she have in all = x
To know the number of CDs in all we have to multiply no. of stacks, no. of CDs on each of 3 shelves
x = 3 × 5 × 3 = 15 × 3 = 45
So, the answer is option D

Question 5.
What is the unknown factor?
7 × _= 35
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

Let the unknown factor be x
7 × x = 35
x = 35/7 = 5
Therefore the correct answer is option B

Question 6.
Which of the following describes a pattern in the table?

Number of packs	1	2	3	4	5
Number of yo-yos	3	6	9	12	?

Options:
a. Add 2.
b. Multiply by 2.
c. Multiply by 3.
d. Add 12.

Answer: Multiply by 3.

Explanation:

Add 3 yo-yos for each pack and multiply no. of pans by 3

Number of Equal Groups Page No 317

Draw counters on your MathBoard. Then circle equal groups. Complete the table.

Question 1.

	Counters	Number of Equal Groups	Number in Each Group
1.	24	3	8
2.	35	__________	7
3.	30	__________	5
4.	16	__________	4
5.	12	__________	6
6.	36	__________	9
7.	18	__________	3
8.	15	__________	5
9.	28	__________	4
10.	27	__________	3

Answer:

	Counters	Number of Equal Groups	Number in Each Group
1.	24	3	8
2.	35	5	7
3.	30	6	5
4.	16	4	4
5.	12	2	6
6.	36	4	9
7.	18	6	3
8.	15	3	5
9.	28	7	4
10.	27	9	3

Explanation:

1. No. of counters = 24
Number in each group = 8
24/8 = 3
So, the number of equal groups = 3

2. No. of counters = 35
Number in each group = 7
35/7 = 5
So, the number of equal groups = 5

3. No. of counters = 30
Number in each group = 5
30/5 = 6
So, the number of equal groups = 6

4. No. of counters = 16
Number in each group = 4
16/4 = 4
So, the number of equal groups = 4

5. No. of counters = 12
Number in each group = 6
12/6 = 2
So, the number of equal groups = 2

6. No. of counters = 36
Number in each group = 9
36/9 = 4
So, the number of equal groups = 4

7. No. of counters = 18
Number in each group = 3
18/3 = 6
So, the number of equal groups = 6

8. No. of counters = 15
Number in each group = 5
15/5 = 3
So, the number of equal groups = 3

9. No. of counters = 28
Number in each group = 4
28/4 = 7
So, the number of equal groups = 7

10. No. of counters = 27
Number in each group = 3
27/3 = 9
So, the number of equal groups = 9

Number of Equal Groups Page No 318

Question 1.
Ramon works at a clothing store. He puts 24 pairs of jeans into stacks of 8. How many stacks does Ramon make?
Options:
a. 5
b. 4
c. 3
d. 2

Answer: 3

Explanation:

Ramon puts 24 pairs of jeans into stacks of 8
Split the pair of jeans to 8 groups of the stack
You get 3 pair of jeans for each stack
24/8 = 3
Therefore the correct answer is option C

Question 2.
There are 36 people waiting in line for a hayride. Only 6 people can ride on each wagon. If each wagon is full, how many wagons are needed for all 36 people?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: 6

Explanation:

There are 36 people waiting in line for a hayride.
Only 6 people can ride on each wagon
Split 36 people into 6 groups
That means 36/6 = 6 Wagons
So, the correct answer is option B

Question 3.
Which multiplication sentence does the array show?

Options:
a. 4 × 5 = 20
b. 4 × 6 = 24
c. 4 × 7 = 28
d. 4 × 8 = 32

Answer: 4 × 7 = 28

Explanation:

There are 4 rows and 7 columns
rows × columns = 4 × 7 = 28
Thus the answer is option C

Question 4.
Austin buys 4 boxes of nails for his project. There are 30 nails in each box. How many nails does Austin buy in all?
Options:
a. 12
b. 34
c. 70
d. 120

Answer: 120

Explanation:

Given,
Austin buys 4 boxes of nails for his project
There are 30 nails in each box
No. of nails does Austin buy in all = 30 + 30 + 30 + 30
4 × 30 = 120
So, the correct answer is option D

Question 5.
Which describes the number sentence?
8 + 0 + 8
Options:
a. odd + odd = odd
b. Identity Property of Addition
c. even + even = even
d. Commutative Property of Addition

Answer: Identity Property of Addition

Explanation:

In math, identity is a number, n, that when added to other numbers, gives the same number, n. The additive identity is always zero. This brings us to the identity property of addition, which simply states that when you add zero to any number, it equals the number itself.

Question 6.
Each month for 6 months, Kelsey completes 5 paintings. How many more paintings does she need to complete before she has completed 38 paintings?
Options:
a. 2
b. 6
c. 8
d. 9

Answer: 8

Explanation:

Each month for 6 months
Kelsey completes 5 paintings
x no. of paintings she need to complete before she has completed 38 paintings
6 × 5 = 30 paintings
x + 30 = 38
x = 38 – 30
x = 8
So, the correct answer is option C

Model with Bar Models Page No 323

Write a division equation for the picture.

Question 1.

Answer: 27 ÷ 3 = 9 or 27 ÷ 9 = 3

Explanation:

There are 27 counters and each circle has 9 groups. There are 3 groups of 9 counters.
27 ÷ 3 = 27/3 = 9
27 ÷ 9 = 27/9 = 3

Question 2.

Type below:
___________

Answer: 16 ÷ 8 = 2 or 16 ÷ 2 = 8

Explanation:

The total number of counters is 16 and circle a group of 2 counters. Continue circling groups of 2 until all 16 counters are in the group.
So, Divide Total number of counters by number of equal groups
16 ÷ 8 = 16/8 = 2
Next, Divide total number of counters by no. of counters in each group.
16 ÷ 2 = 16/2 = 8

Question 3.

Type below:
___________

Answer: 16 ÷ 4 = 4

Explanation:

The total number of counters is 16 and circle a group of 4 counters. Continue circling groups of 4 until all 16 counters are in the group
Divide No. of counters by no. of equal groups = 16 ÷ 4 = 4
And then divide no. of counters by no. of counters in each group = 16 ÷ 4 = 4

Question 4.

Type below:
___________

Answer: 18 ÷ 3 = 6 or 18 ÷ 6 = 3

Explanation:

Number of counters = 18
Number of Equal groups = 3
Number of counters in each group = 6
Divide No. of counters by no. of equal groups
18 ÷ 3 = 18/3 = 6
Divide No. of counters by no. of counters in each group
18 ÷ 6 = 18/6 = 3

Complete the bar model to solve. Then write a division equation for the bar model.

Question 5.
There are 15 postcards in 3 equal stacks. How many postcards are in each stack?

________ postcards

Answer: 5 postcards, 15 ÷ 3 = 5

Explanation:

Total number of postcards = 15
Number of equal stacks = 3
Number of postcards in each stack = x
x = No. of postcards/ No. of equal stacks
x = 15/3
x = 5
Thus each stack contains 5 postcards

Question 6.
There are 21 key rings. How many groups of 3 key rings can you make?

________ groups

Answer: 7 groups, 21 ÷ 3 = 7

Explanation:

Divide the 21 key rings into 7 to make 7 groups with 3 key rings each group
21 ÷ 3 = 21/3 = 7 groups

There are 7 groups of 3 key rings.

Problem Solving

Model with Bar Models Page No 324

Question 1.
Jack and his little sister are stacking 24 blocks. They put the blocks in 3 equal stacks. How many blocks are in each stack?
Options:
a. 4
b. 6
c. 7
d. 8

Answer: 8

Explanation:

Total number of blocks = 24
They put the blocks in 3 equal stacks
To know the blocks in each stack, we have to divide no. of blocks by number of equal stacks
24 ÷ 3 = 24/3 = 8 blocks
There are 8 blocks in each stack
So, the correct answer is option D

Question 2.
Melissa made 45 greeting cards. She put them in 5 equal piles. How many cards did she put in each pile?
Options:
a. 9
b. 8
c. 7
d. 6

Answer: 9

Explanation:

Given,
Melissa made 45 greeting cards
She put them in 5 equal piles
To know the number of cards she put in each pile
We have to divide number of cards by no. of equal piles
= 45 ÷ 5 = 45/5 = 9 cards
Thus there are 9 cards in each pile
So, the correct answer is option A

Spiral Review

Question 3.
Angie puts 1 stamp on each envelope. She puts stamps on 7 envelopes. How many stamps does Angie use?
Options:
a. 0
b. 1
c. 7
d. 8

Answer: 7

Explanation:

Angie puts 1 stamp on each envelope
She puts stamps on 7 envelopes
To find Number of stamps Angie use, we have to divide no. of stamps on envelopes by no. of stamps on each envelope
= 7 ÷ 1 = 7

Question 4.
A carnival ride has 8 cars. Each car holds 4 people. How many people are on the ride if all the cars are full?
Options:
a. 34
b. 32
c. 28
d. 24

Answer: 32

Explanation:

Given,
A carnival ride has 8 cars
Each car holds 4 people
1 car = 4 people
8 cars = x
x × 1 = 4 × 8
x = 32
32 people are on the ride if all the cars are full

Use the line plot for 5–6.

Question 5.
How many families have 1 computer at home?
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 6

Explanation:

The line plot shows that 6 families have 1 computer at home

Question 6.
How many families have more than 1 computer at home?
Options:
a. 4
b. 5
c. 7
d. 8

Answer: 8

Explanation:

Number of Families have 2 computers at home = 3
Number of Families have 3 computers at home = 4
Number of Families have 4 computers at home = 1
Number of Families have more than 1 computer at home = 3 + 4 + 1 = 8

Relate Subtraction and Division Page No 329

Write a division equation.

Question 1.

Answer: 16 ÷ 4 = 4

Explanation:

Step 1:

Start with 16

Step 2:

Subtract with 4 until you get 0

Step 3:

Count the number of times you subtract 4

Since you subtract 4 times
There are 4 groups 4 in 16
So 16 ÷ 4 = 4
Sixteen divided by four equals four

Question 2.

______ ÷ ______ = ______

Answer: 12 ÷ 3 = 4

Explanation:

Step 1:

Start at 12

Step 2:

Count back by 3s as many times as you can.

Step 3:

Count the number of times you jumped back 3.

You jumped back 3 four times
There are 4 groups of 3 in 12
12 ÷ 3 = 4

Question 3.

______ ÷ ______ = ______

Answer: 10 ÷ 2 = 5

Explanation:

Step 1:

Start at 10

Step 2:

Count back by 2s as many times as you can.

Step 3:

Count the number of times you jumped back 2.

You jumped back 2 five times
There are 5 groups of 2 in 10
10 ÷ 2 = 5

Question 4.

______ ÷ ______ = ______

Answer: 20 ÷ 5 = 4

Explanation:

Step 1:

Start at 20

Step 2:

Subtract with 5 until you get 0

Step 3:

Count the number of times you subtract with 5

Since you subtract 4 times
There are 4 groups of 5 in 20
So 20 ÷ 5 = 4
Twenty divided by five equals four

Use repeated subtraction or a number line to solve.

Question 7.
8)\( \bar{ 4 0 }\)
________

Answer: 5

Explanation:

Since you subtract 5 times
There are 5 groups of 8 in 40
40 divided by 8 equals 5

Question 8.
9)\( \bar{ 3 6 }\)
________

Answer: 4

Explanation:

You subtract 36 and 9 by 4 times
There are 4 groups of 9 in 36
So, 36 divided by 9 equals 4

Relate Subtraction and Division Page No 330

Question 1.
Which division equation is shown?

Options:
a. 3 × 4 = 12
b. 12 ÷ 6 = 2
c. 12 ÷ 3 = 4
d. 12 ÷ 4 = 3

Answer: 12 ÷ 6 = 2

Explanation:

Step 1:

The count starts at 12

Step 2:

Count back by 6s as many times as you can until you get 0

Step 3:

Count the number of times you jumped back
You jumped back 2 times
There are 2 jumps from 12 to 0
So the correct answer is option B

Question 2.
Isabella has 35 cups of dog food. She feeds her dogs 5 cups of food each day. For how many days will the dog food last?
Options:
a. 6 days
b. 7 days
c. 8 days
d. 9 days

Answer: 7 days

Explanation:

Given that,

Isabella has 35 cups of dog food
She feeds her dogs 5 cups of food each day
To find the number of days will the dog food last
We have to divide the number of cups by the number of cups of food each day
= 35 ÷ 5 = 35/5 = 7
So, the correct answer is option B

Spiral Review

Question 3.
Ellen buys 4 bags of oranges. There are 6 oranges in each bag. How many oranges does Ellen buy?
Options:
a. 10
b. 12
c. 24
d. 30

Answer: 24

Explanation:

Given:
Ellen buys 4 bags of oranges
There are 6 oranges in each bag
Total number of oranges = no. of bags × no. of oranges in each bag
= 4 × 6 = 24
Therefore the correct answer is option B

Question 4.
Each month for 7 months, Samuel mows 3 lawns. How many more lawns does he need to mow before he has mowed 29 lawns?
Options:
a. 1
b. 3
c. 7
d. 8

Answer: 8

Explanation:

Each month for 7 months, Samuel mows 3 lawns
For one month Samuel mows 3 lawns
For 7 months Samuel mows = x
x = 7 × 3 = 21
Now, we need to know how many more lawns he needs to mow before he has mowed 29 lawns
Subtract 21 from 29
= 29 – 21 = 8
So the answer is option D

Use the graph for 5–6.

Question 5.
How many hours did Eli volunteer?
Options:
a. 4 hours
b. 8 hours
c. 9 hours
d. 10 hours

Answer: 9 hours

Explanation:

The bar graph shows that Eli volunteered 9 hours
So, the correct answer is option C

Question 6.
Madi volunteered 2 hours less than Jill. At what number should the bar for Madi end?
Options:
a. 3
b. 6
c. 8
d. 12

Answer: 8

Explanation:

The figure shows that Jill has volunteered 10 hours
If Madi has volunteered 2 hours less than Jill
= 10 – 2 = 8 hours
Thus the correct answer is option C

Mid-Chapter Checkpoint Page No 331

Vocabulary

Choose the best term from the box to complete the sentence.

Question 1.
You _________ when you separate into equal groups.
_________

Answer: Divide

When you divide, you separate into equal groups.

Concepts and Skills

Use counters or draw a quick picture on your MathBoard.
Make or circle equal groups. Complete the table.

Question 2.

Type below:
___________

Answer:

2. Number of counters = 6
Number of equal groups = 2
Number in each group =  __
= 6/2 = 3

3. Number of counters = 30
Number of equal groups = __
Number in each group = 5
= 30/5 = 6

4. Number of counters = 28
Number of equal groups = 7
Number in each group = __
= 28/7 = 4

Write a division equation for the picture.

Question 5.

Type below:
___________

Answer: 8 ÷ 4 = 2 or 8 ÷ 2 = 4

Explanation:

The number of counters is 8 and a circle group of 4 counters.
Continue circling group of 4 until all the 8 counters are in the group
Divide Number of counters by Number of equal groups
= 8 ÷ 2 = 4
Divide Number of counters by number in each group
8 ÷ 4 = 2

Question 6.

Type below:
___________

Answer: 15 ÷ 3 = 5 or 15 ÷ 5 = 3

Explanation:

Number of counters = 15
Number of groups = 3
Number in each group = 5
Divide Number of counters by number of groups
= 15 ÷ 3 = 5
Divide number of counters by number in each group
= 15 ÷ 5 = 3

Write a division equation.

Question 7.

______ ÷ ______ = ______

Answer: 36 ÷ 9 = 4

Explanation:

Step 1:

Starts at 36

Step 2:

Subtract with 9 until you get 0

Step 3:

Count the number of times you subtract with 9

You subtract 4 times
There are 4 groups of 9 with 36
So, 36 ÷ 9 = 4

Question 8.

______ ÷ ______ = ______

Answer: 21 ÷ 3 = 7

Explanation:

Step 1:

Starts at 21

Step 2:

Count back by 3s as many times as you can

Step 3:

Count the number of times you jumped back 3.
You jumped back by 21 seven times
There are 7 jumps of 3 in 21

Mid-Chapter Checkpoint Page No 332

Question 11.
Jayden modeled a division equation with some counters. What division equation could Jayden have modeled?

Type below:
___________

Answer: 14 ÷ 2 = 7 or 14 ÷ 7 = 2

Explanation:

Number of counter = 14
Number in each group = 7
Number of equal groups = 2
So, the division equation is the number of counters by number of equal groups = 14 ÷ 2 = 7
Or, Number of counters by number in each group = 14 ÷ 7 = 2

Question 12.
Lillian bought 24 cans of cat food. There were 4 cans in each pack. How many packs of cat food did Lillian buy?

_________ packs

Answer: 6 packs

Explanation:

Lillian bought 24 cans of cat food
There were 4 cans in each pack
Number of packs of cat food did Lillian buy
24 ÷ 4 = 6 packs

Model with Arrays Page No 337

Use square tiles to make an array. Solve

Question 1.
How many rows of 4 are in 12?
______ rows

Answer: 3 rows

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Explanation:

Step 1:

Total number of tiles are 12

Step 2:
Make a row of 4 tiles

Step 3:

Continue to make as many rows of 4 tiles as you can
We get 4 tiles in each row
3 rows of 4 are in 12

Question 2.
How many rows of 3 are in 21?
______ rows

Answer: 7 rows

■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■
■ ■ ■

Explanation:

Step 1:

Total number of tiles are 21

Step 2:

Make a row of 3 tiles

Step 3:

Continue to make as many rows of 3 tiles as you can
We get 3 tiles in each row
So, 7 rows of 3 are in 21

Question 3.
How many rows of 6 are in 30?
______ rows

Answer: 5 rows

■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■

Explanation:

Step 1:

First of all the count number of tiles = 30

Step 2:

Make a row of 6 tiles

Step 3:

Continue to make as many rows of 6 tiles as you can
We get 6 tiles in each row
So, there are 5 rows of 6 in 30

Question 4.
How many rows of 9 are in 18?
______ rows

Answer: 2 rows

Make an array. Then write a division equation.

Question 5.
20 tiles in 5 rows
______ ÷ ______ = ______

Answer: 20 ÷ 5 = 4

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Explanation:

Total number of tiles = 20
Make a row of 4 tiles
Continue to make as many rows of 4 tiles as you can
We get 4 tiles in each row
So, the division equation is 20 ÷ 5 = 4

Question 6.
28 tiles in 7 rows
______ ÷ ______ = ______

Answer: 28 ÷ 7 = 4

■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■
■ ■ ■ ■

Explanation:

Total number of tiles = 28
Make a row of 4 tiles
Continue to make as many rows of 4 tiles as you can
We get 4 tiles in each row
For 28 tiles we get 7 rows
So, the division equation is 28 ÷ 7 = 4

Question 7.
18 tiles in 9 rows
______ ÷ ______ = ______

Answer: 18 ÷ 9 = 2

■ ■
■ ■
■ ■
■ ■
■ ■
■ ■
■ ■
■ ■
■ ■

Explanation:

Number of tiles = 18
Number of rows = 9
Now we have to make a row of 2 tiles until we complete 18 tiles
So, you get 2 tiles in 9 rows
18 ÷ 9 = 2 tiles

Question 8.
36 tiles in 6 rows
______ ÷ ______ = ______

Answer: 36 ÷ 6 = 6

■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■
■ ■ ■ ■ ■ ■

Explanation:

Total number of tiles = 36
Number of rows = 6
Now you have to make a row of 36 tiles in 6 rows
You get 6 tiles in each row
That means there are 6 tiles each in a row
So, the division equation is 36 ÷ 6 = 6

Problem Solving

Model with Arrays Page No 338

Question 1.
Mr. Canton places 24 desks in 6 equal rows. How many desks are in each row?
Options:
a. 2
b. 3
c. 4
d. 5

Answer: 4

Explanation:

Mr. Canton places 24 desks in 6 equal rows
Each row has x number of desks
Divide the number of desks by number of equal rows
24 ÷ 6 = 4
So, the correct answer is option C

Question 2.
Which division equation is shown by the array?

Options:
a. 12 ÷ 6 = 2
b. 12 ÷ 3 = 4
c. 12 ÷ 2 = 6
d. 12 ÷ 1 = 12

Answer: 12 ÷ 3 = 4

Explanation:

Number of counters is 12 and the number of rows are 3
To know number counters in each row
We have to divide number of counters by number of rows
= 12 ÷ 3 = 4
Thus the answer is option B

Spiral Review

Question 3.
Amy has 2 rows of 4 sports trophies on each of her 3 shelves. How many sports trophies does Amy have in all?
Options:
a. 8
b. 9
c. 12
d. 24

Answer: 24

Explanation:

Amy has 2 rows of 4 sports trophies on each of her 3 shelves
To know the total sports trophies does Amy have in all 3 shelves
We have to multiple number 2 × 4 × 3 = 24
So, the correct answer is option D

Question 4.
What is the unknown factor?
9 × p = 45
Options:
a. 4
b. 5
c. 6
d. 7

Answer: 5

Explanation:

The unknown factor is p
9 × p = 45
p = 45/9 = 5
Therefore p = 5
Thus the answer is option B

Question 5.
Sam has 7 stacks with 4 quarters each. How many quarters does Sam have?
Options:
a. 11
b. 12
c. 24
d. 28

Answer: 28

Explanation:

Sam has 7 stacks with 4 quarters each
Each stack has 4 quarters
So, 7 stacks has 7 × 4 = 28
Thus 7 stacks have 28 quarters

Question 6.
How can you skip count to find how many counters in all?

Options:
a. 3 groups of 2
b. 3 groups of 3
c. 9 groups of 2
d. 18 groups of 2

Answer: 9 groups of 2

Explanation:

Total number of Counters = 18
Number of equal groups = 9
Number in each group = 2
So, there are 9 groups of 2s
Thus the correct answer is option C

Relate Multiplication and Division Page No 343

Complete the equations.

Question 1.

Answer:

5 rows of 4 = 20
5 × 4  = 20
20 ÷ 5 = 4

Explanation:

The above figure shows that there are 5 rows of 4 circles
Total number of circles = 20
The related facts of 20, 5, and 4 are
5 × 4 = 20; 5 rows of 4 = 20; 20 ÷ 5 = 4

Question 2.

4 rows of ______ = 24
4 × ______ = 24
24 ÷ 4 = ______

Answer:

4 rows of 6 = 24
4 × 6 = 24
24 ÷ 4 = 6

Explanation:

Number of counters = 24
Number of equal rows = 4
24 ÷ 4 = 6
The related facts of 24, 6 and 4 are 24 ÷ 4 = 6; 4 × 6 = 24

Question 3.

3 rows of ______ = 24
3 × ______ = 24
24 ÷ 3 = ______

Answer:

3 rows of 8 = 24
3 × 8 = 24
24 ÷ 3 = 8

Explanation:

Total number of counters = 24
Number of equal rows = 3
Divide number of counters by number of equal rows
24 ÷ 3 = 8
Thus the related multiplication and division facts of 24, 3 , 8 are 3 × 8 = 24; 24 ÷ 3 = 8

Complete the equations.

Question 6.
5 × ______ = 35    35 ÷ 7 = ______

Answer: 7, 5

Explanation:

X represents the unknown factor
5 × x = 35
x = 35/5 = 7
Therefore the related multiplication and division facts 35, 5 and 7 are 5 × 7 = 35; 35 ÷ 7 = 5

Question 7.
7 × ______ = 21  21 ÷ 7 = ______

Answer: 3, 3

Explanation:

7 × x = 21
x = 21/7 = 3
So, the related multiplication and division facts of 7, 21 are 7 × 3 = 21; 21÷ 7 = 3

Question 8.
9 × ______ = 27  27 ÷ 9 = ______

Answer: 3, 3

Explanation:

27 ÷ 9 = 3
The related multiplication and division facts of 27 and 9 are 9 × 3 = 27 and 27 ÷ 9 = 3

Question 9.
2 × ______ = 16  16 ÷ 2 = ______

Answer: 8, 8

Explanation:

16 ÷ 2 = 8
The related multiplication and division facts of 16 and 2 are 2 × 8 = 16; 16 ÷ 2 = 8

Question 10.
4 × ______ = 36 36 ÷ 4 = ______

Answer: 9, 9

Explanation:

36 ÷ 4 = 9
So, the related multiplication and division facts of 36 and 4 are 4 × 9 = 36; 36 ÷ 4 = 9

Question 11.
8 × ______ = 40 40 ÷ 8 = ______

Answer: 5, 5

Explanation:

Let x be the unknown factor
8 × x = 40
x = 40/8 = 5
The related facts of 40 and 8 are 8 × 5 = 40; 40 ÷ 8 = 5

Problem Solving

Relate Multiplication and Division Page No 344

Question 1.
Which number will complete the equations?
6 × □ = 24
24 ÷ 6 = □
Options:
a. 3
b. 4
c. 5
d. 6

Answer: 4

Explanation:

24 ÷ 6 = 4
The related multiplication and division facts of 6 and 24 is 6 × 4 = 24; 24 ÷ 6 = 4
So, the correct answer is option B

Question 2.
Alice has 14 seashells. She divides them equally between her 2 sisters. How many seashells does each sister get?
Options:
a. 7
b. 8
c. 12
d. 16

Answer: 7

Explanation:

Alice has 14 seashells
She divides them equally between her 2 sisters
To know the number of seashells each sister get
We have to divide number of seashells by the number of sisters
= 14 ÷ 2 = 7
Thus the answer is option A

Spiral Review

Question 3.
Sam and Jesse can each wash 5 cars in an hour. They both work for 7 hours over 2 days. How many cars did Sam and Jesse wash?
Options:
a. 70
b. 35
c. 24
d. 14

Answer: 70

Explanation:

Sam and Jesse can each wash 5 cars in an hour
They both work for 7 hours over 2 days
To find the total number of cars they washed
we need to multiply 5 × 7 × 2 = 35 × 2 = 70
So, the answer is option A

Question 4.
Keisha skip-counted to find how many counters in all. How many equal groups are there?

Options:
a. 3
b. 4
c. 5
d. 20

Answer: 4

Explanation:

By seeing the above figure we can say that there are 4 groups.
So, the answer is option B

Question 5.
The key for a picture graph showing the number of books students read is: Each = 2 books. How many books did Nancy read if she has by her name?
Options:
a. 2
b. 4
c. 5
d. 6

Answer: 5

Explanation:

Each = 2 books
There are 2 and half books = 2 + 2 + 1 = 5
Thus the answer is 5 i.e., option C

Question 6.
Jan surveyed her friends to find their favorite season. She recorded IIII III for summer. How many people chose summer as their favorite season?
Options:
a. 5
b. 8
c. 9
d. 13

Answer: 8

Explanation:

IIII = 5
III = 3
IIII III = 5 + 3 = 8
So, the people who chose summer as their favorite season are 8
Option B is the correct answer

Write Related Facts Page No 349

Write the related facts for the array.

Question 1.

Answer:

2 × 6 = 12
6 × 2 = 12
12 ÷ 2 = 6
12 ÷ 6 = 2

Explanation:

Total number of counters = 12
Number of rows = 2
Number of counters in each row = 6
So, the related facts of 6, 2 and 12 are 2 × 6 = 12, 6 × 2 = 12, 12 ÷ 2 = 6 and 12 ÷ 6 = 2

Question 2.

Type below:
_________

Answer:

5× 3 = 15
3×5 = 15
15 ÷ 3 = 5
15÷ 5 = 3

Explanation:

Total number of counters = 15
Number of rows = 5
Number of counters in each row = 3
The related facts of 5, 3 and 15 are 5× 3 = 15, 3×5 = 15, 15 ÷ 3 = 5 and 15÷ 5 = 3

Question 3.

Type below:
_________

Answer:

2 × 4 = 8
4× 2 = 8
8 ÷ 2 = 4
8 ÷ 4 = 2

Explanation:

Total number of counters = 8
Number of rows = 2
Number of counters in each row = 4
The related facts of 8, 2, 4 are 2 × 4 = 8, 4× 2 = 8, 8 ÷ 2 = 4 and 8 ÷ 4 = 2

Write the related facts for the set of numbers.

Question 4.
3, 7, 21
Type below:
_________

Answer:

3 × 7 = 21
7 × 3 = 21
21 ÷ 3 = 7
21 ÷ 7 = 3

Explanation:

Total number of counters = 21
The related facts of 3, 7, 21 are 3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7 and 21 ÷ 7 = 3

Complete the related facts.

Question 7.
4 × 9 = _______
9 × _______ = 36
36 ÷ _______ = 4
_______ ÷ 4 = 9

Answer: The related facts of 4, 9 and 36 are given below

4 × 9 = 36
9 × 4 = 36
36 ÷ 9 = 4
36 ÷ 4 = 9

Question 8.
_______ × 7 = 35
_______ × 5 = 35
_______ ÷ 7 = 5
35 ÷ 5 _______

Answer:

5 × 7 = 35
7 × 5 = 35
35 ÷ 7 = 5
35 ÷ 5= 7

Explanation:

Let the unknown factor be x
x × 7 = 35
x = 35/7 = 5
5 × 7 = 35

x × 5 = 35
x = 35/5 = 7
7 × 5 = 35

x ÷ 7 = 5
x = 5 × 7 = 35
35 ÷ 7 = 5

35 ÷ 5 = x
x = 35/5 = 7
35 ÷ 5= 7

Question 9.
6 × _______ = 18
3 × 6 _______
18 ÷ _______ = 3
_______ ÷ 3 = 6

Answer:

6 × 3 = 18
3 × 6 = 18
18 ÷ 6 = 3
18 ÷ 3 = 6

Explanation:

Let the unknown factor be x
6 × x = 18
x = 18/6 = 3
6 × 3 = 18

3 × 6 = x
x = 18
3 × 6 = 18

18 ÷ x = 3
x = 18/3 = 6
18 ÷ 6 = 3

x ÷ 3 = 6
x = 6 × 3 = 18
18 ÷ 3 = 6

Problem Solving 

Write Related Facts Page No 350

Question 1.
Which number completes the set of related facts?
5 × □ = 40  40 ÷ □ = 5
□ × 5 = 40  40 ÷ 5 = □
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:

i. 5 × □ = 40
□ = 40/5 = 8
ii. 40 ÷ □ = 5
□ = 40/5 = 8
iii. □ × 5 = 40
□ = 40/5 = 8
iv. 40 ÷ 5 = □
40/5 = □
□ = 8
So, the answer is 8

Question 2.
Which equation is not in the same set of related facts as 4 × 7 = 28?
Options:
a. 7 × 4 = 28
b. 4 + 7 = 11
c. 28 ÷ 4 = 7
d. 28 ÷ 7 = 4

Answer: 4 + 7 = 11

Explanation:

The related facts of 4, 7 and 28 are 4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7, 28 ÷ 7 = 4
But 4 + 7 = 11 is not set of related multiplication and division equations.

Spiral Review

Question 3.
Beth runs 20 miles each week for 8 weeks. How many miles does Beth run in 8 weeks?
Options:
a. 16 miles
b. 28 miles
c. 100 miles
d. 160 miles

Answer: 160 miles

Explanation:

Beth runs 20 miles each week for 8 weeks
Each week Beth runs 20 miles
For 8 weeks = x miles
x = 8 × 20
x = 160 miles
So, the answer is 160 miles

Question 4.
Find the product.
5 × 0
Options:
a. 0
b. 1
c. 5
d. 10

Answer: 0

Explanation:

Any number multiplied by 0 is always 0.
So, the answer is option A.

Question 5.
Uri’s bookcase has 5 shelves. There are 9 books on each shelf. How many books in all are in Uri’s bookcase?
Options:
a. 14
b. 36
c. 45
d. 54

Answer: 45

Explanation:

Uri’s bookcase has 5 shelves
There are 9 books on each shelf
Number of books on 5 shelves = y
y = 9 × 5 = 45
Thus the answer is option C

Question 6.
There are 6 batteries in one package. How many batteries will 6 packages have?
Options:
a. 12
b. 18
c. 24
d. 36

Answer: 36

Explanation:

There are 6 batteries in one package
Number of batteries in 6 packages = x
x = 6 × 6 = 36
Thus the number of batteries in 6 packages = 36

Division Rules for 1 and 0 Page No 355

Find the quotient.

Question 1.

Answer: 3

Explanation:

Any number divided by 1 equals that number. The quotient is the number
So, 3/1 = 3 is the quotient

Question 2.
8 ÷ 8 = ________

Answer: 1

Explanation:

Any number divided by the same number other than 0 equals 1. The quotient is always 1
8/8 = 1
So, the quotient is 1

Question 3.
________ = 0 ÷ 6

Answer: 0

Explanation:

Zero divided by any number is always 0. The quotient is 0.
0/6 = 0
Thus the quotient is 0

Question 6.
0 ÷ 2 = ________

Answer: 0

0 divided by any number is always 0.
0/2 = 0
So, the quotient is 0

Question 7.
0 ÷ 3 = ________

Answer: 0

Explanation:

0 divided by any number is always 0.
0/3 = 0
So, the quotient is 0

Question 8.
________ = 0 ÷ 4

Answer: 0

Explanation:

0 divided by any number is 0
0/4 = 0
Thus the quotient is 0

Question 9.
7)\( \bar{ 7  }\)
________

Answer: 1

Explanation:

Any number divided by the same number is always 1.
7/7 = 1
So, the quotient is 1

Question 10.
1)\( \bar{ 6  }\)
________

Answer: 6

Explanation:

Any number divided by 1 is the same number.
6/1 = 6
So, the quotient is 6

Question 11.
9)\( \bar{  0 }\)
________

Answer: 0

Explanation:

0 divided by any number remains 0.
0/9 = 0
Thus the quotient is 0

Question 12.
1)\( \bar{ 5  }\)
________

Answer: 5

Explanation:

Any number divided by 1 gives the same number as a quotient
5/1 = 5
Therefore the quotient is 5

Question 13.
1)\( \bar{  0 }\)
________

Answer: 0

Explanation:

0 divided by anything is 0
0/1 = 0
So, the quotient is 0

Question 14.
4)\( \bar{ 4  }\)
________

Answer: 1

Explanation:

Any number divided by the same number gives the quotient as 1.
4/4 = 1
So, the quotient is 1

Question 15.
1)\( \bar{ 10 }\)
________

Answer: 10

The number which is divided by 1 gives the same number as a quotient.
10/1 = 10
Thus the quotient is 10

Question 16.
2)\( \bar{ 2  }\)
________

Answer: 1

Explanation:

Any number divided by the same number is 1.
2/2 = 1
Thus the quotient is 1

Problem Solving

Division Rules for 1 and 0 Page No 356

Question 1.
Candace has 6 pairs of jeans. She places each pair on its hanger. How many hangers does Candace use?
Options:
a. 0
b. 1
c. 6
d. 12

Answer: 6

Explanation:

Given,
Candace has 6 pairs of jeans
She places each pair on its own hanger
That means one pair of jeans for one hanger
To find the number of hangers we need to divide the total number of hangers by each pair
6 ÷ 1 = 6
So, option C is the correct answer

Question 2.
There are 0 birds and 4 bird cages. Which division equation describes how many birds are in each cage?
Options:
a. 0 ÷ 4 = 0
b. 4 ÷ 4 = 1
c. 4 ÷ 1 = 4
d. 0 × 4 = 0

Answer: 0 ÷ 4 = 0

Explanation:

There are no birds so nothing to divide. Zero divided by anything is 0.
So, the answer is 0 ÷ 4 = 0

Spiral Review

Question 3.
There are 7 plates on the table. There are 0 sandwiches on each plate. How many sandwiches are on the plates in all?
7 × 0
Options:
a. 0
b. 1
c. 7
d. 70

Answer: 0

Explanation:

There are 7 plates on the table
There are 0 sandwiches on each plate
Any number multiplied with 0 is always 0.
So, the answer is option A.

Question 4.
Which shows a way to break apart the array to find the product?

Options:
a. (3 × 5) + (3 × 2)
b. (2 × 8) + (1 × 8)
c. (4 × 7) + (1 × 7)
d. (3 × 6) + (3 × 3)

Answer: (3 × 5) + (3 × 2)

Explanation:

There are 3 rows and 7 columns
The columns are divided into 2 parts 5 and 2.
By using the distributive property we can write it as (3 × 5) + (3 × 2)
Thus the answer is option A

Question 5.
Which of the following describes a pattern in the table?

Options:
a. Add 5.
b. Multiply by 2.
c. Subtract 1.
d. Multiply by 6.

Answer:

Multiply by 6.

Explanation:

Multiple 6 with several vans.
By seeing the above table we can say that it is the multiple of 6.
So, the answer is option D

Question 6.
Use the graph.

How many more cans did Sam bring in than Lee?
Options:
a. 4
b. 5
c. 7
d. 9

Answer: 9

Explanation:

Number of cans sam brings = 18
Number of cans Lee bring = 9
To know number of cans Sam bring in than Lee we have to subtract
Number of cans of Lee from Number of cans of Sam = 18 – 9 = 9
By using the above graph we can say that number of cans Sam bring in than Lee is 9.
Thus the correct answer is option D

Review/Test Page No 361

Question 1.
For numbers 1a–1d, select True or False for each equation.
a. 3 ÷ 1 = 1
i. True
ii. False

Answer: False

Explanation:

Any number divided by 1 is always the same number. The quotient is 1.
So, the above equation is false.

Question 1.
b. 0 ÷ 4 = 0
i. True
ii. False

Answer: True

Explanation:

0 divided by any number is always 0. So, the above statement is true.

Question 1.
c. 7 ÷ 7 = 1
i. True
ii. False

Answer: True

Explanation:

Any number divided by the same number remains 1. So, the given statement is true.

Question 1.
d. 6 ÷ 1 = 6
i. True
ii. False

Answer: True

Explanation:

Any number divided by 1 will be the same number. Thus the statement given above is true.

Question 2.
Elizabeth has 12 horses on her farm. She puts an equal number of horses in each of 3 pens. How many horses are in each pen?
Circle a number that makes the sentence true.
There are horses in each pen.
_________

Answer: 12 ÷ 3 = 4

There are horses in each pan

Question 3.
Chris plants 25 pumpkins seeds in 5 equal rows. How many seeds does Chris plant in each row?
Make an array to represent the problem. Then solve the problem.

_______ seeds
Explain:
_________

Answer: 5 seeds

Explanation:

Total number of seeds = 25
Number of equal rows = 5
25 ÷ 5 = 5 seeds

Page No. 358

Question 4.
Becca spent 24 minutes walking around a track. It took her 3 minutes to walk each time around the track. How many times did Becca walk around the track?

Make equal groups to model the problem. Then explain how you solved the problem.
_______ times

Answer: 24 ÷ 3 = 8 times

Question 5.
There are 7 cars in an amusement park ride. There are 42 people divided equally among the 7 cars. An equal number of people ride in each car. How many people ride in one car?

_______people

Answer: 6 people

Explanation:

Number of cars = 7
There are 42 people divided equally among the 7 cars
Divide the total number of people by the number of cars
You get, 42 ÷ 7 = 6 people

Question 6.
Select the equations that represent the array. Mark all that apply.

Options:
a. 3 × 5 = ■
b. 2 × ■ = 12
c. ■ ÷ 3 = 5
d. 5 × ■ = 15
e. 12 ÷ 3 = ■
f. 15 ÷ 5 = ■

Answer: 3 × 5 = ■; ■ ÷ 3 = 5; 5 × ■ = 15; 15 ÷ 5 = ■

Explanation:

Related facts are a set of related multiplication and division equations.

Number of rows = 3
Number of blocks in each row = 5
Total Number of blocks = 15
So, the relation between these 3 numbers are 3 × 5 = ■; ■ ÷ 3 = 5; 5 × ■ = 15; 15 ÷ 5 = ■

Review/Test Page No 359

Question 7.
Eduardo visited his cousin for 28 days over the summer. There are 7 days in each week. How long, in weeks, was Eduardo’s visit?
Part A
Draw jumps on the number line to model the problem.

Type below:
___________

Answer:

Starts at 0
Count by 7 as many times as you can
Count the number of times you jumped back 7
You have jumped 4 times
So, there are 4 groups of 7 in 28
28 ÷ 7 = 4

Question 7.
Part B
Write a division equation to represent the model.
Type below:
___________

Answer: 28 ÷ 7 = 4

Question 9.
There are 56 apples packed in 7 baskets with the same number of apples in each basket. How many apples are in each basket?
For numbers, 9a–9d, choose Yes or No to tell whether the equation represents the problem.
a. 56 + 7 = ■
i. yes
ii. no

Answer: No

Explanation:

56 + 7 = 63 ≠ 8
So, the answer is no

Question 9.
b. 7 × ■ = 56
i. yes
ii. no

Answer: Yes

Explanation:

7 × ■ = 56
■ = 56/7 = 8
So, the answer is yes

Question 9.
c. 56 ÷ ■ = 8
i. yes
ii. no

Answer: Yes

Explanation:

56 ÷ ■ = 8
■ = 56/8 = 7
So, the answer is yes

Question 9.
d. 56 − ■ = 8
i. yes
ii. no

Answer: No

Explanation:

56 − ■ = 8
■ = 64 ≠ 7
So, the answer is no

Question 10.
Stefan has 24 photos to display on some posters. Select a way that he could display the photos in equal groups on the posters. Mark all that apply.
Options:
a. 6 photos on each of 4 posters
b. 7 photos on each of 3 posters
c. 4 photos on each of 6 posters
d. 5 photos on each of 5 posters
e. 3 photos on each of 8 posters
f. 7 photos on each of 4 posters

Answer: A, C, E

A. 6 photos on each of 4 posters
6 x 4 = 24 photos ✓

B. 7 photos on each of 3 posters
7 x 3 = 21 ≠ 24 photos

C. 4 photos on each of 6 posters
4 x 6 = 24 photos ✓

D. 5 photos on each of 5 posters
5 x 5 = 25 ≠ 24 photos

E. 3 photos on each of 8 posters
3 x 8 = 24 photos ✓

F. 7 photos on each of 4 posters
7 x 4 = 28 ≠ 24 photos

Review/Test Page No 360

Question 11.
Debbie made this array to model a division equation. Which equation did Debbie model? Mark all that apply.

Options:
a. 14 ÷ 7 = 2
b. 28 ÷ 4 = 7
c. 28 ÷ 7 = 4
d. 14 ÷ 2 = 7

Answer: 28 ÷ 4 = 7

Explanation:

Total Number shaded blocks = 28
Number of equal rows = 4
To write the division equation
we have to divide number of blocks by number of equal rows
28 ÷ 7 = 7
So, the correct answer is option B

Question 12.
Mrs. Edwards made a total of 40 fingers on some gloves she knitted. How many gloves did Mrs. Edwards knit?

__________ gloves

Answer: 40 ÷ 5 = 8

Explanation:

Mrs. Edwards made a total of 40 fingers on some gloves she knitted
Number in each group = 5
Divide Number of fingers by number in each group
= 40 ÷ 5 = 8
Number of equal groups = 8

Question 13.
Make true equations. Select a number to complete the equation.

7 ÷ 7 = ________
7 ÷ 1 = ________
0 ÷ 7 = ________

Answer:

7 ÷ 7 = 1
7 ÷ 1 = 7
0 ÷ 7 = 0

Explanation:

7 ÷ 7 = 1
Any number divided by the same numbers is always 1. So the quotient is 1
7 ÷ 1 = 7
Any number divided by 1 gives the same number as the quotient.
0 ÷ 7 = 0
Zero divided by any number is always 0. So, the quotient is 0.

Review/Test Page No 361

Question 15.
Write a division equation to represent the repeated subtraction.

Type below:
________

Answer: 32 ÷ 8 = 4

Explanation:

Step 1:

Start at 32

Step 2:

Subtract with 8 until you get 0

Step 3:

Count the number of times you subtract with 8
Since you subtract 4 times
There are 4 groups of 8 in 32
32 ÷ 8 = 4
Thirty two divided by eight equals four

Question 16.
Write related facts for the array. Explain why there are not more related facts.

Type below:
________

Answer:

There are 6 rows of 6 squares.
The related facts are:
6 x 6 = 36; 36 ÷ 6 = 6
An array represents multiplication because it has rows and columns and the total number of cells is the product of its rows and columns.
Also, division is related to multiplication.
So, the only related facts are multiplication and division.

Question 17.
Darius bakes 18 muffins for his friends. He gives each of his friends an equal number of muffins and has none left over.
Part A
Draw a picture to show how Darius divided the muffins and complete the sentence.
Darius gave muffins to ________ friends.
Type below:
________

Answer:

If one muffin for 18 friends

18 = 1 × 18

If 2 muffins for 9 friends

18 = 2 × 9

If 3 muffins for 6 friends

18 = 3 × 6

Six muffins for 3 friends

18 = 6 × 3

If 9 muffins for 2 friends

So, Darius gave muffins to 2, 3, 6, 9, 18 friends

Question 17.
Part B
Could Darius have given all of his muffins equally to 4 of his friends? Explain why or why not.
Type below:
________

Answer: No

No, because if he divides 18 muffins to 4 people, then they get 4 muffins each, and two are not given.
4 × 4 + 2 = 18

Review/Test Page No 362

Question 18.
Circle numbers to complete the related facts.
× 8 = 72   72 ÷ = 8
______                                              _______

Answer: 9 × 8 = 72; 72 ÷ 9 = 8

× 8 = 72; 72 ÷ = 8

Question 19.
Use the numbers to write related multiplication and division facts.

Type below:
__________

Answer: 45 ÷ 9 = 5; 45 ÷ 5 = 9

Explanation:

The multiplication and division facts for 45, 9 and 5 are
45 ÷ 5 = 9
45 ÷ 9 = 5
9 × 5 = 45

Question 20.
Tyrone took 16 pennies from his bank and put them in 4 equal stacks. How many pennies did Tyrone put in each stack? Show your work.

__________ pennies

Answer: 4 pennies

16 ÷ 4 = 4 pennies

Explanation:

Total number of pennies = 16
Number of equal stacks = 4
Divided number of pennies by number of equal stacks to know the pennies in each stack
16 ÷ 4 = 4

Try to solve exercise questions and cross check your answers from Go Math Grade 3 Answer Key Chapter 6 Understand Division Extra Practice. This way you can assess your strengths and weaknesses and concentrate on the areas you are lagging.

Detailed Solutions are provided in the 3rd Grade Go Math Answer Key Chapter 6 Understand Division making it easy for you to understand.

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

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

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

Lesson 1: Multiply with 2 and 4

• Multiply with 2 and 4 Page No 195
• Multiply with 2 and 4 Lesson Check Page No 196

Lesson 2: Multiply with 5 and 10

• Multiply with 5 and 10 Page No 201
• Multiply with 5 and 10 Lesson Check Page No 202

Lesson 3: Multiply with 3 and 6

• Multiply with 3 and 6 Page No 207
• Multiply with 3 and 6 Lesson Check Page No 208

Lesson 4: Algebra • Distributive Property

• Distributive Property Page No 213
• Distributive Property Lesson Check Page No 214

Lesson 5: Multiply with 7

• Multiply with 7 Page No 219
• Multiply with 7 Lesson Check Page No 220

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint Page No 221
• Mid-Chapter Checkpoint Page No 222

Lesson 6: Algebra • Associative Property of Multiplication

• Associative Property of Multiplication Page No 227
• Associative Property of Multiplication Lesson Check Page No 228

Lesson 7: Algebra • Patterns on the Multiplication Table

• Patterns on the Multiplication Table Page No 233
• Patterns on the Multiplication Table Lesson Check Page No 234

Lesson 8: Multiply with 8

• Multiply with 8 Page No 239
• Multiply with 8 Lesson Check Page No 240

Lesson 9: Multiply with 9

• Multiply with 9 Page No 245
• Multiply with 9 Lesson Check Page No 246

Lesson 10: Problem Solving • Multiplication

• Multiplication Page No 251
• Multiplication Lesson Check Page No 252

Chapter 4 Review/Test

• Review/Test Page No 253
• Review/Test Page No 254
• Review/Test Page No 255
• Review/Test Page No 256
• Review/Test Page No 257
• Review/Test Page No 258

Multiply with 2 and 4 Page No 195

Write a multiplication sentence for the model.

Question 1.

Think: There are 2 groups of
5 counters.

Answer:
2 × 5 = 10

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

Question 2.

______ × ______ = ______

Find the product.

Answer:
4×3 = 12

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

Question 3.
2
× 6
——–
________

Answer:
2×6 = 12

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

Question 6.
4
× 6
———
_________

Answer:
4×6 = 24

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

Question 7.
4
× 4
———
_________

Answer:
4×4 = 16

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

Question 8.
2
× 7
——–
_________

Answer:
2×7 = 14

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

Question 9.
4
× 5
———
_________

Answer:
4×5 = 20

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

Question 10.
2
× 4
——–
_________

Answer:
2×4 = 8

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

Problem Solving

Multiply with 2 and 4 Lesson Check Page No 196

Lesson Check

Question 1.
Which multiplication sentence matches the model?

Options:
a. 3 × 2 = 6
b. 4 × 2 = 8
c. 4 × 4 = 16
d. 4 × 8 = 32

Answer:
b

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

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

Answer:
c

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

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

Answer:
b

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

Question 4.
The table shows the lengths of some walking trails.

How many feet longer is Mountain Trail than Harmony Trail?
Options:
a. 216 feet
b. 264 feet
c. 316 feet
d. 528 feet

Answer:
c

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

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

Answer:
c

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

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

Answer:
c

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

Multiply with 5 and 10 Page No 201

Find the product.

Question 1.
5 × 7 = 35

Answer:
35

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

Question 2.
5 × 1 = _______

Answer:
5

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

Question 6.
_______ = 4 × 5

Answer:
20

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

Question 7.
5 × 10 = _______

Answer:
50

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

Question 8.
7 × 5 = ________

Answer:
35

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

Question 9.
_______ = 5 × 5

Answer:
25

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

Question 10.
5 × 8 = _________

Answer:
40

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

Question 11.
______ = 5 × 9

Answer:
45

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

Question 12.
10 × 0 = _________

Answer:
0

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

Question 15.
5
× 3
——–
________

Answer:
15

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

Question 16.
10
× 4
——–
_________

Answer:
40

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

Question 17.
5
× 0
——-
_________

Answer:
0

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

Question 18.
10
× 8
——-
__________

Answer:
80

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

Question 19.
5
× 2
——-
__________

Answer:
10

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

Question 20.
10
× 6
——–
_________

Answer:
60

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

Problem Solving

Multiply with 5 and 10 Lesson Check Page No 202

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

Answer:
60

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

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

Answer:
40

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

Spiral Review

Question 3.
Mr. Miller’s class voted on where to go for a field trip. Use the picture graph to find which choice had the most votes.

Options:
a. Science Center
b. Aquarium
c. Zoo
d. Museum

Answer:
c. Zoo

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

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

Question 4.
Zack made this table for his survey.

How many students were surveyed in all?
Options:
a. 38
b. 43
c. 47
d. 49

Answer:
c. 47

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

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

Answer:
b. 28

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

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

Answer:
a. 568

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

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

Multiply with 3 and 6 Page No 207

Find the product.

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

Answer:
24

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

Question 2.
3 × 7 = _______

Answer:
21

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

Question 3.
________ = 2 × 6

Answer:
12

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

Question 4.
________ = 3 × 5

Answer:
15

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

Question 5.
1 × 3 = ________

Answer:
3

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

Question 9.
4
× 3
——
________

Answer:
12

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

Question 10.
6
× 5
——
_________

Answer:
30

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

Question 11.
2
× 3
——
_________

Answer:
6

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

Question 12.
6
× 3
——–
_________

Answer:
18

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

Question 13.
10
× 6
——-
_________

Answer:
60

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

Question 14.
3
× 6
——-
__________

Answer:
18

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

Question 15.
7
× 6
——-
__________

Answer:
42

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

Question 16.
3
× 0
——-
_________

Answer:
0

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

Question 17.
9
× 6
——-
__________

Answer:
54

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

Question 18.
3
× 3
——-
__________

Answer:
9

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

Problem Solving

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

Answer:
12 hits

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

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

Answer:
30 muffins

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

Multiply with 3 and 6 Lesson Check Page No 208

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

Answer:
b. 12

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

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

Answer:
c. 27

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

Spiral Review

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

Answer:
a. 285

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

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

Answer:
c. 10

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

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

Answer:
d. 16

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

Question 6.
What multiplication sentence does this array show?

Options:
a. 5 × 6 = 30
b. 6 × 6 = 36
c. 5 × 5 = 25
d. 1 × 6 = 6

Answer:
a. 5 × 6 = 30

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

Distributive Property Page No 213

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

Question 1.

(3 × 7) + (3 × 7)
42

Answer:
42

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

Question 2.

_________

Answer:
32

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

Question 3.

___________

Answer:
54

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

Question 4.

_________

Answer:
56

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

Problem Solving

Distributive Property Lesson Check Page No 214

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

Answer:
c. 7 × 6 = (7 × 3) + (7 × 3)

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

Question 2.
What is one way to break apart the array?

Options:
a. (2 × 6) + (2 × 6)
b. (4 × 2) + (4 × 2)
c. (4 × 4) + (4 × 4)
d. (6 × 3) + (6 × 3)

Answer:
a. (2 × 6) + (2 × 6)

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

Spiral Review

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

Answer:
c. 450

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

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

Answer:
a. 104

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

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

Answer:
d. 808

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

Question 6.
Which sport do 6 students play?

a. Football
b. Baseball
c. Basketball
d. Soccer

Answer:
a. Football

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

Multiply with 7 Page No 219

Find the product.

Question 1.
6 × 7 = 42

Answer:
42

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

Question 2.
________ = 7 × 9

Answer:
63

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

Question 3.
_______ = 1 × 7

Answer:
7

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

Question 4.
3 × 7 = _______

Answer:
21

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

Question 7.
7 × 8 = _________

Answer:
56

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

Question 8.
______ = 4 × 7

Answer:
28

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

Question 9.
7
× 5
——-
__________

Answer:
35

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

Question 10.
7
× 1
——-
_________

Answer:
7

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

Question 11.
6
× 7
——-
__________

Answer:
42

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

Question 12.
7
× 4
——-
__________

Answer:
28

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

Question 13.
2
× 7
——-
___________

Answer:
14

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

Question 14.
10
× 7
——
____________

Answer:
70

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

Question 15.
3
× 7
——-
____________

Answer:
21

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

Question 16.
7
× 9
——
___________

Answer:
63

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

Question 17.
8
× 7
——-
__________

Answer:
56

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

Question 18.
7
× 0
——
__________

Answer:
0

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

Problem Solving

Multiply with 7 Lesson Check Page No 220

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

Answer:
b. 56

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

Question 2.
What product does the array show?

Options:
a. 14
b. 17
c. 21
d. 24

Answer:
c. 21

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

Spiral Review

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

Answer:
c. 21

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

Question 4.
How many more people chose retriever than poodle?

Options:
a. 31
b. 39
c. 41
d. 49

Answer:
b. 39

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

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

Answer:
a. 90

Explanation:

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

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

Answer:
c. 20

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

Mid-Chapter Checkpoint Page No 221

Vocabulary

Choose the best term from the box to complete the sentence.

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

Answer:
Commutative Property of Multiplication

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

Answer:
Distributive Property of Multiplication

Concepts and Skills

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

Question 3.

__________

Answer:
7 x 5 = 35

Explanation:

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

Question 4.

__________

Answer:
9 x 4 = 36

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

Find the product.

Question 5.
3 × 1 = __________

Answer:
3

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

Question 6.
5 × 6 = _________

Answer:
30

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

Question 7.
________ = 7 × 7

Answer:
49

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

Question 8.
2 × 10 = _________

Answer:
20

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

Question 9.
2
× 1
——–
_________

Answer:
2

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

Question 12.
6
× 0
——
___________

Answer:
0

Explanation:

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

Question 13.
3
× 8
——-
__________

Answer:
24

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

Mid-Chapter Checkpoint Page No 222

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

Answer:
36

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

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

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

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

Associative Property of Multiplication Page No 227

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

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

Answer:
30

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

Question 2.
(4 × 3) × 2 =
________

Answer:
(4 × 3) × 2 = 4 x (3 x 2)
24

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

Question 3.
2 × (2 × 8) =
________

Answer:
2 × (2 × 8) = (2 x 2) x 8
32

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

Question 4.
9 × (2 × 1) =
________

Answer:
9 × (2 × 1) = (9 × 2) × 1
18

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

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

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

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

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

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

Answer:
( 3 × 3 ) × 2 =
18

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

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

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

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

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

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

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

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

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

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

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

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

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

Problem Solving

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

Answer:
$24

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

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

Answer:
36

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

Associative Property of Multiplication Lesson Check Page No 228

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

Answer:
d. 20

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

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

Answer:
d. 36

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

Spiral Review

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

Answer:
30

Explanation:

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

Question 4.
Trevor made a picture graph to show how many minutes each student biked last week. This is his key.
Each = 10 minutes.
What does stand for?
Options:
a. 2 minutes
b. 10 minutes
c. 20 minutes
d. 25 minutes

Answer:
d. 25 minutes

Explanation:
Given = 10 minutes. So, half time symbol = 5 minutes.  Therefore, = 10 + 10 + 5 = 25 minutes.

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

Answer:
b. 140

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

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

Answer:
d. 30

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

Patterns on the Multiplication Table Page No 233

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

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

Answer:
even

Explanation:
Products with 2 as a factor are even.

Question 2.
4 × 6 = ________

Answer:
even

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

Question 3.
8 × 3 = ________

Answer:
even

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

Question 4.
2 × 3 = _________

Answer:
even

Explanation:
Products with 2 as a factor are even.

Use the multiplication table. Describe a pattern you see.

Question 8.
in the column 5
_________

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

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

Question 9.
in the row for 10
________

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

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

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

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

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

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

Answer:
The row for 4.

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

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

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

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

Patterns on the Multiplication Table Lesson Check Page No 234

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

Answer:
d. 4 × 9

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

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

Answer:
a. Even and then odd

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

Spiral Review

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

Answer:
a. 12

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

Question 4.
Use the picture graph.

How many students have green eyes?
Options:
a. 4
b. 8
c. 12
d. 16

Answer:
d. 16

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

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

Answer:
b. 12

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

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

Answer:
b. 982

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

Multiply with 8 Page No 239

Find the product.

Question 1.
8 × 10 = 80

Answer:
80

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

Question 2.
8 × 8 = ________

Answer:
64

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

Question 3.
8 × 5 = ________

Answer:
40

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

Question 6.
8 × 7 = ________

Answer:
56

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

Question 7.
6 × 8 = ________

Answer:
48

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

Question 8.
_______ = 9 × 8

Answer:
72

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

Question 9.
8
× 2
——
________

Answer:
16

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

Question 10.
6
× 8
——-
________

Answer:
48

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

Question 11.
8
× 7
——
_________

Answer:
56

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

Question 12.
0
× 8
——-
____________

Answer:
0

Explanation:

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

Question 13.
8
× 5
——
___________

Answer:
40

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

Question 14.
8
× 8
——–
___________

Answer:
64

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

Question 17.
8
× 1
——
___________

Answer:
8

Explanation:

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

Question 18.
4
× 8
——
___________

Answer:
32

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

Problem Solving

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

Answer:
48

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

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

Answer:
80

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

Multiply with 8 Lesson Check Page No 240

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

Answer:
d. 40

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

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

Answer:
c. 56

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

Spiral Review

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

Answer:
c. 553

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

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

Answer:
b. 230

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

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

Answer:
b. 4

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

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

Answer:
d. 25

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

Multiply with 9 Page No 245

Find the product.

Question 1.
10 × 9 = 90

Answer:
90

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

Question 2.
2 × 9 = ________

Answer:
18

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

Question 3.
9 × 4 = ________

Answer:
36

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

Question 4.
0 × 9 = ________

Answer:
0

Explanation:

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

Question 5.
1 × 9 = ________

Answer:
9

Explanation:

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

Question 8.
6 × 9 = ________

Answer:
54

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

Question 9.
9
× 4
——–
________

Answer:
36

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

Question 10.
5
× 9
——–
________

Answer:
45

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

Question 11.
9
× 7
——–
________

Answer:
63

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

Question 12.
2
× 9
——–
________

Answer:
18

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

Question 13.
9
× 9
——–
________

Answer:
81

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

Question 14.
10
× 9
——–
________

Answer:
90

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

Question 17.
6
× 9
——–
________

Answer:
54

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

Question 18.
9
× 1
——–
________

Answer:
9

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

Problem Solving

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

Answer:
27

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

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

Answer:
$36

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

Multiply with 9 Lesson Check Page No 246

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

Answer:
a. 63

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

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

Answer:
c. $45

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

Spiral Review

Question 3.
The table shows the hair color of girls in Kim’s class. How many girls have brown hair?

Options:
a. 1
b. 3
c. 4
d. 6

Answer:
d. 6

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

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

Answer:
c. $36

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

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

Answer:
a. 63

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

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

Answer:
a. 63

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

Multiplication Page No 251

Solve.

Question 1.
Henry has a new album for his baseball cards. He uses pages that hold 6 cards and pages that hold 3 cards. If Henry has 36 cards, how many different ways can he put them in his album?
Henry can put the cards in his album 5 ways.

Answer:
5 ways

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

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

Rows With 2 Plants	___8__	___7___	____6__	___5___	__4____	____3__	_____2_	_____1_
Rows With 1 Plants	____1__	___3___	___5___	___7___	___9___	____11__	___13___	____15__
Total Plants	____17__	___17___	__17____	__17____	___17___	___17___	____17__	____17__
Ms. Hernandez can plant the tomato plants	___8___	Ways.

Answer:
8 ways

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

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

Number of Nickels	___1___	___2___	____3__	____4__
Number of Pennies	___20___	___15___	___10___	____5__
Total Value	___25¢___	___25¢___	___25¢___	___25¢___
Bianca could have	___4___	Combination of 25 ¢.

Answer:
4 ways

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

Multiplication Lesson Check Page No 252

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

Question 1.

Answer:
b. 2

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

Spiral Review

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

Answer:
c. 468

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

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

Answer:
b. 240

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

Question 4.
Tyler made a picture graph to show students’ favorite colors. This is the key for his graph.
Each = 3 votes.
If 12 students voted for green, how many should there be in the green row of the graph?
Options:
a. 3
b. 4
c. 9
d. 12

Answer:
b. 4

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

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

Answer:
d. 30

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

Review/Test Page No 253

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

Answer:
20 spools

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

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

Answer:
i. True

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

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

Answer:
i. True

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

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

Answer:
ii. False

Explanation:

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

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

Answer:
i. True

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

Review/Test Page No 254

Question 5.
Circle groups to show 3 × (2 × 3).

Type below:
__________

Answer:
18

Explanation:

3 × (2 × 3) = 3 x 6 = 18.

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

Answer:
b. 4
c. 6
e. 8

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

Question 7.
Lisa completed the table to describe the product of a mystery one-digit factor and each number.

Part A
Give all of the possible numbers that could be Lisa’s mystery one-digit factor.
Type below:
__________

Answer:
0, 2, 4, 6, 8

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

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

Review/Test Page No 255

Question 8.
Kate drew 7 octagons. An octagon has 8 sides. How many sides did Kate draw?

_________ sides

Answer:
56

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

Question 10.
Break apart the array to show 8 × 6 = (4 × 6) + (4 × 6).

Answer:

 

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

Question 11.
Circle the symbol that makes the multiplication sentence true.
9 × 6 3 × (3 × 9)
_________

Answer:
<

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

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

Answer:
18

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

Review/Test Page No 256

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

Answer:
4 x (5 x 3)

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

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

Answer:
28 bandages

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

Review/Test Page No 257

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

Answer:
i. True

Explanation:

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

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

Answer:
ii. False

Explanation:

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

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

Answer:
ii. False

Explanation:

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

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

Answer:
i. True

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

Question 18.
Circle the number that makes the multiplication sentence true.
10 × = 40

Answer:
4

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

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

Answer:
ii. no

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

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

Answer:
i. yes

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

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

Answer:
ii. no

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

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

Answer:
i. yes

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

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

Answer:
$24

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

Question 21.
Write a multiplication sentence using the following numbers and symbols.

Type below:
__________

Answer:
6 x (5 x 2) = 60

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

Review/Test Page No 258

Question 22.
Louis started a table showing a multiplication pattern.
Part A
Complete the table. Describe a pattern you see in the products.

Type below:
__________

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

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

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

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

Question 23.
Use the number line to show the product of 4 × 8.

4 × 8 = _______

Answer:
32

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

Conclusion

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

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

Practice using Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication and learn various question types on Multiplication. Solve as many questions as possible in the 3rd Grade HMH Go Math Ch 3 Understand Multiplication Answer Key and become pro in the chapter. Thus, you can answer any kind of question framed on the concept and clear your tests or assessments with higher scores.

HMH Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication

To help you out with chapter 3 Understand Multiplication we have jotted down all the exercise problems in your Go Math Textbook. Simply tap on the respective chapter you wish to prepare and learn the fundamentals included within it easily. Go Math Grade 3 Answer Key Ch 3 Understand Multiplication is provided in a comprehensive manner for better understanding.

Lesson 1: Count Equal Groups

• Count Equal Groups Page No 143
• Count Equal Groups Lesson Check Page No 144

Lesson 2: Algebra • Relate Addition and Multiplication

• Relate Addition and Multiplication Page No 149
• Relate Addition and Multiplication Lesson Check Page No 150

Lesson 3: Skip Count on a Number Line

• Skip Count on a Number Line Page No 155
• Skip Count on a Number Line Lesson Check Page No 156

Mid-Chapter Checkpoint

• Page No 157
• Page No 158

Lesson 4: Problem Solving • Model Multiplication

• Model Multiplication Page No 163
• Model Multiplication Lesson Check Page No 164

Lesson 5: Model with Arrays

• Model with Arrays Page No 169
• Model with Arrays Lesson Check Page No 170

Lesson 6: Algebra • Commutative Property of Multiplication

• Commutative Property of Multiplication Page No 175
• Commutative Property of Multiplication Lesson Check Page No 176

Lesson 7: Algebra • Multiply with 1 and 0

• Multiply with 1 and 0 Page No 181
• Multiply with 1 and 0 Lesson Check Page No 182

Chapter 3 Review/Test

• Chapter 3 Review Test Page No 183
• Chapter 3 Review Test Page No 184
• Chapter 3 Review Test Page No 185
• Chapter 3 Review Test Page No 186
• Chapter 3 Review Test Page No 187
• Chapter 3 Review Test Page No 188

Count Equal Groups Page No 143

Draw equal groups. Skip count to find how many.

Question 1.
2 groups of 2 4

Answer: 4

Explanation:
There are two groups of 2
There are 2 two’s.
We skip count by 2’s. (2, 4)
So, there are 4 in all.

Count equal groups to find how many.

Question 5.

______ groups of _______ , _______ in all

Answer: 4, 3, 12

Explanation:
There are three counters in each group.
There are 4 equal groups.
We skip count by 3’s until you say 4 numbers. (3,6,9,12)
So, there are 4 groups of 3, 12 in all.

Question 6.

______ groups of _______ , _______ in all

Answer: 4, 4, 16

Explanation:
There are 4 counters in each group
There are 4 equal groups.
We skip count by 4’s until you say 4 numbers. (4,8,12,16)
There are 4 groups of 4, 16 in all

Problem Solving

Question 7.
Marcia puts 2 slices of cheese on each sandwich. She makes 4 cheese sandwiches. How many slices of cheese does Marcia use in all?
_________ slice of cheese

Answer: 8

Explanation:
Draw 2 counters (cheese) in each group.
There are 4 equal groups (sandwiches).
We skip count by 2’s until you say 4 numbers (4,8)
There are 8 slices of cheese.

Question 8.
Tomas works in a cafeteria kitchen. He puts 3 cherry tomatoes on each of 5 salads. How many tomatoes does he use?
_________ tomatoes

Answer: 15

Explanation:
Draw 3 counters (tomatoes) in each group.
There are 5 equal groups (salads).
We skip count by 3’s until you say 5 numbers (3,6,9,12,15)
There are 15 tomatoes in all.

Count Equal Groups Lesson Check Page No 144

Question 1.
Jen makes 3 bracelets. Each bracelet has 3 beads. How many beads does Jen use?

Options:
a. 12
b. 9
c. 6
d. 3

Answer: b

Explanation:
There are 3 beads in each group.
There are 3 equal groups (bracelets).
Now, skip count by 3’s until you say three numbers (3,6,9)
Jen use a total of 9 beads.

Question 2.
Ian has 5 cards to mail. Each card needs 2 stamps. How many stamps does Ian need?

Options:
a. 2
b. 5
c. 10
d. 15

Answer: c

Explanation:
There are 5 equal groups (cards) with two counters (stamps) in each group.
Now, skip count by 2’s until you say five numbers (2,4,6,8,10)
Ian need a total of 1o stamps.

Spiral Review

Question 3.
There were 384 people at a play on Friday night. There were 512 people at the play on Saturday night. Which is the best estimate of the total number of people who attended the play on both nights?
Options:
a. 900
b. 800
c. 700
d. 500

Answer: a

Explanation:
Step 1: Round each number to nearest hundred.
384 —-> 400
512  —-> 500
Step 2: Add the rounded numbers
400 + 500 = 900
The best estimate of the total number of people who attended the play on both nights are 900.

Question 4.
Walking the Dog Pet Store has 438 leashes in stock. They sell 79 leashes during a one-day sale. How many leashes are left in stock after the sale?
Options:
a. 459
b. 441
c. 369
d. 359

Answer: d

Explanation: Use place value to subtract
Subtract 438 – 79
Estimate 450 – 100 =

Step 1
Subtract the ones.
8 < 9, so regroup.
3 tens 8 ones = 2 tens ____ ones

On subtracting the ones place decimals, we get 9

Step 2
Subtract the tens.
2 < 3, so regroup.
4 hundreds 2 tens = 3 hundreds _____ tens

On subtracting the ones and tens place decimals, we get 59

Step 3:
Subtract the hundreds
Then, add to check your answer.
 

Question 5.
The Lakeside Tour bus traveled 490 miles on Saturday and 225 miles on Sunday. About how many more miles did it travel on Saturday?
Options:
a. 500 miles
b. 400 miles
c. 300 miles
d. 100 miles

Answer: c

Explanation:
Use compatible numbers
Step 1: Round each number to nearest hundred.
490 —-> 500
225 —-> 200
Step 2: Subtract the rounded numbers.

(i) Working each column from right to left

(ii) 0 minus 0 is 0

(iii) 0 minus 0 is 0

(iv) 5 minus 2 is 3

Question 6.
During one week at Jackson School, 210 students buy milk and 196 students buy juice. How many drinks are sold that week?
Options:
a. 496
b. 406
c. 396
d. 306

Answer: b

Explanation:
Use place value to add two addends.
Add 210 + 196
Estimate 200 + 200

Step 1:
Add the ones.

Step 2:

Add the tens.

Step 3:
Add the hundreds. Regroup the tens as hundreds.

Relate Addition and Multiplication Page No 149

Draw a quick picture to show the equal groups. Then write related addition and multiplication sentences.

Question 1.
3 groups of 5

5 + 5 + 5 = 15
3 × 5 = 15

Answer: 15

Explanation:
Addition Sentence:
There are 5 counters in each group.
There are 3 groups.
Now, add equal groups
5 + 5 + 5 = 15
Multiplication Sentence:
Since there are same number of counters in each circle, you can multiply to find how many in all.
Use multiplication method to find the total counters in equal groups.
Factor x Factor = Product
5    x     3       =  15

Question 2.
3 groups of 4
_____ + _____ + _____ = ______
_____ × _____ = ______

Answer: 4 + 4 + 4  = 12
3 x 4 = 12

Explanation: Addition Sentence
Draw 4 counters in each group.
There are total 3 groups.
Now, the addition sentence is 4 + 4 + 4 = 12

Multiplication sentence
Draw 4 counters in each circle or group.
Since there are same number of counters in each group, multiply groups and counters to find how many there are altogether.
3 x 4 = 12
factor x factor = product

Complete. Write a multiplication sentence.

Question 5.
7 + 7 + 7 = _____
_____ × _____ = ______

Answer: 7 + 7 + 7 = 21
3 x 7 = 21

Explanation:
7 + 7 + 7 = 21
This is addition sentence, from this we can find the total no of groups and counters.
From above sentence, we can tell that there are 3 groups and 7 counters in each group.
Multiplication Sentence
There are 3 groups and 7 counters in each group.
Since there are same number of counters in each group, multiply counters and groups to find how many there are altogether.
3  x  7 =  21

Question 6.
3 + 3 + 3 = _____
_____ × _____ = ______

Answer: 3 + 3 + 3 = 9
3 x 3 = 9

Explanation:
3 + 3 + 3 = 9
This is addition sentence, from this we can find the total no of groups and counters.
From above sentence, we can tell that there are 3 groups and 3 counters in each group.
Multiplication Sentence
There are 3 groups and 3 counters in each group.
Since there are same number of counters in each group, multiply counters and groups to find how many there are altogether.
3  x  3 =  9

Problem Solving

Question 7.
There are 6 jars of pickles in a box. Ed has 3 boxes of pickles. How many jars of pickles does he have in all? Write a multiplication sentence to find the answer.
_____ × _____ = ______ jars

Answer: 3 x 6 = 18 jars

Explanation:
Draw 3 boxes as Pickle boxes.
Draw 6 counters in each box to show jars.
Now, find the number of counters (jars).
Since, there are same number of jars in each pickle box, you can multiply to find how many in all.
3 groups of 6 = 3 x 6 = 18

Relate Addition and Multiplication Lesson Check Page No 150

Question 1.
Which is another way to show
3 + 3 + 3 + 3 + 3 + 3?
Options:
a. 5 × 3
b. 4 × 3
c. 8 × 3
d. 6 × 3

Answer: d

Explanation:
The given question is in the form of addition sentence. Now, we can find the no of counters and groups using it.
Draw 6 circles to show equal groups.
Then, draw 3 counters in each circle.
When you combine equal groups, you can multiply to find how many in all.
No. of equal groups x no of counters = total no of counters
6 x 3 = 18

Question 2.
Use the model. How many counters are there in all?

Options:
a. 8
b. 10
c. 12
d. 14

Answer: b

Explanation:
From the above figure, we can see there are two equal groups.
There are 5 counters in each group.
Now, multiplication sentence to find the number of counters.
No. of equal groups x No. of counters in each group = Total no. of counters
2 x 5 = 10

Spiral Review

Question 3.
A school gave 884 pencils to students on the first day of school. What is 884 rounded to the nearest hundred?
Options:
a. 800
b. 880
c. 890
d. 900

Answer: d

Explanation:
We need to round 884 to nearest hundred.
Now, look at the digit to the right which is 8.

8 > 5
So, the hundreds digit increases by one.
Write 9 as the hundreds digit.
Write zeros as the tens and ones digits.
So, 884 rounded to nearest hundred is 900

Question 4.
Find the difference.
6 3 2
– 2 7 4
———
Options:
a. 906
b. 442
c. 358
d. 354

Answer: c

Explanation:
Step-1:
Working each column from right to left.

Step-2:
Subtract the ones. Since, 2 < 4 , you must regroup.
3 tens 2 ones = 2 tens ______ ones.

Step-3:
Subtract the tens. Since 2 < 7, you must regroup.
6 hundreds 2 tens = 5 hundreds ______ ones.

Step-4:
Subtract the hundreds.

Step-5:
Add to check answer.

Question 5.
The line plot below shows how many points Trevor scored in 20 games.

In how many games did Trevor score at least 18 points?
Options:
a. 3
b. 5
c. 6
d. 10

Answer: d

Explanation:
The numbers in the line plot shows the points scored by Trevor.
Each ✗ in the figure stands for 1 game.
Find 18 points scored on the number line.
In the above line plot, we can see the three ✗s above 18, four ✗s above 19, 3 ✗s above 20.
So, We can say Trevor scored at least 18 points in 10 games.

Question 5.
In how many games did Trevor score 18 points or fewer?
Options:
a. 7
b. 10
c. 13
d. 15

Answer: c

Explanation:
The numbers in the line plot shows the points scored by Trevor.
Each ✗ in the figure stands for 1 game.
Find 18 and below 18 points scored on the number line.
In the above line plot, we can see the three ✗s above 18, five ✗s above 17, two ✗s above 16, three ✗s above 15 .
So, We can say Trevor scored at least 18 points in 13 games.

Question 6.
Darrien read 97 pages last week. Evan read 84 pages last week. How many pages in all did the boys read?
Options:
a. 13
b. 171
c. 181
d. 271

Answer: c

Explanation:
Add 97 and 84
Step 1:
Add ones. Regroup the ones as tens and ones.

Step 2:
Add tens.

Step 3:
Add hundreds.

Skip Count on a Number Line Page No 155

Draw jumps on the number line to show equal groups. Find the product.

Question 1.
6 groups of 3

6 × 3 = 18

Answer: 18

Explanation:
1 jump on the number line is considered as 1 group.
There are 6 jumps on the number line. So, there are 6 groups.
The length of each jump is 3.
Begin at 0. Skip count by 3’s.
Multiply 6 x 3 = 18

Question 2.
3 groups of 5

3 × 5 = _______

Answer: 15

Explanation:

1 jump on the number line is considered as 1 group.
There are 5 jumps on the number line. So, there are 5 groups.
The length of each jump is 3.
Begin at 0. Skip count by 3’s.
Multiply 3 x 5 = 15.

Write the multiplication sentence the number line shows.

Question 3.
2 groups of 6

______ × _____ = _______

Answer: 12

Explanation:
1 jump on the number is considered as 1 group.
There are 2 jumps on number line. So, there are 2 groups.
The length of each jump is 2.
Begin at 0. Skip count by 6’s.
Multiply 2 x 6 = 12.

Problem Solving

Skip Count on a Number Line Lesson Check Page No 156

Question 1.
Louise skip counts by 4 on a number line to find 5 x 4. How many jumps should she draw on the number line?
Options:
a. 3
b. 4
c. 5
d. 9

Answer: c

Explanation:
Given no. of skip counts on a number line = 4
Product = no. of jumps x length of each jump
Given product = 5 x 4
From the given data, we can say that no of jumps = 5
So, no of jumps drawn on the number line = 5.

Question 2.
Theo needs 4 boards that are each 3 feet long to make bookshelves. How many feet of boards does he need altogether?
Options:
a. 12 feet
b. 7 feet
c. 4 feet
d. 3 feet

Answer: a

Explanation:
Given no. of boards = 4
Length of each board = 3 feet
Begin at 0. Skip count by 3’s.
Product = 4 x 3 = 12
So, Theo needs 12 feet of boards altogether.

Spiral Review

Question 3.
Estimate the sum.
5 1 8
+ 2 5 1
Options:
a. 200
b. 700
c. 800
d. 900

Answer: c

Explanation:
Use Compatible numbers.
518 —-> 500
251 —-> 300
Perform addition

Question 4.
Which number would you put in a frequency table to show ?
Options:
a. 5
b. 6
c. 7
d. 8

Answer: d

Explanation:

Question 5.
A manager at a shoe store received an order for 346 pairs of shoes. What is 346 rounded to the nearest hundred?
Options:
a. 400
b. 350
c. 340
d. 300

Answer: d

Explanation:
Round 346 to nearest hundred.

Since 4 < 5, the digit in the rounding place stays same. i.e, 3
Now, write zeros to the right of the rounding place (tens and ones place)
So, 346 rounded to nearest hundred is 300.

Question 6.
Toby is making a picture graph. Each picture of a book is equal to 2 books he has read. The row for Month 1 has 3 pictures of books. How many books did Toby read during Month 1?
Options:
a. 2
b. 3
c. 6
d. 8

Answer: c

Explanation:
Given, each picture  = 2 books
Row for month 1 = 3 pictures of books = 3 x 2 = 6
So, Toby read 6 books during month 1.

Mid-Chapter Checkpoint Page No 157

Choose the best term from the box.

Question 1.
When you combine equal groups, you can _______________ to find how many in all.
_________

Answer: Multiply

Explanation:
When equal groups are combined together, multiplication operation is performed to find the total.

Question 2.
The answer in a multiplication problem is called the _________________ .
_________

Answer: Product

Explanation:
The Product is the answer to a multiplication problem.

Question 3.
The numbers you multiply are called the ______________ .
_________

Answer: factors

Explanation:
The numbers which are multiplied are called factors.

Concepts and Skills

Count equal groups to find how many.

Question 4.

_______ groups of _______ ; _______ in all

Answer:
3 groups of 3; 9 in all

Explanation:
From the figure, we can say that there are 3 equal groups.
Each group has three counters.
So, the total no of counters are 9 in all.

Question 5.

_______ groups of _______ ; _______ in all

Answer:
4 groups of 5; 20 in all

Explanation:
From the figure, we can say that there are 4 equal groups.
Each group has five counters.
So, the total no of counters are 20 in all.

Question 6.

_______ groups of _______ ; _______ in all

Answer:
2 groups of 10; 20 in all

Explanation:
From the figure, we can say that there are 2 equal groups.
Each group has 10 counters.
So, the total no of counters are 20 in all.

Write related addition and multiplication sentences.

Draw jumps on the number line to show equal groups.
Find the product.

Question 9.
6 groups of 3

_______ × _______ = _______

Answer: 6 x 3 = 18

Explanation:
Given, 6 groups of 3
No. of jumps = 6
Length of each jump = 3
Product = No. of jumps x length of each jump = 6 x 3 = 18

Mid-Chapter Checkpoint Page No 158

Question 10.
Beth’s mother cut some melons into equal slices. She put 4 slices each on 8 plates. Write a multiplication sentence to show the total number of melon slices she put on the plates.
Type below:
_________

Answer:  8 x 4 = 32

Explanation:
Given data,
There are 8 groups which is shown as plates.
Each group has 4 counters which is shown as slices.
Since, there are equal no. of slices in each plate, we can multiply to find the total number of melon slices.
Now, we can write multiplication sentence as 8 x 4 = 32.

Question 11.
Avery had 125 animal stickers. She gave 5 animal stickers to each of her 10 friends. How many animal stickers did she have left? What number sentences did you use to solve?
_________ stickers left

Answer: Multiplication and Subtraction Sentence, 75

Explanation:
Given, Total no. of animal stickers = 125
She gave 5 animal stickers to each of her 10 friends.
Use multiplicative sentence to find no. of stickers given to her friends.
Product = 5 x 10= 50
Total no. of stickers given to her friends = 50
Now, Total no. of stickers she left with = 125 – 50 = 75.

Question 12.
Matt made 2 equal groups of marbles. Write a multiplication sentence to show the total number of marbles.

Type below:
_________

Answer: 2 x 8 = 16

Explanation:
From the above figure, we can see
There are 2 equal groups.
Each group has 8 marbles.

Question 13.
Lindsey has 10 inches of ribbon. She buys another 3 lengths of ribbon, each 5 inches long. How much ribbon does she have now?
__________ inches of ribbon

Answer: 25 inches of ribbon

Explanation:
Given, Lindsey has 10 inches of ribbon.
She buys another 3 lengths of ribbon, each 5 inches long.
Use multiplication sentence to find length of 5 inches = 3 groups of 5
Product = 3 x 5 = 15 inches
Now, add to find how much ribbon lindsey has in all.
15 + 10 = 25
Total length of ribbon = 25 inches.

Question 14.
Jack’s birthday is in 4 weeks. How many days is it until Jack’s birthday? Describe how you could use a number line to solve
__________ days

Answer:  28

Explanation:
Given, Jack’s birthday is in 4 weeks.
Since each week has 7 days, length of each jump = 7
Use number line to find the no. of days.
No. of jumps = 4
Now, begin at o. Skip count by 7’s by drawing jumps on the number line.
Multiply no. of jumps and length of each jump
4 x 7 = 28
So, jack’s birthday is in 28 days.

Problem Solving Model Multiplication Page No 163

Draw a diagram to solve each problem.

Question 1.
Robert put some toy blocks into 3 rows. There are 5 blocks in each row. How many blocks are there in all?
15 blocks

Answer: 15 blocks

Explanation:
Given, Robert put some toy blocks into 3 rows.
Each row contain 5 blocks.
Now, use bar model to find the no. of blocks in all.
Write 5 in each box to show 5 blocks in each of the 3 rows.
Since, there are equal groups, we can multiply to find the number of blocks in all.
3 x 5 = 15 blocks
So, there are 15 blocks in all.

Question 4.
In Sorhab’s classroom, there are 3 rows with 7 desks in each row. How many desks are there in all?
_________ desks

Answer: 21 desks

Explanation:
Given, there are 3 rows.
Each row contain 7 desks.
Now, use bar model to find the no. of desks in all.
Write 7 in each box to show 7 desks in each of the 3 rows.
Since, there are equal groups, we can multiply to find the number of desks in all.
3 x 7 = 21 desks
So, there are  21 desks in all.

Question 5.
Maya visits the movie rental store. On one wall, there are 6 DVDs on each of 5 shelves. On another wall, there are 4 DVDs on each of 4 shelves. How many DVDs are there in all?
___________ DVDs

Answer: 46 DVD’s

Explanation:
Given, there are 2 walls.
On one wall, there are 5 shelves.
Each shelf has 6 DVDs.
Now, use bar model to find the no. of DVDs on one wall.
Write 6 in each box to show 6 DVDs on each of the 5 shelves.
Since, there are equal groups, we can multiply to find the number of DVDs on one wall.
5 x 6 = 30 DVDs
So, there are 30 DVD’s on one wall.
On another wall, there are 4 shelves.
Each shelf has 4 DVDs.
Now, use bar model to find the no. of DVDs on another wall.
Write 4 in each box to show 4 DVDs on each of the 4 shelves.
Since, there are equal groups, we can multiply to find the number of DVDs on another wall.
4 x 4 = 16 DVDs
So, there are 16 DVD’s on another wall.
Now, find the total no. of DVD’s on both all the walls.
Add. 30 + 16 = 46 DVDs.
So, there are 46 DVD’s in all.

Question 6.
The media center at Josh’s school has a computer area. The first 4 rows have 6 computers each. The fifth row has 4 computers. How many computers are there in all?
___________ computers

Answer: 28 computers

Explanation:
Given, there are 4 rows.
Each row contain 6 computers.
Now, use bar model to find the no. of computers in all.
Write 6 in each box to show 6 computers in each of the 4 rows.
Since, there are equal groups, we can multiply to find the number of computers in all.
4 x 6 = 24 computers
So, there are 24 computers in all.
There is another fifth row with 4 computers.
Now, use bar model to find the no. of computers in all.
No. of computers in fifth row = 4 x 1 = 4 computers.
Add the computers in all rows to find how many in all.
24 + 4 = 28
So, there are 28 computers in all.

Model Multiplication Lesson Check Page No 164

Question 1.
There are 5 shelves of video games in a video store. There are 6 video games on each shelf. How many video games are there in all?
Options:
a. 35
b. 30
c. 20
d. 11

Answer: b

Explanation:
Given, there are 5 shelves.
Each shelf contain 6 video games.
Now, use bar model to find the no. of video games in all.
Write 6 in each box to show 6 video games in each of the 5 shelves.
Since, there are equal groups, we can multiply to find the number of shelves in all.
5 x 6 = 30 shelves
So, there are 30 shelves in all.

Question 2.
Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row. He sees 8 trombone players. How many flute or trombone players does Ken see?
Options:
a. 2
b. 6
c. 16
d. 20

Answer: d

Explanation:
Given, there are 6 flute players in each row.
There are 2 rows.
Now, use bar model to find the no. of flute players in all.
Write 6 in each box to show 6 flute players in each of the 2 rows.
Since, there are equal groups, we can multiply to find the number of flute players in all.
2 x 6 = 12 flute players
Given, there are 8 trombone players.
Now, add flute and trombone players
12 + 8 = 20
So, there are 20 flute or trombone players.

Spiral Review

Question 3.
What is the sum of 438 and 382?
Options:
a. 720
b. 810
c. 820
d. 910

Answer: c

Explanation:
Step 1:
Add ones. Regroup ones as tens and ones.

Step 2:
Add tens. Regroup tens as hundreds and tens.

Step 3:
Add the hundreds.

Question 4.
Estimate the sum.
6 2 2
+ 8 4
———
Options:
a. 500
b. 600
c. 700
d. 800

Answer: c

Explanation:
Use compatible numbers.
622 —-> 600
84  —–> 100

Question 5.
Francine uses 167 silver balloons and 182 gold balloons for her store party. How many silver and gold balloons in all does Francine use?
Options:
a. 15
b. 345
c. 349
d. 359

Answer: c

Explanation:
Given, Silver balloons = 167
Gold balloons = 182
Add Silver and gold balloons to find total in all.
Step 1: Add ones.

Step 2: Add tens. Regroup tens as hundreds and tens.

Step 3: Add hundreds.

So, total no. of silver and gold balloons in all does Francine use = 349

Question 6.
Yoshi is making a picture graph. Each picture of a soccer ball stands for two goals he scored for his team. The row for January has 9 soccer balls. How many goals did Yoshi score during January?
Options:
a. 18
b. 16
c. 11
d. 9

Answer: a

Explanation:
Given, each picture = 2 goals
Row for January = 9 soccer balls
Consider each picture as 9 soccer balls.
Now, find the goals did Yoshi score during January.
9 x 2 = 18
So, 18 goals did Yoshi score during January.

Model with Arrays Page No 169

Write a multiplication sentence for the array.

Question 1.

3 × 7 = 21

Answer: 3 x 7 = 21

Explanation:
In the above figure, we can see there are same no. of tiles in each row.
There are 3 rows with 7 tiles in each row.
Now, multiplication sentence for array can be written as number of rows x no. of tiles in each row.
Multiply. 3 x 7 = 21

Question 2.

2 × 5 = _______

Answer: 10

Explanation:
In the above figure, we can see there are same no. of tiles in each row.
There are 2 rows with 5 tiles in each row.
Now, multiplication sentence for array can be written as number of rows x no. of tiles in each row.
Multiply. 2 x 5 = 10

Draw an array to find the product.

Question 3.
4 × 2 = _______

Answer: 8

Explanation:
Make an array by placing the same no. of tiles in each row.
From the given data, make an array with 4 rows of 2 tiles.
Now, draw an array.
In the above figure, we can see there are same no. of tiles in each row.
There are 4 rows with 2 tiles in each row.
Now, multiplication sentence for array can be written as number of rows x no. of tiles in each row.
Multiply. 4 x 2 = 8

Question 6.
2 × 8 = _______

Answer: 16

Explanation:
Make an array by placing the same no. of tiles in each row.
From the given data, make an array with 2 rows of 8 tiles.
Now, draw an array.
In the above figure, we can see there are same no. of tiles in each row.
There are 2 rows with 8 tiles in each row.
Now, multiplication sentence for array can be written as number of rows x no. of tiles in each row.
Multiply. 2 x 8 = 16

Problem Solving

Question 7.
Lenny is moving tables in the school cafeteria. He places all the tables in a 7 × 4 array. How many tables are in the cafeteria?
_________ tables

Answer: 28 tables

Explanation:
Given array = 7 x 4
Now, make an array with 7 rows of 4 tiles.
Draw an array and find the no. of tables.
Multiply. 7 x 4 = 28
So, there are 28 tables in the cafeteria.

Question 8.
Ms. DiMeo directs the school choir. She has the singers stand in 3 rows. There are 8 singers in each row. How many singers are there in all?
_________ singers

Answer: 24 singers

Explanation:
Given, no. of singers in each row = 8
No. of rows = 3
Now, make an array with 3 rows of 8 singers.
Find the no. of singers by multiplying no. of rows with singers.
Multiply. 3 x 8 = 24 singers.
So, there are 24 singers in all.

Model with Arrays Lesson Check Page No 170

Question 1.
What multiplication sentence does this array show?

Options:
a. 2 × 3 = 6
b. 6 × 3 = 18
c. 3 × 4 = 12
d. 3 × 5 = 15

Answer: d

Explanation:
From the above figure, we can see that the array consists of 3 rows and 5 tiles.
Now, the multiplications sentence is 3 x 5 = 15

Question 2.
What multiplication sentence does this array show?

Options:
a. 3 × 9 = 27
b. 3 × 8 = 24
c. 3 × 7 = 21
d. 4 × 5 = 20

Answer: a

Explanation:
From the above figure, we can see that the array consists of 3 rows and 9 tiles.
Now, the multiplications sentence is 3 x 9 = 27

Spiral Review

Question 3.
Use the table to find who traveled 700 miles farther than Paul during summer vacation.

Options:
a. Andrew
b. Bonnie
c. Susan
d. Tara

Answer: d

Explanation:
From the table, we can say that paul travelled 233 miles.
Now, use break apart strategy to find sums.
Paul –>      233 = 200 + 30 + 3
Andrew –> 380 = 300 + 80+ 0
Bonnie –>  790 = 700 + 90+ 0
Tara –>      933 = 900 + 30+ 3
Susan –>   853 = 800 + 50+ 3
From the above sums, we can say that Tara travelled farther miles than paul.

Question 4.
Use the bar graph to find what hair color most students have.

Options:
a. Brown
b. Black
c. Blond
d. Red

Answer: a

Explanation:
The title shows hair color for students.
The length of bar tells the no. of students had each color.
Now, Find out the which color maximum no. of students have.
We can see that the brown color is the highest.

Question 5.
Spencer ordered 235 cans of tomatoes to make salsa for the festival. What is 235 rounded to the nearest ten?
Options:
a. 200
b. 230
c. 240
d. 300

Answer: c

Explanation:
Round 235 to nearest ten.
The digit to the right of rounding place is 5.
So, the digit in the rounding place is increased by one.
Write zero to the round of rounding digit.
Now, it becomes 240.

Question 6.
Which bar would be the longest on a bar graph of the data?

Options:
a. Cheese
b. Pepperoni
c. Vegetable
d. Sausage

Answer: a

Explanation:
Make a bar graph.
Step 1:
Write a title at the top to tell what the graph is about. Label the side of the graph to tell about the bars. Label the bottom of the graph to explain what the numbers tell.
Step 2:
Choose numbers for the bottom of the graph so that most of the bars will end on a line. Since the least number is 1 and the greatest number is 5, make the scale 0-5.
Step 3: Draw and shade a bar to show the number for each pizza topping.
From the bar graph, we can say that the cheese bar would be the longest on a bar graph of the data.

Commutative Property of Multiplication Page No 175

Write a multiplication sentence for the model. Then use the Commutative Property of Multiplication to write a related multiplication sentence.

Question 1.

5 × 2 = 10
2 × 5 = 10

Answer: 5 × 2 = 10
2 × 5 = 10

Explanation:
From the figure, we can say that there are 5 rows.
There are two tiles in each row.
From the given array, the multiplication sentence can be written as 5 x 2 = 10
The Commutative property of multiplication have the same factors in different order.
So, by using commutative property, Multiplication sentence is written as 2 x 5 = 10.

Question 2.

______ × _____ = _______
______ × _____ = _______

Answer:
6 x 4 = 24
4 x 6 = 24

Explanation:
From the figure, we can say that there are 6 rows.
There are 4 tiles in each row.
From the given array, the multiplication sentence can be written as 6 x 4 = 24
The Commutative property of multiplication have the same factors in different order.
So, by using commutative property, Multiplication sentence is written as 4 x 6 = 24.

Question 3.

______ × _____ = _______
______ × _____ = _______

Answer:
3 x 4 = 12
4 x 3 = 12

Explanation:
From the figure, we can say that there are 3 equal groups.
There are 4 counters in each group.
From the given array, the multiplication sentence can be written as 3 x 4 = 12
The Commutative property of multiplication have the same factors in different order.
So, by using commutative property, Multiplication sentence is written as 4 x 3 = 12.

Question 4.

______ × _____ = _______
______ × _____ = _______

Answer:
2 x 6 = 12
6 x 2 = 12

Explanation:
From the figure, we can say that there are 2 equal groups.
There are 6 counters in each group.
From the given array, the multiplication sentence can be written as 2 x 6 = 12
The Commutative property of multiplication have the same factors in different order.
So, by using commutative property, Multiplication sentence is written as 6 x 2 = 12.

Problem Solving

Commutative Property of Multiplication Lesson Check Page No 176

Question 1.
Which is an example of the Commutative Property of Multiplication?
Options:
a. 8 × 4 = 8 × 4
b. 4 × 2 = 2 × 4
c. 2 × 8 = 4 × 4
d. 2 + 4 = 2 × 4

Answer: b

Explanation:
The Commutative Property of Multiplication states that when you change the order
of the factors, the product stays the same. From the given options, 4 x 2 = 2 x 4 is an example of commutative property of multiplication.

Question 2.
What factor makes the number sentence true?
7 × 4 = ■ × 7
Options:
a. 2
b. 4
c. 7
d. 28

Answer: b

Explanation:
The Commutative Property of Multiplication states that when you change the order
of the factors, the product stays the same. From the question, we can see that 7 x 4 = 28;
Then 4 x 7 = 28

Spiral Review

Question 3.
Ms. Williams drove 149 miles on Thursday and 159 miles on Friday. About how many miles did she drive altogether the two days?
Options:
a. about 150 miles
b. about 200 miles
c. about 300 miles
d. about 400 miles

Answer: c

Explanation:

Given, miles driven by Ms. Williams on Thursday = 149
Miles driven by Ms. Williams on Friday = 159
By using compatible numbers, we can find the no. of miles did she drive altogether the two days.
149 —> 150
159 —> 150

So, the no. of miles driven altogether is about 300 miles.

Question 4.
Inez has 699 pennies and 198 nickels. Estimate how many more pennies than nickels she has.
Options:
a. about 500
b. about 600
c. about 700
d. about 900

Answer: a

Explanation:

Given, there are 699 pennies and 198 nickels.
Now, estimate to find how many more pennies than nickels she has.
Use compatible numbers to compute it.
699 —> 700
198 —> 200

So, Inez has 500 more pennies than nickels.

Question 5.
This year, the parade had 127 floats. That is 34 fewer floats than last year. How many floats were in the parade last year?
Options:
a. 161
b. 151
c. 103
d. 93

Answer: a

Explanation:
Given, no. of floats this year = 127
No. of floats last year are 34 greater than this year.
Now, estimate the no. of floats in the parade last year
Perform Addition operation
Step 1: Add ones. Regroup the ones as tens and ones.

Step 2: Add tens.

Step 3: Add hundreds.

The total no. of floats in the parade last year = 161

Question 6.
Jeremy made a tally table to record how his friends voted for their favorite pet. His table shows next to Dog. How many friends voted for a dog?
Options:
a. 6
b. 8
c. 10
d. 12

Answer: d

Explanation:
Count the tally marks. It shows 12. So, the no. of friends who voted for dog = 12

Multiply with 1 and 0 Page No 181

Find the product.

Question 1.
1 × 4 = 4

Answer: 4

Explanation:
The Identity Property of Multiplication states that the product of any numberand 1 is that number.
So, 1 x 4 = 4

Question 2.
0 × 8 = _______

Answer: 0

Explanation:
The Zero Property of Multiplication states that the product of zero and any number is zero
So, 0 x 8 = 0

Question 3.
0 × 4 = _______

Answer: 0

Explanation:
The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 0 x 4 = 0

Question 4.
1 × 6 = _______

Answer: 6

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 1 x 6 = 6

Question 5.
3 × 0 = _______

Answer: 0

The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 3 x 0 = 0

Question 6.
0 × 9 = _______

Answer: 0

The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 0 x 9 = 0

Question 10.
4 × 0 = _______

Answer: 0

The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 4 x 0 = 0

Question 11.
7 × 1 = _______

Answer: 7

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 7 x 1 = 7

Question 12.
1 × 5 = _______

Answer: 5

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 1 x 5 = 5

Question 13.
3 × 1 = _______

Answer: 3

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 3 x 1 = 3

Question 14.
0 × 7 = _______

Answer: 0

The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 0 x 7 = 0

Question 15.
1 × 9 = _______

Answer: 9

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 1 x 9 = 9

Question 16.
5 × 0 = _______

Answer: 0

The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 5 x 0 = 0

Question 18.
2 × 0 = _______

Answer: 0

The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 2 x 0 = 0

Question 19.
5 × 1 = _______

Answer: 5

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 5 x 1 = 5

Question 20.
1 × 0 = _______

Answer: 0

Explanation:
The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 1 x 0 = 0

Question 21.
0 × 0 = _______

Answer: 0

Explanation:
The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 1 x 0 = 0

Question 22.
1 × 3 = _______

Answer: 3

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 1 x 3 = 3

Question 23.
9 × 0 = _______

Answer: 0

Explanation:
The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 9 x 0 = 0

Question 24.
1 × 1 = _______

Answer: 1

Explanation:
The Identity Property of Multiplication states that the product of any number and 1 is that number.
So, 1 x 1 = 1

Problem Solving

Multiply with 1 and 0 Lesson Check Page No 182

Question 1.
There are 0 bicycles in each bicycle rack. If there are 8 bicycle racks, how many bicycles are there in all?
Options:
a. 80
b. 8
c. 1
d. 0

Answer: d

Explanation:
There are 0 bicycles in each bicycle rack.
There are 8 bicycle racks.
No. of bicycles in all = 8 x 0 = 0

Question 2.
What is the product?
1 × 0 = _______
Options:
a. 0
b. 1
c. 10
d. 11

Answer: a

Explanation:
The Zero Property of Multiplication states that the product of zero and any number is zero.
So, 1 x 0 = 0

Spiral Review

Question 3.
Mr. Ellis drove 197 miles on Monday and 168 miles on Tuesday. How many miles did he drive in all?
Options:
a. 29 miles
b. 255 miles
c. 365 miles
d. 400 miles

Answer: c

Explanation:
Given, no. of miles driven on Monday = 197
no. of miles driven on Tuesday = 168
Perform addition to find the no. of miles driven in all

Question 4.
What multiplication sentence does the array show?
■ ■ ■ ■ ■ ■
Options:
a. 1 × 6 = 6
b. 3 × 2 = 6
c. 2 × 6 = 12
d. 5 + 1 = 6

Answer: a

Explanation:
Given array shows 1 row with 6 tiles.
So, multiplication sentence can be written as 1 x 6 = 6

Use the bar graph for 5–6.

Question 5.
How many cars were washed on Friday and Saturday combined?
Options:
a. 55
b. 80
c. 90
d. 120

Answer: b
Explanation:
From the bar graph, we can see that no. of cars washed on Friday = 25
No. of cars washed on Saturday = 55
Total no. of cars washed on Friday and Saturday = 80

Question 6.
How many more cars were washed on Saturday than on Sunday?
Options:
a. 95
b. 30
c. 25
d. 15

Answer: d

Explanation:
From the bar graph, we can see that cars washed on Saturday = 55
Cars washed on Sunday = 40
55-40 = 15
15 more cars were washed on Saturday than on Sunday.

Chapter 3 Review Test Page No 183

Question 2.
Nadia has 4 sheets of stickers. There are 8 stickers on each sheet. She wrote this number sentence to represent the total number of stickers.

4 × 8 = 32

What is a related number sentence that also represents the total number of stickers she has?
Options:
a. 8 + 4 =■
b. 4 + 4 + 4 + 4 = ■
c. 8 × 8 = ■
d. 8 × 4 = ■

Answer: d

Explanation:
Given, there are are 4 sheets of stickers.
Each sheet has 8 stickers.
Given total no. of stickers represented as = 4 x 8 = 32
By using commutative property of multiplication, related number sentence can be represented as 8 x 4 =32

Question 3.
Lindsay went hiking for two days in Yellowstone National Park. The first jump on the number line shows how many birds she saw the first day. She saw the same number of birds the next day.

Write the multiplication sentence that is shown on the number line.
______ × _______ = _______

Answer: 2 x 8 = 16

Explanation:
Given, the total no. of jumps = 2
From the figure, we can see that there are two jumps which begins at 0 and skip count by 8’s.
Product = No. of jumps x Length of each jump.
Now, multiplication sentence can be written as 2 x 8 = 16

Chapter 3 Review Test Page No 184

Question 4.
Paco drew an array to show the number of desks in his classroom. Write a multiplication sentence for the array.

________ desks

Answer: 21 desks

Explanation:
In the given array, there are three rows.
Each row has 7 desks.
Now, multiplication sentence can be written as no. of rows x no. of desks in each row.
Multiply. 3 x 7 = 21 desks

Question 5.
Alondra makes 4 necklaces. She uses 5 beads on each necklace. For numbers 5a–5d, choose Yes or No to tell if the number sentence could be used to find the number of beads Alondra uses.
a. 4 × 5 = ■
i. yes
ii. no

Answer: i

Explanation: Given, there are 4 necklaces.
Each necklace uses 5 beads.
Now, number sentence (multiplication) can be written as 4 groups of 5 = 4 x 5
So, the answer is yes

Question 5.
b. 4 + 4 + 4 + 4 = ■
i. yes
ii. no

Answer: ii

Given, there are 4 necklaces.
Each necklace uses 5 beads.
Now, number sentence (addition) can be written as 4 groups of 5 = 5 + 5 + 5 + 5
So, the answer is no.

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

Answer: i

Given, Given, there are 4 necklaces.
Each necklace uses 5 beads.
Now, number sentence (addition) can be written as 4 groups of 5 = 5 + 5 + 5 + 5
So, the answer is yes.

Question 5.
d. 5 + 4 = ■
i. yes
ii. no

Answer: ii

Given, there are 4 necklaces.
Each necklace uses 5 beads.
Now, number sentence (addition) can be written as 4 groups of 5 = 4 x 5
Using commutative property of multiplication, it can be written as 5 x 4, but given question is 5 + 4.
So, the answer is no.

Question 6.
John sold 3 baskets of apples at the market. Each basket contained 9 apples. How many apples did John sell? Make a bar model to solve the problem.

_______ apples

Answer:27 apples

Explanation:
Given, there are 3 baskets of apples.
Each basket contains 9 apples.
Draw a bar model with 3 boxes to show 3 baskets.
Write 9 in each box to show 9 apples.
Since, there are equal groups, we can multiply to find No. of apples john sold.
3 x 9 = 27 apples.

Chapter 3 Review Test Page No 185

Question 7.
Select the number of sentences that show the Commutative Property of Multiplication. Mark all that apply.
Options:
a. 3 × 2 = 2 × 3
b. 4 × 9 = 4 × 9
c. 5 × 0 = 0
d. 6 × 1 = 1 × 6
e. 7 × 2 = 14 × 1

Answer: a

Explanation:
The Commutative Property of Multiplication states that when you change the order of the factors, the product stays the same.
So, 3 x 2 = 2 x 3 is the answer.

Question 9.
Sonya needs 3 equal lengths of wire to make 3 bracelets. The jump on the number line shows the length of one wire in inches. How many inches of wire will Sonya need to make the 3 bracelets?

_________ inches

Answer: 18 inches

Explanation:
Given, Length of one wire = jump on the number line
From the figure, we can see that length of wire = 6 inches
3 equal lengths of wire is required for 3 bracelets.
So, no. of jumps = 3
length of each jump = 6 inches
Multiply. 3 x 6 = 18
So, sonya need 18 inches of wire to make 3 bracelets.

Chapter 3 Review Test Page No 186

Question 11.
Jorge displayed 28 cans of paint on a shelf in his store.

Select other ways Jorge could arrange the same number of cans. Mark all that apply.
Options:
a. 2 rows of 14
b. 1 row of 28
c. 6 rows of 5
d. 8 rows of 3
e. 7 rows of 4

Answer: e

Explanation:
Given, There are 28 cans of paint on a shelf in a store.
In the given array, there are 4 rows with 7 cans in each row.
So, there are 4 rows of 7.
By using commutative property of multiplication, it can be arranged in 7 rows of 4.

Question 12.Choose the number that makes the statement true. The product of any number and is zero.

Answer: 0

Explanation:
The Zero Property of Multiplication states that the product of any number and zero is zero.
So, the answer is 0.

Question 13.
James made this array to show that 3 × 5 = 15.

Part A
James says that 5 × 3 = 15. Is James correct? Draw an array to explain your answer.
a. yes
b. no

Answer: Yes.

Explanation: Draw an array to show 5 rows with 3 tiles in each row.
Then, Multiplication sentence can be written as no. of rows x no. of tiles in each row
5 x 3 = 15

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

Answer: Commutative Property of Multiplication

Explanation:
The Commutative Property of Multiplication supports this answer. Because it states that the product of any two factors in reverse order remains the same.

Chapter 3 Review Test Page No 187

Question 14.
Julio has a collection of coins. He puts the coins in 2 equal groups. There are 6 coins in each group. How many coins does Julio have? Use the number line to show your work.

________ coins

Answer: 12 coins

Explanation:
There are 2 equal groups.
There are 6 coins in each group.
Find total no. of coins by using number line.
Begin at 0. Skip count by 6s by drawing jumps on the number line.
So, no. of jumps = 2
Length of each jump = 6
Multiply. 2 x 6 = 12
Total no. of coins Julio have = 12

Question 15.
Landon collects trading cards.
Part A
Yesterday, Landon sorted his trading cards into 4 groups. Each group had 7 cards. Draw a bar model to show Landon’s cards. How many cards does he have?
________ trading cards

Answer: 28 trading cards

Explanation:
No. of groups = 4
Each group has 7 cards.
Draw a bar model to show the cards.
Draw 4 boxes in the bar model.
Write 7 in each box to show 7 cards.
Since, there are equal groups, multiply to find the no. of cards.
Multiply. 4 x 7 = 28 cards.

Question 15.
Part B
Landon buys 3 more packs of trading cards today. Each pack has 8 cards. Write a multiplication sentence to show how many cards Landon buys today. Then find how many cards Landon has now. Show your work.
Type below:
_________

Answer:52 cards

Explanation:
Given, Landon buys 3 more packs of trading cards
Each pack has 8 cards.
Multiplication Sentence = 3 x 8 = 24.
Total no. of cards = 28 + 24 = 52 cards.

Question 17.
Carlos spent 5 minutes working on each of the 8 math problems. He can use 8 × 5 to find the total amount of time he spent on the problems.
For numbers, 17a–17d, choose Yes or No to show which are equal to 8 × 5.
a. 8 + 5
i. yes
ii. no

Answer: No

Explanation:
Given, Carlos spent 5 minutes working on each of 8 math problems.
Given Sentence = 8 x 5
As there are 8 problems with 5 minutes spent on each, the total time can be find out using multiplication sentence.
So, the answer is no.

Question 17.
b. 5 + 5 + 5 + 5 + 5
i. yes
ii. no

Answer: No

Given, Carlos spent 5 minutes working on each of 8 math problems.
Given Sentence = 8 x 5 = 40
But given option 5 + 5 + 5 + 5 + 5 = 25.
So, the answer is no

Question 17.
c. 8 + 8 + 8 + 8 + 8
i. yes
ii. no

Answer: Yes
Explanation:
Given, Carlos spent 5 minutes working on each of 8 math problems.
Given Sentence = 8 x 5 = 40
Given option = 8 + 8 + 8 + 8 + 8 = 40
So, the answer is yes

Question 17.
d. 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
i. yes
ii. no

Answer: Yes
Explanation:
Given, Carlos spent 5 minutes working on each of 8 math problems.
Given Sentence = 8 x 5 = 40
Given option = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40
So, the answer is yes.

Chapter 3 Review Test Page No 188

Question 19.
Jayson is making 5 sock puppets. He glues 2 buttons on each puppet for its eyes. He glues 1 pompom on each puppet for its nose.
Part A
Write the total number of buttons and pompoms he uses. Write a multiplication sentence for each.
Eyes, Noses
_________ buttons _________ pompoms

Answer: Eyes
10 buttons,
5 x 2 = 10

Noses
5 pompoms
5 x 1 = 5

Explanation:
Given, there are 5 sock puppets
Each puppet has 2 buttons for its eyes
Each puppet has 1 pompom for its nose
Total no. of buttons
Multiplication Sentence = 5 x 2 = 10
Total no. of pompoms
Multiplication Sentence = 5 x 1 = 5

Question 19.
Part B
After making 5 puppets, Jayson has 4 buttons and 3 pompoms left. What is the greatest number of puppets he can make with those items if he wants all his puppets to look the same? Draw models and use them to explain.
_________ puppets

Answer: 2 puppets

Explanation:
Given, there are no. of puppets = 5
There are 4 buttons and 3 pompoms.
Each puppet requires 2 buttons and 1 pompom.
So, he can make 2 puppets with the left items.