All the solutions provided in **McGraw Hill Math Grade 4 Answer Key PDF Chapter 3 Lesson 5 Multiplication Properties and Division Rules** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 3 Lesson 5 Multiplication Properties and Division Rules

**Math in My World**

Example 1

The table shows Jenny’s and Cliff’s chores. Jenny earns $3 for each chore and Cliff earns $2 for each chore. How much does each person earn for completing chores?

Complete each number sentence.

So, each person earns ___. The order in which the factors are multiplied does not change the product.

Answer:

Given that,

Jenny has 2 chore.

Cliff has 3 chore.

Jenny earns $3 for each chore.

Cliff earns $2 for each chore.

So, each person earns $6.

It is commutative property of multiplication.

Example 2

There are 9 party favors and 9 guests. How many party favors will each guest get?

Complete the number sentence.

A nonzero number divided by the same number is 1.

So, each guest will get ____ party favor.

Answer:

Given that,

There are 9 party favors and 9 guests.

It is multiplicative identity.

So, each guest will get 1 party favor.

**Talk Math**

Explain why the Identity Property of Multiplication uses 1 while the Identity Property of Addition uses 0.

Answer:

The addition is the process of adding one number to another number. It is 2 + 0 = 2.

The multiplication is the process any number multiplied by 1 then you get same number.

It is 2 x 1 = 2.

**Guided Practice**

**Identify the property or rule shown by each equation.**

Question 1.

12 × 0 = 0

Answer:

Any number is multiplying by 0 then you get the product is 0 is the Zero property.

12 x 0 = 0.

So, It is the Zero property of multiplication.

Question 2.

8 × 5 = 5 × 8

Answer:

The order in which the factors are multiplied does not change the product is called commutative property of multiplication.

8 × 5 = 40.

5 × 8 = 40.

Therefore 8 × 5 = 5 × 8.

It is Commutative property of multiplication.

**Independent Practice**

**Identify the property or rule shown by each equation.**

Question 3.

6 ÷ 1 = 6

Answer:

6 divided by 1 equal to 6.

6 ÷ 1 = 6.

It is ones in division rule.

Any number divided by 1 equal to the itself is called ones in division.

Question 4.

10 ÷ 10 = 1

Answer:

10 divided 10 equal to 1.

10 ÷ 10 = 1.

A nonzero number divided by the same number is 1.

It is multiplicative identity.

Question 5.

8 × 0 = 0

Answer:

Multiplication of 8 with 0 then you get 0.

8 x 0 = 0.

Any number multiplying with 0 then you get 0.

It is a zero property of multiplication.

Question 6.

0 ÷ 12 = 0

Answer:

0 divided by 12 equal to 0.

0 ÷ 12 = 0.

It is Zero divided by any number rule.

The 0 dividing by any number gives 0.

Question 7.

22 × 1 = 22

Answer:

Multiplication of 22 with 1 then you get 22.

22 x 1 = 22.

Any number divided by 1 then the product is 1 is called the identity property of multiplication.

It is the identity property of multiplication.

Question 8.

4 × 3 = 3 × 4

Answer:

Multiplication of 4 with 3 then you get 12.

4 x 3 = 12,

Multiplication of 3 with 4 then you get 12.

3 x 4 = 12.

It is a commutative property of multiplication.

**Algebra Find each unknown number. Identify the property or rule.**

Question 9.

3 ÷ = 1

= ____

Answer:

3 divided by 3 equal to 1.

3 ÷ 3 = 1.

It is multiplicative identity.

It is any number divided by itself then the product is 1.

Question 10.

× 8 = 8 × 4

= ___

Answer:

Multiplication of 4 with 8 then you get 32.

Multiplication f 8 with 4 then you get 32.

4 x 8 = 32.

8 x 4 = 32.

It is commutative property of multiplication.

Question 11.

÷ 11 = 0

= ___

Answer:

0 divided by 11 equal to 0.

0 ÷ 11 = 0.

It is Zero divided by any number rule.

The 0 dividing by any number gives 0.

Question 12.

× 1 = 15

= ____

Answer:

Multiplication of 15 with 1 then you get 15.

15 x 1 = 15.

It is the identity property of multiplication.

**Problem Solving**

Question 13.

On a hiking trip, Tamika and Bryan hiked 7 miles a day. They hiked for 5 days. Kurt and Sade hiked 5 miles a day. How many days did it take Kurt and Sade to hike the same distance as Tamika and Bryan? Write a number sentence to solve.

Answer:

Given that,

Tamika and Bryan hiked 7 miles a day. They hiked for 5 days.

It is 7 x 5 = 35.

Tamika and Bryan hiked 35 miles in 5 days.

Kurt and Sade hiked 5 miles a day.

If the Kurt and Sade hike for 7 days.

It is 5 x 7 = 35.

Therefore Kurt and Sade hiked for 7 days to same distance has Tamika and Bryan.

Question 14.

There are 6 shelves in the library that each have 8 books displayed. How many books are on all of the shelves? Use the Commutative Property to write the multiplication sentence in two ways. Then solve.

Answer:

Given that,

There are 6 shelves in the library that each have 8 books displayed.

It is 6 x 8 = 48.

Therefore the number of books in all is 48.

The another way is 8 x 6 = 48.

Question 15.

**Mathematical PRACTICE 7 Identify Structure** Explain why it is helpful to understand the Identity Property of Multiplication.

Answer:

Identity Property of Multiplication is any number multiplied by 1 then the product is it self.

Identity Property of Multiplication is used in mathematics to solve the missing numbers of variables.

**HOT Problems**

Question 16.

**Mathematical PRACTICE 1 Make a Plan** Write a multiplication problem that uses the Commutative Property of Multiplication to solve.

Answer:

Ravi has 4 packs of flowers with 3 flowers in each pack. He has 3 leaves of birds with 4 leaves in each pack. Write two multiplication sentences to show how many flowers and leaves are there.

The number of flowers are 4 x 3 = 12.

The number of leaves are 3 x 4 = 12.

Therefore 4 x 3 = 3 x 4.

It is a commutative property of multiplication.

Question 17.

**? Building on the Essential Question** How do multiplication properties and division rules help you to multiply and divide?

Answer:

The division is the inverse of multiplication. so, the rules of both the division and multiplication are same. so, multiplication properties and division rules help you to multiply and divide.

### McGraw Hill My Math Grade 4 Chapter 3 Lesson 5 My Homework Answer Key

**Practice**

**Identify the property or rule shown by each equation.**

Question 1.

9 ÷ 1 = 9

Answer:

9 divided by 1 equal to 9.

9 ÷ 1 = 9.

It is ones in division rule.

Any number divided by 1 equal to the itself is called ones in division.

Question 2.

33 × 1 = 33

Answer:

33 x 1 = 33.

Here the 33 is multiplying with 1 then you get the number 33.

It is the identity property of multiplication.

**Problem Solving**

**Complete each number sentence. Identify the property or rule.**

Question 3.

5 ÷ ___ = 5

Answer:

5 divided by 1 equal to 5.

5 ÷ 1 = 5.

It is ones in division rule.

Any number divided by 1 equal to the itself is called ones in division.

Question 4.

9 × 8 = 8 × ____

Answer:

Multiplication of 9 with 8 then you get 72.

Multiplication of 8 with 9 equal to 72.

9 x 8 = 72.

8 x 9 = 72.

Therefore 9 x 8 = 8 x 9.

It is commutative property of multiplication.

Question 5.

___ ÷ 12 = 0

Answer:

0 divided by 12 equal to 0.

0 ÷ 12 = 0.

It is Zero divided by any number.

The 0 dividing by any number gives 0.

Question 6.

**Mathematical PRACTICE 7 Identify Structure** Dennis has 3 packs of pens with 2 pens in each pack. He has 2 packs of pencils with 3 pencils in each pack. Write two multiplication sentences to show how many pens and pencils he has.

Answer:

Given that,

Dennis has 3 packs of pens with 2 pens in each pack.

It is 3 x 2 = 6.

He has 2 packs of pencils with 3 pencils in each pack.

It is 2 x 3 = 6.

Therefore the the pencils and pes are equal it is 6.

It is commutative property of multiplication.

**Vocabulary Check**

**Write a number sentence for each rule or property.**

Question 7.

Ones in Division ______

Answer:

It means any number divided by 1 equal to the itself is called ones in division.

Question 8.

Commutative Property of Multiplication ______

Answer:

The order in which the factors are multiplied does not change the product is called commutative property of multiplication.

Question 9.

Zeros in Division ________

Answer:

It is Zero divided by any number.

The 0 dividing by any number gives 0.

Question 10.

Zero Property of Multiplication

_______________

Answer:

Any number is multiplying by 0 then you get the product is 0 is called the Zero property.

Question 11.

Identity Property of Multiplication

_______________

Answer:

If any number multiplying with 1 it gives the same number itself is called identity property of multiplication.

**Test Practice**

Question 12.

The Zero Property of Multiplication tells you that 25 × 0 is equal to what number?

A. 0

B. 1

C. 7

D. 25

Answer:

The Zero Property of Multiplication tells you that 25 × 0 is equal to 0.

Option A is the correct answer.