# Big Ideas Math Answers Grade 3 Chapter 2 Multiplication Facts and Strategies

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## Big Ideas Math Book 3rd Grade Answer Key Chapter 2 Multiplication Facts and Strategies

Multiplication Facts and Strategies chapter consists of the topics like Multiply by 2, Multiply by 5, Multiply by 10, Multiply by 0 or 1, Use the Distributive Property. The solutions in Big Ideas Math Book 3rd Grade Answer Key Chapter 2 Multiplication Facts and Strategies are prepared by the math experts according to the latest edition. Scroll down this page to get the solutions for all the questions. Tap the link to check out the topics covered in this Multiplication Facts and Strategies chapter.

Lesson 1 – Multiply by 2

Lesson 2 – Multiply by 5

Lesson 3 – Multiply by 10

Lesson 4 – Multiply by 0 or 1

Lesson 5 – Use the Distributive Property

Lesson 6 – Problem Solving: Multiplication

### Lesson 2.1 Multiply by2

Explore and Grow

Model 3 × 2 using equal groups.

3 × 2 = ____

2 + 2 + 2 = 6
Multiplication is 3 × 2 = 6

Structure
How can you use the model to find 4 × 2?

Think and Grow Multiply by 2

Answer: 4 × 2 = 8

2 + 2 + 2 + 2 =8
4 × 2 = 8

Example Find 6 × 2.
Model six groups of two.

A multiple of a number is the product of that number and any other counting number.

There are 6 groups and 2 counters in each group.
So add all the counters in each group.
2 + 2 + 2 + 2 + 2 + 2 = 12
Multiply the number of groups and the number of counters in each group.
6 × 2 = 12

Example
Complete the table and the statements.

Show and Grow

Question 1.
Complete the equations for the model.

2 + 2 + 2 + 2 = 8
4 × 2 = 8

Find the product
Question 2.
7 × 2 = ____

Explanation:
2 + 2 + 2 + 2 + 2 + 2 + 2 = 14
7 × 2 = 14

Question 3.
2 × 3 = _____

Explanation:
2 + 2 + 2 = 6
2 × 3 = 6

Apply and Grow: Practice

Complete the equations for the model
Question 4.

Answer: 2 + 2 + 2 + 2 + 2 = 10
2 × 5 = 10

Explanation:
By seeing the above figure we can say that there are 2 counters in 5 groups.
Add the number of counters in each group.
That means 2 + 2 + 2 + 2 + 2 = 10
Multiply the number of groups and number of counters in each group.
2 × 5 = 10

Question 5.

Answer: 9 + 9 = 18
9 × 2 = 18

Explanation:
There are 9 counters in each group
Total number of groups = 2
9 + 9 = 18
Multiply the number of groups and number of counters in each group
9 × 2 = 18

Find the product
Question 6.

Multiply the two numbers 2 and 2.
2 × 2 = 4

Question 7.

Multiply the two numbers 3 and 2.
3 × 2 = 6

Question 8.

Explanation:
Multiply the two numbers 2 and 10.
2 × 10 = 20

Question 9.

Any number multiplied with 1 will be the same number.
1 × 2 = 2

Question 10.

Explanation:
Multiply the two numbers 6 and 2.
6 × 2 = 12

Question 11.

Explanation:
Multiply the two numbers 2 and 8.
2 × 8 = 16

Question 12.

Explanation:
Multiply the two numbers with 4 and 2.
4 × 2 = 8

Question 13.

Explanation:
Multiply the two numbers 7 and 2.
7 × 2 = 14

Find the missing factor.
Question 14.
2 × ___ = 14

Explanation:
Let the missing factor be x
2 × x = 14
x = 14/2 = 7
X = 7
Thus the missing factor is 7.

Question 15.
2 × ____ = 20

Explanation:
Let the missing factor be y
2 × y = 20
y = 20/2
y = 10
Therefore the missing factor y is 10.

Question 16.
5 × ____ = 10

Explanation:
Let a be the missing factor
5 × a = 10
a = 10/5
a = 2
Thus the missing factor is 2.

Question 17.
How many gloves are in 9 pairs of gloves?

Explanation:
Given that there are 9 pairs of gloves
Each pair contains 2 gloves
9 × 2 = 18
There are 18 gloves in 9 pairs.

Question 18.
Structure
How are the models similar? How are they different?

Answer: There are 8 counters in 2 groups. Counters are similar but the groups are different.

Think and Grow: Modeling Real Life

A sled dog team must have at least 6 rows of 2 dogs. A musher has 15 dogs. Does he have enough dogs for a team?
Multiplication equation:

The musher ______ have enough dogs for a team.

Given,
A sled dog team must have at least 6 rows of 2 dogs.
6 × 2 = 12
A musher has 15 dogs.
15 – 12 = 3 dogs
Therefore the musher has enough dogs for a team.

Show and Grow

Question 19.
Your teacher asks you to make 2 rows of 8 chairs. There are18 chairs. Do you have enough chairs?

Explanation:
Given,
Your teacher asks you to make 2 rows of 8 chairs. There are18 chairs.
2 × 8 = 16
Thus 16 chairs are enough to arrange 8 chairs in 2 rows.

Question 20.
You have 5 pairs of socks. Do you have enough socks to make 12 sock puppets?

DIG DEEPER!
You want to make as many sock puppets as you can with the socks that you have. You need 2 googly eyes for each puppet. How many googly eyes do you need?

Explanation:
Given that, there are 5 pairs of socks.
You need 2 googly eyes for each puppet.
5 × 2 = 10
Thus you need 10 googly eyes.

### Multiply by 2 Homework & Practice 2.1

Complete the equations for the model.
Question 1.

Observe the figure given above,
There are 3 groups and 2 counters in each group.
Add the number of counters in each group.
2 + 2 + 2 = 6
Multiply the number of groups and number of counters in each group.
3 × 2 = 6

Question 2.

There are 2 groups and 6 counters in each group.
Add the number of counters in each group.
6 + 6 = 12
Multiply the number of groups and number of counters in each group
2 × 6 = 12

Find the product.
Question 3.

Explanation:
Multiply the two numbers 4 and 2.
4 × 2 = 8

Question 4.

Explanation:
Multiply the two numbers 10 and 2.
10 × 2 = 20

Question 5.

Explanation:
Multiply the two numbers 2 and 8.
2 × 8 = 16

Question 6.

Explanation:
Multiply the two numbers 2 and 9.
2 × 9 = 18

Question 7.

Explanation:
Multiply the two numbers 7 and 2.
7 × 2 = 14

Question 8.

Multiply the two numbers 2 and 2.
2 × 2 = 4

Question 9.

Explanation:
Multiply the two numbers 5 and 2.
5 × 2 = 10

Question 10.

Explanation:
Multiply the two numbers 2 and 1.
2 × 1 = 2

Find the missing factor.
Question 11.
2 × ___ = 16

Explanation:
Let the missing factor be x.
2 × x = 16
x = 16/2
x = 8
Thus the missing factors is 8.

Question 12.
2 × ___ = 18

Explanation:
Let the missing factor be a.
2 × a = 18
a = 18/2
a = 9
Thus the missing factor is 9.

Question 13.
____ × 3 = 6

Explanation:
Let the missing factor be y.
y × 3 = 6
y = 6/3 = 2
y = 2
Therefore the missing factor is 2.

Question 14.
A pendulum swings once every 2 seconds. How long will it take for the pendulum to swing 4 times?

Explanation:
Given,
A pendulum swings once every 2 seconds.
2 × 4 = 8
x = 4/2 = 2

Question 15.
Repeated Reasoning
Complete the multiplication table.

Question 16.
You buy a shirt that costs $7 and a pair of pants that costs 2 times as much. Write a multiplication equation to show the cost of the pants. _____ × _____ = ____ How much money do you spend in all? _____ Answer:$7 × 2 = $14 Explanation: Given, You buy a shirt that costs$7 and a pair of pants that costs 2 times as much.
Multiply the cost of the shirt and the cost of the pants.
7 × 2 = 14

Question 17.
Modeling Real Life
A plumber needs to install handles in 9 sinks. Each sink has a hot water handle and a cold water handle. He has 19 handles. Does he have enough handles?

Explanation:
Given that,
A plumber needs to install handles in 9 sinks.
Each sink has a hot water handle and a cold water handle.
The total number of handles = 19 handles.
9 × 2 = 18
Thus he has enough handles.

Question 18.
Modeling Real Life
You have 6 pairs of chopsticks. Do you have enough chopsticks for 4 people if they each get a pair?

DIG DEEPER!
You want to make wrappers for each pair of chop sticks that you have. You need 2 pieces of paper for each wrapper.How many pieces of paper do you need?

Explanation:
Given that there are 6 pairs of chopsticks.
Each pair has 2 chopsticks.
6 × 2 = 12
You need 2 pieces of paper for each wrapper.
12 × 2 = 24
Thus I need 24 pieces of paper for 12 chopsticks.

Review & Refresh

Compare
Question 19.

923 is greater than 854.

Question 20.

621 is greater than 63.

Question 21.

746 is less than 752.

### Lesson 2.2 Multiply by 5

Explore and Grow

Question 1.
Model 3 × 5 on the number line

3 × 5 = ____

Question 2.
Model 4 × 5 on the number line

4 × 5 = ____

Structure
Compare your models. How are the models the same? How are they different?

Think and Grow: Multiply by 5

Example
Find 8 × 5.
Skip count by 5s eight times.

Explanation:
The count starts from 0.
The counters jump for every 5s.
There are 8 jumps of 5
8 × 5 = 40

Example
Complete the table and the statements.

• Multiples of 5 end in 5s Facts ____ or _____ .
• An odd number times 5 is always an ______ number.
• An even number times 5 is always an ______ number.

Multiples of 5 end in 5s Facts 0 or 5.
• An odd number times 5 is always an odd number.
• An even number times 5 is always an even number.

Show and Grow

Question 1.
Complete the model and the equation.

Explanation:
The count starts from 0.
The counters jump for every 5s.
There are 6 jumps of 5.
6 × 5 = 30

Find the product.
Question 2.
9 × 5 = ____

Explanation:
Multiply the two numbers 9 and 5.
9 × 5 = 45

Question 3.
5 × 4 = _____

Explanation:
Multiply the two numbers 5 and 4.
5 × 4 = 20

Apply and Grow: Practice

Complete the model and the equation
Question 4.

Explanation:
The count starts from 0.
The counters jump for every 5s.
There are 3 jumps of 5.
3 × 5 = 15

Question 5.

Answer: 5 × 2 = 10

Find the product
Question 6.

Explanation:
Multiply the two numbers 4 and 5.
4 × 5 = 20

Question 7.

Explanation:
Multiply the two numbers 5 and 10.
5 × 10 = 20

Question 8.

Explanation:
Multiply the two numbers 8 and 5.
8 × 5 = 40

Question 9.

Explanation:
Multiply the two numbers 9 and 5.
9 × 5 = 45

Question 10.

Explanation:
Multiply the two numbers 6 and 5.
6 × 5 = 30

Question 11.

Explanation:
Multiply the two numbers 5 and 1.
5 × 1 = 5

Question 12.

Explanation:
Multiply the two numbers 5 and 5.
5 × 5 = 25

Question 13.

Explanation:
Multiply the two numbers 5 and 7.
5 × 7 = 35

Find the missing factor.
Question 14.
5 × ____ = 35

Explanation:
Let the missing factor be a.
5 × a = 35
a = 35/5 = 7
a = 7
Thus the missing factor is 7.

Question 15.
____ × 5 = 50

Explanation:
Let the missing factor be x.
x × 5 = 50
x = 50/5
x = 10
Thus the missing factor is 10.

Question 16.
10 = 2 × ____

Explanation:
Let the missing factor be p.
10 = 2 × p
p = 10/2 = 5
p = 5
Thus the missing factor is 5.

Question 17.
Number Sense
Which numbers are multiples of 5? Think: How do you know?

Answer: The multiples of 5 are 50, 20, 5, 85.

Question 18.
DIG DEEPER!
Use each number to complete the Venn diagram

Think and Grow: Modeling Real Life

A summer camp is in session 5 days each week for 8 weeks. Each day,1 camper is chosen to lead the camp song. There are 35 campers. Can each camper lead the camp song?

Multiplication equation:
Each camper ____ lead the camp song.

Explanation:
Given,
A summer camp is in session 5 days each week for 8 weeks. Each day,1 camper is chosen to lead the camp song. There are 35 campers.
5 days – 1 week
? – 8 weeks
8 × 5 = 40 days
There are 35 campers.
Thus Each camper can lead the camp song.

Show and Grow

Question 19.
Your teacher has 5 packs of spinning toys. There are 5 toys in each pack. There are 27 students in your class. Does every student get a spinning toy?

Explanation:
Given,
Your teacher has 5 packs of spinning toys. There are 5 toys in each pack. There are 27 students in your class.
5 × 5 = 25
27 – 25 = 2
Thus 2 students will not get a spinning toy.

Question 20.
You recycle 9 bottles and receive 5¢ for each bottle. You spend 25¢ on a pack of gum. How many cents do you have left?
DIG DEEPER!
How many more bottles do you need to recycle to buy another pack of gum?

Explanation:
You recycle 9 bottles and receive 5¢ for each bottle. You spend 25¢ on a pack of gum.
9 × 5 = ¢45
¢45 – ¢25 = ¢20

### Multiply by 5 Homework & Practice 2.2

Complete the model and the equation.
Question 1.

Answer: 5 × 4 = 20

Explanation:
The count starts from 0.
The count jumps for every 5.
From the figure, we can see there are 4 jumps of 5.
5 × 4 = 20

Question 2.

Answer: 5 × 1 = 5

Find the product
Question 3.

Explanation:
Multiply the two numbers 5 and 3.
5 × 3 = 15

Question 4.

Explanation:
Multiply the two numbers 5 and 10.
5 × 10 = 50

Question 5.

Explanation:
Multiply the two numbers 8 and 5.
8 × 5 = 40

Question 6.

Explanation:
Multiply the two numbers 5 and 2
5 × 2 = 10

Question 7.

Explanation:
Multiply the two numbers 5 and 9.
5 × 9 = 45

Question 8.

Explanation:
Multiply the two numbers 5 and 7.
5 × 7 = 35

Question 9.

Explanation:
Multiply the two numbers 5 and 5.
5 × 5 = 25

Question 10.

Explanation:
Multiply the two numbers 5 and 6.
5 × 6 = 30

Find the missing factor.
Question 11.
5 × ___ = 20

Explanation:
Let the missing factor be t.
5 × t = 20
t = 20/5
t = 4
Thus the missing factor is 4.

Question 12.
45 = 5 × ____

Explanation:
Let the missing factor be a.
45 = 5 × a
a = 45/5
a = 9

Question 13.
____ × 5 = 15

Explanation:
Let the missing factor be x.
x × 5 = 15
x = 15/5
x = 3

Question 14.
There are 8 teams in a basketball tournament. Each team has 5 players. How many players are in the tournament?

Explanation:
Given,
There are 8 teams in a basketball tournament. Each team has 5 players.
8 × 5 = 40
Therefore there are 40 players in the tournament.

Question 15.
Reasoning
Newton has some nickels. He says they have a total value of 14 cents. Explain how you know that Newton is incorrect.
Given,
Newton has some nickels. He says they have a total value of 14 cents.
Convert from cents to nickels.
1 nickel = 5 cents
14 cents = 2.8 nickels

Question 16.
Number Sense
Tell whether the number is a multiple of 2, 5, or both. Explain.
25 & 16
25 is a multiple of 5.
16 is a multiple of 2.

Question 17.
Modeling Real Life
A firefighter visits 5 houses. Each house has 3 smoke detectors that need a new battery.She has 18 batteries. Does every smoke detector get a new battery?
Given,
A firefighter visits 5 houses.
Each house has 3 smoke detectors that need a new battery.
She has 18 batteries.
5 × 3 = 15
18 – 15 = 3
So, every smoke detector gets a new battery.

Question 18.
Modeling Real Life
Descartes earns $5 for each lawn that he mows. He mows 7 lawns. He spends$20 on a video game. How much money does he have left?

DIG DEEPER!
How many more lawns does Descartes have to mow to buy another video game?

Given,
Descartes earns $5 for each lawn that he mows. He mows 7 lawns. 5 × 7 =$35
He spends $20 on a video game.$35 – $20 =$15

Review & Refresh

Question 19.
Count by tens.
____, 20, ____, 40, ____, ____, 70, ____, ____, _____

Answer: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

### Lesson 2.3 Multiply by 10

Question 1.
Explore 6 × 10 on the tape diagram.

6 × 10 = ___

Structure
How can you see the model to find 7 × 10?

10 + 10 + 10 + 10 + 10 + 10 + 10 = 70
7 × 10 = 70

Think and Grow: Multiply by 10

Example
Find 4 × 10.
Model four groups of ten.

Example
Complete the table and the statements

Show and Grow

Question 1.
Complete the model and the equations.

10 + 10 + 10 = 30
3 × 10 = 30

Find the product
Question 2.
8 × 10 = ____
Explanation:
10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 80
Thus 8 × 10 = 80

Question 3.
10 × 5 = ____

Explanation:
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 50
Thus 10 × 5 = 50

Apply and Grow: Practice

Complete the model and the equations.
Question 4.

10 + 10 + 10 + 10 + 10 = 50
5 × 10 = 50

Question 5.

Explanation:
10 + 10 = 20
2 jumps of 10.
2 × 10 = 20

Find the product
Question 6.

Explanation:
Multiply the two numbers 4 and 10.
4 × 10 = 40

Question 7.

Explanation:
Multiply the two numbers 10 and 10.
10 × 10 = 100

Question 8.

Explanation:
Multiply the two numbers 10 and 7
10 × 7 = 70

Question 9.

Explanation:
Multiply the two numbers 9 and 10.
9 × 10 = 90

Question 10.

Explanation:
Multiply the two numbers 6 and 10.
6 × 10 = 60

Question 11.

Explanation:
Multiply the two numbers 2 and 10.
2 × 10 = 20

Question 12.

Explanation:
Multiply the two numbers 10 and 3.
10 × 3 = 30

Question 13.

Explanation:
Multiply the two numbers 10 and 1.
10 × 1 = 10

Tell Whether the product is even or odd.
Question 14.
6 × 2 = ____

Explanation:
6 × 2 = 12
An even number is an integer that can be divided by two and remain an integer or has no remainder.
12 is an even number.

Question 15.
5 × 3 = ___

Explanation:
5 × 3 = 15
An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction.
15 is an odd number.

Question 16.
8 × 10 = _____

Explanation:
8 × 10 = 80
An even number is an integer that can be divided by two and remain an integer or has no remainder.
80 is an even number.

Question 17.
5 × 10 = ____

Explanation:
5 × 10 = 50
An even number is an integer that can be divided by two and remain an integer or has no remainder.
50 is an even number.

Question 18.
10 × 7 = _____

Explanation:
7 × 10 = 70
An even number is an integer that can be divided by two and remain an integer or has no remainder.
70 is an even number.

Question 19.
5 × 7 = ____

Explanation:
5 × 7 = 35
An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction.
35 is an odd number.

Question 20.
There are 10 millimeters in 1 centimeter. The width of a cell phone is 6 centimeters. What is the width of the phone in millimeters?

Explanation:
Given,
There are 10 millimeters in 1 centimeter. The width of a cell phone is 6 centimeters
Convert from centimeters to millimeters.
1 cm = 10 mm
6 cm = 6 × 10mm = 60mm
Thus the width of the phone in millimeters is 60mm.

Question 21.
Patterns
Complete the table using the words even or odd

Think and Grow: Modeling Real Life

Newton has 8 dimes. Descartes has 75¢. Who has more money?
Multiplication equation:

_____ has more money.

Explanation:
Given,
Newton has 8 dimes. Descartes has 75¢.
1 dime =  ¢10
8 dimes = 8 × ¢10 = ¢80
¢80 – ¢75 = ¢5
Thus Newton has more money than Descartes.

Show and Grow

Question 22.
You have 10 nickels. Your friend has 46¢. Who has more money?

Explanation:
Convert from nickels to cents.
1 Nickel = ¢5
10 Nickels = 10 × ¢5 = ¢50
¢50 – ¢46 = ¢4
Thus I have more money.

Question 23.
You have 34 trading cards. You buy 3 packs of cards. Each pack has 10 cards. How many trading cards do you have now?

Explanation:
You have 34 trading cards. You buy 3 packs of cards. Each pack has 10 cards.
1 pack = 10 cards
3 packs = 3 × 10 cards = 30 cards
34 cards + 30 cards = 74 cards

Question 24.
Your teacher has 10 calculators. Each calculator uses 4 batteries. The batteries come in packs of 10. How many packs of batteries does your teacher buy? Explain.

Explanation:
Given,
Your teacher has 10 calculators. Each calculator uses 4 batteries. The batteries come in packs of 10
1 calculator = 4 batteries
10 calculators = 10 × 4 batteries = 40 batteries
Each pack contains 10 batteries
Thus the teacher needs to buy 4 packs of batteries.

### Multiply by 10 Homework & Practice 2.3

Complete the model and the equation
Question 1.

10 + 10 + 10 + 10 + 10 = 50
5 × 10 = 50

Question 2.

10 + 10 + 10 = 30
3 × 10 = 30

Find the product
Question 3.

Explanation:
Multiply the two numbers 10 and 4.
First, multiply 4 with 0
Next multiply 4 with 1
4 × 0 = 0
4 × 1 = 4
10 × 4 = 40

Question 4.

Explanation:
Multiply the two numbers 8 and 10.
8 × 10 = 80

Question 5.

Explanation:
Multiply the two numbers 10 and 10.
10 × 10 = 100

Question 6.

Explanation:
Multiply the two numbers 10 and 2.
10 × 2 = 20

Question 7.

Explanation:
Multiply the two numbers 10 and 9.
10 × 9 = 90

Question 8.

Explanation:
Multiply the two numbers 10 and 7.
10 × 7 = 70

Question 9.

Explanation:
Multiply the two numbers 10 and 1.
10 × 1 = 10

Question 10.

Explanation:
Multiply the two numbers 10 and 5.
10 × 5 = 50

Find the missing factor
Question 11.
10 × ____ = 90

Explanation:
Let the missing factor be r.
10 × r = 90
r = 90/10
r = 9
Thus the missing factor is 9.

Question 12.
60 = 10 × ____

Explanation:
Let the missing factor be s.
60 = 10 × s
s = 60/10
s = 6
Thus the missing factor is 6.

Question 13.
____ × 10 = 70

Explanation:
Let the missing factor be t.
t × 10 = 70
t = 70/10
t = 7
Thus the missing factor is 7.

Question 14.
Structure
You buy a thank-you card for $1. You pay using all dimes. How many dimes do you use? Answer: 10 Explanation: Given, You buy a thank-you card for$1. You pay using all dimes.
Convert from the dollar to dime.
1 dollar = 10 dime
Thus you use 10 dimes.

Question 15.
Number Sense
In bowling, knocking down all 10 pins at once is called a strike. You roll strikes in your first two turns and knock down 4 pins in your third turn. How many pins do you knock down in all?

Explanation:
Given,
In bowling, knocking down all 10 pins at once is called a strike.
You roll strikes in your first two turns and knock down 4 pins in your third turn.
1 turn = 10 pins
2 turns = 20 pins
20 + 4 = 24 pins
10 + 24 = 34 pins

Question 16.
Reasoning
Ten years is called a decade. Your neighbor is 70 years old. For how many decades has he been alive? Explain.

Explanation:
Given,
Ten years is called a decade. Your neighbor is 70 years old.
? = 70 years
70 × 1/10 = 7
Thus he has been alive for 7 decades.

Question 17.
Modeling Real Life
You have 2 dimes. Your friend has a 24¢. Who has more money?
Answer: My friend has more money

Explanation:
Given,
You have 2 dimes. Your friend has 24¢
1 dime = ¢10
2 dimes = 2 × ¢10 = ¢20
¢24 – ¢20 = ¢4

Question 18.
Modeling Real Life
Your teacher has 35 balloons. She buys 4 packs of balloons. Each pack has 10 balloons. How many balloons does she have now?

Explanation:
Given,
She buys 4 packs of balloons.
Each pack has 10 balloons
1 pack = 10 balloons
4 packs = 4 × 10 balloons = 40 balloons
35 + 40 = 75 balloons

Review & Refresh

Find the difference.
Question 19.

4 8 9
-1 8 7
3 0 2

Question 20.

Question 21.

### Lesson 2.4 Multiply by 0 or 1

Explore and Grow

Question 1.
Draw an array to find the products

Question 2.
What pattern do you see?
Answer: We can see the multiplication pattern in the above question.

Repeated Reasoning
How can you see the pattern to find 5 × 0?
5 × 0 = _____
Any number multiplied by 0 is always 0.

Think and Grow: The Multiplication Property of 0 and 1

Multiplication Property of Zero:The product of any number and 0 is 0.
Multiplication Property of One:The product of any number and 1 is that number.
Example
There are 4 groups with 1 counter in each group. How many counters are there in all?

Example
There are 4 groups with 0 counters in each group. How many counters are there in all?

Show and Grow

Write an equation for the model.

Question 1.

Answer: 7 × 0 = 0
There are no counters in the groups. So, the equation for the above figure is 7 × 0 = 0.

Question 2.

Answer: 3 × 1 = 3
There is 1 counter in each group. Thus the equation for the above figure is 3 × 1 = 3

Find the product.
Question 3.
8 × 1 = _____

Explanation:
Multiply 8 by 1.
Any number multiplied by 1 is always itself.
8 × 1 = 8

Question 4.
6 × 0 = _____

Explanation:
Multiply 6 by 0.
Any number multiplied by 0 is always 0.
6 × 0 = 0

Apply and Grow: Practice

Complete the equation for the model.

Question 5

Explanation:
There are 0 counters in the group.
Number of groups = 5
Number of counters = 0
5 × 0 = 0

Question 6.

Explanation:
There are 2 counters.
Number of counters in each group = 1
Number of groups = 2
2 × 1 = 2

Find the product.
Question 7

Explanation:
Multiply 1 by 1
Any number multiplied by 1 is always itself.
1 × 1 = 1

Question 8.

Explanation:
Any number multiplied by 0 is always 0.
2 × 0 =0

Question 9.

Explanation:
Any number multiplied by 0 is always 0.
0 × 0 =0

Question 10.

Explanation:
Any number multiplied by 1 is always itself.
1 × 9 = 9

Find the missing factor.
Question 11.
10 × ____ = 0

Explanation:
Let the missing factor be x
10 × x = 0
x = 0/10
x = 0
Thus the missing factor is 0

Question 12.
____ × 1 = 5

Explanation:
Let the missing factor be y.
y × 1 = 5
y = 5/1
y = 5
Thus the missing factor is 5.

Question 13.
1 × _____ = 8

Explanation:
Let the missing factor be z.
1 × z = 8
z = 8/1
z = 8

Compare.
Question 14.

Explanation:
1 × 4 = 4
6 × 0 = 0
4 is greater than 0.
4 > 0
Thus 1 × 4 > 6 × 0

Question 15.

Explanation:
9 × 0 = 0
7 × 0 =0
0 is equal to 0.
Thus 9 × 0 = 7 × 0

Question 16.

Explanation:
3 × 1 = 3
6 × 1 = 6
3 is less than 6.
3 < 6
Thus 3 × 1 < 6 × 1

Question 17.
Logic
Complete each statement with always, sometimes never.
The product of any number and 0 is ______ 0.
The product of any number and 1 is ________ that number.
The product of any number and 0 is always 0.
The product of any number and 1 is the same that number.

Question 18.
Structure
Use the model to complete the statements. Which two properties are shown?

There are 5 groups of 1 = 1 group of 5
5 × 1 = 1 × 5
5 = 5

Think and Grow: Modeling Real Life

There are 4 performers riding unicycles and 3 performers using balance boards in a talent show.How many wheels are used in the talent show?

Multiplication equations:
There are ______ wheels used in the talent show.

Answer: 4 wheels are used in the talent show.

Show and Grow

Question 19.
A is a performance by 1 person. A is a performance by 2 people. There are 5 students performing solos and 0 students performing duets at a school concert. How many students perform a solo or a duet?

Explanation:
Given,
A is a performance by 1 person. A is a performance by 2 people.
There are 5 students performing solos and 0 students performing duets at a school concert.
5 + 0 = 5
Therefore 5 students performing a solo or duet.

Question 20.
A group of 6 adults and 9 students attend a school concert. What is the total cost for the group?

DIG DEEPER!
How much money would it cost the group to attend the concert if the tickets cost $1 for all ages? Explain. Answer: Given that, A group of 6 adults and 9 students attend a school concert. 1 adult =$1
6 adults = 6 × $1 =$6
There is no ticket price for students.
$6 + 0 =$6
If the ticket price is $1 for all the students. 9 + 6 = 15 15 ×$1 = $15 Thus the ticket price for all the students is$15.

### Multiply by 0 or 1 Homework & Practice 2.4

Complete the equation for the model.
Question 1.

Explanation:
Number of groups = 3
Number of counters in each group = 0
The equation for the model is 3 × 0 = 0

Question 2.

Explanation:
Number of groups = 8
Number of counters in each group = 1
The equation for the model is 8 × 1 = 8

Find the product
Question 3.

Explanation:
Multiply the two numbers 10 and 1.
Any number multiplied by 1 is the same number.
10 × 1 = 10

Question 4.

Explanation:
Multiply the two numbers 6 and 0.
Any number multiplied by 0 is always 0.
6 × 0 = 0

Question 5.

Explanation:
Multiply the two numbers 1 and 7.
Any number multiplied by 1 is the same number.
1 × 7 = 7

Question 6.

Explanation:
Multiply the two numbers 1 and 0.
Any number multiplied by 0 is always 0.
0 × 1 = 0

Find the missing factor
Question 7.
_____ × 4 = 0

Explanation:
Let the missing factor be x
x × 4 = 0
x = 0/4
x = 0
Thus the missing factor is 0

Question 8.
1 × ____ = 2

Explanation:
Let the missing factor be x
1 × x = 2
x = 2/1
x = 2
Thus the missing factor is 2.

Question 9.
9 × ____ = 9

Explanation:
Let the missing factor be x
9 × x = 9
x = 9/9
x = 1
Thus the missing factor is 1.

Compare
Question 10.

Explanation:
Any number multiplied by 0 is always 0.
0 × 9 = 10 × 0

Question 11.

Explanation:
Any number multiplied by 0 is always 0.
Any number multiplied by 1 is the same number.
4 × 1 = 4
8 × 0 = 0
4 > 0
Thus 4 × 1 > 8 × 0

Question 12.

Explanation:
Any number multiplied by 1 is the same number.
6 × 1 = 1 × 6

Question 13.
Logic
Which equation is true?

Answer: All the equations are false.
i. 8 × 0 = 8 + 0
0 = 8 (false)
ii. 3 × 1 = 3 + 1
3 = 4 (false)
iii. 6 + 1 = 6 × 1
7 = 6 (false)
iv. 4 × 1 = 4 × 0
4 = 0 (false)

Question 14.
Writing
How are the problems the same? How are they different?
5 × 1 = 5  5 + 0 = 5
The answers for the problems are same. But the difference is the first equation is multiplication and the second equation is addition.

Question 15.
Modeling Real Life
U.S. presidents can serve two 4-year terms. A president serves the ﬁrst term, but is not reelected. How many years does the president serve?

Explanation:
Given,
U.S. presidents can serve two 4-year terms. A president serves the ﬁrst term, but is not reelected.
2 × 4 = 8
Thus the president serves 8 years.

Question 16.
Modeling Real Life
There are 5 adults and 8 children in a group. What is the total cost for the group to ride the Ferris wheel?

DIG DEEPER!
How much money would it cost the group toride the Ferris wheel if the tickets cost $1 for all ages? Explain. Answer:$13

Explanation:
The ticket price for adult is $1 The ticket price for student is free The total price is 5 ×$1 = $5 The ticket price for an adult is$1
The ticket price for the student is free
Total = 5 + 8 = 13
The total price is 13 × $1 =$13

Review & Refresh

Question 17.
Use the array to fill in the blanks.

3 rows 6 columns
3 × 6 = 18

### Lesson 2.5 Use the Distributive Property

Explore and Grow

Break apart the 4 × 7 array into two smaller arrays. Write an equation for each new array.

Equation: _____
Equation: ____

Structure
Find the sum of your two products. Compare the sum to the total number of objects in the original array. What do you notice?
Equation: 2 × 7
Equation: 2 × 7

Explanation:
By using the distributive property we can find the sum of the two products of the above array.
Distribute 4 to 2 and 2.
4 × 7 = (2 + 2) × 7
= (2 × 7) + (2 × 7)

Think and Grow: Use the Distributive Property with Addition

Show and Grow
Question 1.
Use the Distributive Property to show two different ways to find 2 × 4

In the first figure distribute 4 to 2 and 2.
In the second figure distribute 2 to 1 and 1.

Apply and Grow: Practice

Use the Distributive Property to find the product
Question 2.

Distribute 4 to 2 and 2.
4 × 7 = (2 + 2) × 7
4 × 7 = (2 × 7) + (2 × 7)
4 × 7 = 14 + 14
4 × 7 = 28

Question 3.

Distribute 6 to 3 and 3.
6 × 6 = 6 × (3 + 3)
6 × 6 = (6 × 3) + (6 × 3)
6 × 6 =  18 + 18
6 × 6 = 36

Use the Distributive Property to fill in the blanks.

Question 4.
7 × 4 = 7 × (___ + 2)
= (7 × ___) + (____ × 2)
= ___ + ____
= ____

Explanation:
Distribute 4 to 2 and 2.
7 × 4 = 7 × (2 + 2)
= (7 × 2) + (7 × 2)
= 14 + 14
= 28

Question 5.
3 × 6 = (___ + ___) × 6
= (___ × 6) + (____ × 6)
= ___ + ____
= ____
3 × 6 = (1 + 2) × 6
= (1 × 6) + (2 × 6)
= 6 + 12
= 18

Question 6.
Which one Doesn’t Belong? Which expression cannot be used to find 3 × 7?

Answer: 3 × (7 + 1)

Explanation:
i. 3 × (5 + 2) = 3 × 7
ii. 3 × (7 + 1) = 3 × 8
iii. (2 + 1) × 7 = 3 × 7
iv. (1 + 2) × 7 = 3 × 7
The second expression does not belong to 3 × 7.

Question 7.
Writing
Explain how you can use the Distributive Property to find 5 × 12.
Given expression 5 × 12
First, distribute 12 to 6 and 6.
5 × 12 = 5 × (6 + 6)
5 × 12 = (5 × 6) + (5 × 6)
5 × 12 = 30 + 30
5 × 12 = 60

Think and Grow: Modeling Real Life

A scooter rental center has 6 rows of scooters. There are 9 scooters in each row. Can 50 people each rent a scooter at the same time?
Multiplication expression:
Distributive Property:
50 people _______ each rent a scooter at the same time.

Answer: 50 people can each rent a scooter at the same time.

Explanation:
Given,
A scooter rental center has 6 rows of scooters. There are 9 scooters in each row.
6 × 9 = (3 + 3) × 9
6 × 9 = (3 × 9) + (3 × 9)
6 × 9 = 27 + 27
6 × 9 = 54
54 – 50 = 4
Thus 50 people can each rent a scooter at the same time.

Show and Grow

Question 8.
A roller-coaster train has 9 rows of seats. There are 4 seats in each row. Can a group of 38 students ride the roller coaster at the same time?

Given,
A roller-coaster train has 9 rows of seats. There are 4 seats in each row.
We can find the product by using the distributive property.
9 × 4 = 9 × (2 + 2)
9 × 4 = (9 × 2) + (9 × 2)
9 × 4 = 18 + 18
9 × 4 = 36
We have to find whether a group of 38 students ride the roller coaster at the same time.
36 – 38 = -2
Thus a group of 38 students cannot ride the roller coaster at the same time.

Question 9.
DIG DEEPER!
A joke book has 20 pages. There are 5 jokes on each page. You read 16 jokes. How many jokes do you have left to read?
Given that,
A joke book has 20 pages.
There are 5 jokes on each page.
Total jokes = 20 × 5 = 100 jokes
100 – 16 = 84 jokes
∴ 84 jokes are left to read.

### Use the Distributive Property Homework & Practice 2.5

Use the Distributive Property to find the product
Question 1.

Distribute 4 to 2 and 2.
4 × 4 = 4 × (2 + 2)
4 × 4 = (4 × 2) + (4 × 2)
4 × 4 = 8 + 8
4 × 4 = 16

Question 2.

Distribute 3 to 1 and 2.
3 × 9 = (1 + 2) × 9
3 × 9 = (1 × 9) + (2 × 9)
3 × 9 = 9 + 18
3 × 9 = 27

Use the Distributive Property to fill in the blanks.
Question 3.
8 × 6 = ___ × (5 + ____)
= (8 × 5) + (____ × ____)
= ___ + ___
= ____
8 × 6 = 8 × (5 + 1)
= (8 × 5) + (8 × 1)
= 40 + 8
= 48

Question 4.
7 × 7 = 7 × (5 + ____)
= (____ × 5) + (7 × ____)
= ____ + ____
= ____
7 × 7 = 7 × (5 + 2)
= (7 × 5) + (7 × 2)
= 35 + 14
= 49

Question 5.
Structure
Which ways can you break apart the array?

(7 × 5) + (7 × 1)
(5 × 6) + (2 + 6)

Explanation:
Distribute 6 to 5 and 1.
7 × 6 = 7 × (5 + 1)
7 × 6 = (7 × 5) + (7 × 1)
7 × 6 = 35 + 7
7 × 6 = 42
Distribute 7 to 5 and 2.
7 × 6 = (5 + 2) × 6
7 × 6 = (5 × 6) + (2 + 6)
7 × 6 = 30 + 12
7 × 6 = 42

Question 6.
Logic
Your friend breaks apart an array into a 4 × 5 array and 4 × 2 array.Draw a picture to show the original array.

Question 7.
DIG DEEPER!
Is the equation true? Does it demonstrate the Distributive Property? Explain.?

The above equation is true.
4 × 8 = (4 × 5) + (4 × 2) + (4 × 1)
4 × 8 = 20 + 8 + 4
4 × 8 = 32

Question 8.
Modeling Real Life
Newton sleeps 9 hours each night. How many hours does he sleep in 1 week?

Given,
Newton sleeps 9 hours each night.
1 week = 7 days
9 × 7 = 63 hours
Thus Newton sleeps 63 hours in 1 week.

Question 9.
Modeling Real Life
There are 3 lanes of cars sitting at a red light. Each lane has 6 cars in it. How many cars are sitting at the red light?
Given that,
There are 3 lanes of cars sitting at a red light. Each lane has 6 cars in it.
3 × 6 = 3 × (3 + 3)
3 × 6 = 3 × 3 + 3 × 3
3 × 6 = 9 + 9
3 × 6 = 18
Thus 18 cars are sitting at the red light.

Review & Refresh

Question 10.
Some kids are at an arcade. Seventeen of them leave. There are 39 left. How many kids were at the arcade to start?
Given,
Some kids are at an arcade. Seventeen of them leave. There are 39 left.
39 + 17 = 56

### Lesson 2.6 Problem Solving: Multiplication

Explore and Grow

Use any strategy to solve
You, Newton, and Descartes each have 4 marbles. How many marbles are there in all?

Given that,
You, Newton, and Descartes each have 4 marbles
3 × 4 = 12 marbles
Thus there are 12 marbles in all.

Repeated Reasoning
Explain to your partner how you solved the problem.
Given that,
Each person has 4 marbles
1 = 4 marbles
3 = 4 × 3 = 12 marbles
By this, we can say that there are 12 marbles in all.

Think and Grow: Using the Problem-Solving PlanHow

Example
A bookshelf has 5 shelves. There are 8 comic books on each shelf. You take 3 of them to read. How many comic books are left on the shelves?

Understand the Problem

What do you know?
• There are ______ shelves.
• There are _____ comic books on each shelf.
• You take _____ comic books to read.

• There are 5 shelves.
• There are 8 comic books on each shelf.
• You take 3 comic books to read.

What do you need to ﬁnd?
• You need to find how many _____ are left on the shelves after you take _____ of them.

Answer: • You need to find how many comic books are left on the shelves after you take 3 of them.

Make a Plan

How will you solve?
• Multiply _____ by ______ to find how many ______ are on the shelves.
• Then subtract ______ from the product.

• Multiply the number of shelves by the numbers of books on each shelf to find how many ______ are on the shelves.
• Then subtract the number of books read from the product.

Solve

There are ______ comic books left on the shelves.

5 × 8 = 40
40 – 3 = 37
There are 37 comic books left on the shelves

Show and Grow

Question 1.
A photo album has 10 pages. Each page holds 6 photos. You put 52 photos in the album. How many more photos can you put in the album?

Given,
A photo album has 10 pages. Each page holds 6 photos.
You put 52 photos in the album.
10 × 6 = 60 photos
60 – 52 = 8 photos
Thus you can put 8 more photos in the album.

Apply and Grow: Practice

Question 2.
Your classroom has 5 groups of desks with 5 desks in each group. There are 22 students in your class. What information do you know that would help you find how many empty desks there are?

Given,
Your classroom has 5 groups of desks with 5 desks in each group.
5 × 5 = 25 desks
There are 22 students in your class.
25 – 22 = 3
Thus there are 3 empty desks in the classroom.

Question 3.
You buy 2 boxes of cherry gelatin, 4 boxes of strawberry gelatin, and 3 boxes of orange gelatin. Each box contains 2 packets of gelatin. How many packets of gelatin do you buy?
Given,
You buy 2 boxes of cherry gelatin, 4 boxes of strawberry gelatin, and 3 boxes of orange gelatin. Each box contains 2 packets of gelatin.
1 box – 2 packets of gelatin
2 box – 4 packets of gelatin
4 boxes – 4 × 2 = 8 packets of gelatin
3 boxes – 3 × 2 = 6 packets of gelatin
4 + 8 + 6 = 18 packets of gelatin.
Therefore you can buy 18 packets of gelatin.

Question 4.
A pack of gum has 5 pieces. You have 3 packs of gum and give4 friends each 1 piece. How many pieces of gum do you have left?

Given,
A pack of gum has 5 pieces. You have 3 packs of gum.
Total number of packs = 5 × 3 = 15 pieces
and give4 friends each 1 piece.
15 – 4 = 11 pieces
Thus 11 pieces of gum have left.

Think and Grow: Modeling Real Life

Descartes has four $10 bills, seven$5 bills, and one $2 bill. How much money does he have in all? Understand the problem: Make a plan: Solve: Descartes has$ _____.

Given,
Descartes has four $10 bills, seven$5 bills, and one $2 bill. 4 ×$10 = $40 7 ×$5 = $35 1 ×$2 = $2$40 + $35 +$2 = $72 Show and Grow Question 5. A teacher has 10 boxes of dry-erase markers. Five boxes have4 markers each, 2 boxes have 8 markers each, and 3 boxes have10 markers each. How many dry-erase markers does the teacher have in all? Answer: Given, A teacher has 10 boxes of dry-erase markers. Five boxes have4 markers each, 2 boxes have8 markers each, and 3 boxes have10 markers each. 5 boxes – 4 markers 2 boxes – 8 markers 3 boxes – 10 markers Add all the markers in all 10 boxes. 4 + 8 + 10 = 22 markers Therefore the teacher has 22 markers in all. Question 6. DIG DEEPER! You sell candles as a fundraiser. You earn$2 for each small candle you sell, $5 for each medium candle, and$10 for each large candle. You pay $8 to have the candles shipped. How much money do you raise? Answer: Given, You sell candles as a fundraiser. You earn$2 for each small candle you sell, $5 for each medium candle, and$10 for each large candle. You pay $8 to have the candles shipped. 7 ×$2 = $14 9 ×$5 = $45 6 ×$10 = 60
$119 –$8 = $111 ### Problem Solving: Multiplication Homework & Practice 2.6 Question 1. You buy 2 books and 3 magazines. Each book costs$8 and each magazine costs $2. How much money do you spend in all? Answer: Given, You buy 2 books and 3 magazines. Each book costs$8 and each magazine costs $2. 1 book –$8
2 books – 2 × $8 =$16
1 magazine – $2 3 magazines – 3 ×$2 = $6$16 + $6 =$22
Thus you spend $22 in all. Question 2. In a game, teams earn 10 points for each correct answer and lose 5 points for each incorrect answer. Your team answers 7 questions correctly and 3 questions incorrectly. How many points does your team have? Answer: Given, In a game, teams earn 10 points for each correct answer and lose 5 points for each incorrect answer. Your team answers 7 questions correctly and 3 questions incorrectly. 1 – 10 points 7 – 10 × 7 = 70 points 1 wrong answer – 5 points 3 – 5 × 3 = 15 points 70 – 15 = 55 points Question 3. An origami cube requires 3 pieces of orange paper, 2 pieces of yellow paper, and 1 piece of blue paper. You make 5 cubes. How many pieces of paper do you need? Answer: Given, An origami cube requires 3 pieces of orange paper, 2 pieces of yellow paper, and 1 piece of blue paper. You make 5 cubes. Each cube needs 3 + 2 + 1 = 6 pieces of paper. 5 cubes – 6 × 5 = 30 pieces of papers Thus you need 30 pieces of paper to make 5 cubes. Question 4. Writing Write and solve your own word problem that involves multiplication. Answer: To make a cuboid you need 3 pieces of yellow paper, 3 pieces of pink paper. You need to make 7 cuboids. How many pieces of paper are required to make 7 cuboids? Each cuboid needs 3 + 3 = 6 pieces of paper. 7 × 6 = 42 pieces of paper Thus you need 42 pieces of paper to make 7 cuboids. Question 5. Modeling Real Life A group of students orders 6 small, 5 medium, and 3 large smoothies. The students pay with ﬁve$10 bills. How much change do they receive?

Given,
A group of students orders 6 small, 5 medium, and 3 large smoothies.
The students pay with ﬁve $10 bills. 1 small –$2
6 small – 6 × $2 =$12
1 Medium – $4 5 medium – 5 ×$4 = $20 1 large –$5
3 large – 3 × $5 =$15
12 + 20 + 15 = $47$50 – $47 =$3
Thus the students receive $3 change. Review & Refresh Question 6. Answer: 6 2 7 Question 7. Answer: 9 2 2 Question 8. Answer: 7 5 0 ### Multiplication Facts and Strategies Performance Task Question 1. Three students make a model of our solar system. a. Student A buys foam spheres to make the Sun and the planets. He pays with a$10 bill. What is his change?

Given,
Student A buys foam spheres to make the Sun and the planets.
$10 –$1 = $9 Thus the change is$9
b. Student B buys wooden rods to attach each planet to the sun. She pays with two $5 bills. What is her change? Answer: Given, Student B buys a wooden rod for each planet and sun. Cost of the wooden rod is$1
9 planets and 1 sun
9 × 1 + 1 × 1 = 9 + 1 = $10 Thus the change for student B is 0. c.Student C spends$13 on 3 paintbrushes and some bottles of paint. How many bottles of paint does Student C buy?

Cost of 1 paintbrush = $1 3 paintbrushes cost = 3 ×$1 = $3 Cost of bottle of paint =$2
For $10 you get 5 bottles of paint. Thus Student C buys 5 bottles of paint. d. What is the total cost of the project? If the 3 students divide the cost equally, how much would they each spend? Answer: The total cost of the project =$1 + $13 +$10 = $24$24/3 = $8 ### Multiplication Facts and Strategies Activity Three in a Row: Multiplication Directions: 1. Players take turns. 2. On your turn, spin both spinners. Multiply the two numbers and cover the product. 3.The first player to get three counters in a row, horizontally, vertically, or diagonally, wins! Answer: Game A: 10 × 1, 2 × 2, 1 × 2 2 × 3, 5 × 1, 10 × 2 2 × 4, 10 × 5, 0 × 3 Game B: 1 × 3, 10 × 4, 10 × 5 1 × 1, 0 × 4, 10 × 3 5 × 3, 5 × 5, 10 × 1 ### Multiplication Facts and Strategies Chapter Practice 2.1 Multiply by 2 Find the Product Question 1. Answer: 14 Explanation: Multiply the number by 2. 7 × 2 = 14 Question 2. Answer: 6 Explanation: Multiply the number by 2. Multiply the two numbers 3 and 2. 3 × 2 = 6 Question 3. Answer: 4 Explanation: Multiply the number by 2. Multiply the two numbers 2 and 2. 2 × 2 = 4 Question 4. Answer: 18 Explanation: Multiply the number by 2. Multiply the two numbers 2 and 9. 2 × 9 = 18 Find the missing factor. Question 5. 2 × ___ = 2 Answer: 1 Explanation: Let the missing factor be x. 2 × x = 2 x = 2/2 = 1 x = 1 Thus the missing is 1. Question 6. 2 × ___ = 20 Answer: 10 Explanation: Let the missing factor be x. 2 × x = 20 x = 20/2 = 10 x = 10 Thus the missing factor is 10. Question 7. ____ × 4 = 8 Answer: 2 Explanation: Let the missing factor be b. b × 4 = 8 b = 8/4 b = 2 Thus the missing factor is 2. 2.2 Multiply by 5 Question 8. Answer: 15 Explanation: Multiply the number by 5. 5 × 3 = 15 Question 9. Answer: 50 Explanation: Multiply the number by 5. 5 × 10 = 50 Question 10. Answer: 40 Explanation: Multiply the number by 5. 8 × 5 = 40 Question 11. Answer: 10 Explanation: Multiply the number by 5. 5 × 2 = 10 Question 12. Number Sense Lightning strikes our planet 6 times every second. How many lightning strikes occur in 5 seconds? Answer: 30 seconds Explanation: Given, Lightning strikes our planet 6 times every second. Lightning strikes for 5 seconds is 6 × 5 = 30 seconds 2.3 Multiply by 10 Find the product Question 13. Answer: 80 Explanation: Multiply the product by 10. 10 × 8 = 80 Question 14. Answer: 100 Explanation: Multiply the product by 10. 10 × 10 = 100 Question 15. Answer: 40 Explanation: Multiply the product by 10. 10 × 4 = 40 Question 16. Answer: 70 Explanation: Multiply the product by 10. 10 × 7 = 70 2.4 Multiply by 0 and 1 Find the product Question 17. Answer: 6 Explanation: Any number multiplied by 1 will be the same number. 1 × 6 = 6 Question 18. Answer: 0 Explanation: Any number multiplied by 0 will be always 0. 0 × 3 = 0 Question 19. Answer: 0 Explanation: Any number multiplied by 0 will be always 0. 1 × 0 = 0 Question 20. Answer: 4 Explanation: Any number multiplied by 1 will be the same number. 4 × 1 = 4 Compare Question 21. Answer: = Explanation: Any number multiplied by 0 will be always 0. 0 × 10 = 0 9 × 0 = 0 0 = 0 Thus 0 × 10 = 9 × 0 Question 22. Answer: > Explanation: Any number multiplied by 0 will be always 0. Any number multiplied by 1 will be the same number. 2 × 1 = 2 5 × 0 = 0 2 > 0 Thus 2 × 1 > 5 × 0 Question 23. Answer: < Explanation: Any number multiplied by 1 will be the same number. 7 × 1 = 7 1 × 8 = 8 7 < 8 Thus 7 × 1 < 1 × 8 2.5 Use the Distributive Property Use the Distributive Property to fill in the blanks. Question 24. 7 × 3 = (____ + 2) × 3 = (____ × 3) + (2 × ____) = ____ + ____ = ____ Answer: 7 × 3 = (5 + 2) × 3 = (5 × 3) + (2 × 3) = 15 + 6 = 21 Question 25. 6 × 6 = 6 × (___ + ____) = (6 × ____) + (6 × ____) = ____ + ____ = ____ Answer: 6 × 6 = 6 × (3 + 3) = (6 × 3) + (6 × 3) = 18 + 18 = 36 2.5 Problem Solving: Multiplication Question 26. You place your trading card collection into an album that has 5 pages. You put 9 cards on each page. Some of the cards are the same, so you give 3 cards to a friend. How many trading cards do you have left? Answer: 30 Explanation: Given, You place your trading card collection into an album that has 5 pages. You put 9 cards on each page. Some of the cards are the same, so you give 3 cards to a friend. 9 × 5 = 45 cards If 3 cards are the same, then 5 × 3 = 15 45 – 15 = 30 Thus 30 trading cards are left. Question 27. Modeling Real Life In a game, you start with ten$1 bills, five $5 bills, and two$10 bills. How much money do you start with in all?
Answer: $55 Explanation: In a game, you start with ten$1 bills, five $5 bills, and two$10 bills.
10 $1 bills = 10 ×$1 = $10 5$5 bills = 5 × $5 =$25
2 $10 bills = 2 ×$10 = $20 10 + 25 + 20 =$55