All the solutions provided in **McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 8 Multiplication Properties** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 6 Lesson 8 Multiplication Properties

**Math in My World**

**Example 1**

A coach had 16 players in each of 2 groups. Each player scored 5 goals. Find the total number of goals scored.

Find (16 × 2) × 5.

Since you can easily multiply 2 and 5, change the way the numbers are grouped.

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

It is easier to find 2 × 5 than 16 × 2. You can group the numbers differently to find 2 × 5 first.

So, the total number of goals scored is _____________.

Answer:

160 goals.

Explanation:

A coach had 16 players in each of 2 groups = 16 x 2 = 32

Each player scored 5 goals.

The total number of goals scored = 32 x 5 = 160 goals.

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

**Example 2**

Find the unknown in the equation

35.5 × __________ = 17 × 35.5.

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

So, the unknown is ___________.

Answer:

17

Explanation:

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

35.5 × 17 = 17 × 35.5

603.5 = 603.5

So, the unknown is 7

**Example 3**

Find the unknown in the equation 17 × __________ = 17.

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

So, the unknown is __________.

Answer:

Unknown number is 1.

Explanation:

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

17 x 1 = 17

So, the unknown is 1.

**Guided Practice**

Draw lines to match the multiplication property used in each equation.

Answer:

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

**Talk Math**

Explain how you could use mental math and multiplication properties to find (5.5 × 50) × 2.

Answer:

550

Explanation:

The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.

(5.5 × 50) × 2 = 5.5 x (50 x 2)

275 x 2 = 5.5 x 100

550 = 550

**Independent Practice**

**Use properties of multiplication to find each product mentally. Show your steps and identify the properties that you used.**

Question 4.

(5.1 × 2) × 50 = ____________

Answer:

510

Explanation:

The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.

(5.1 x 2) x 50 = 5.1 x (50 x 2)

10.2 x 50 = 5.1 x 100

510 = 510

(5.1 × 2) × 50 = 510 or 5.1 x (50 x 2) = 510.

Question 5.

4 × (2.5 × 6) = ____________

Answer:

60

Explanation:

The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.

4 x (2.5 x 6) = (4 x 6) x 2.5

4 x 15 = 24 x 2.5

60 = 60

4 x (2.5 x 6) = 60 or (4 x 6) x 2.5 = 60.

Question 6.

(9.8 × 500) × 2 = ____________

Answer:

9,800

Explanation:

The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.

(9.8 x 500) x 2 = 9.8 x (2 x 500)

4900 x 2 = 9.8 x 1000

9800 = 9800

(9.8 x 500) x 2 = 9800 or 9.8 x (2 x 500) = 9800

Question 7.

(1.4 × 50) × 20 = ____________

Answer:

1400

Explanation:

The above multiplication applies the Associative Property of Multiplication which states that the way in which factors are grouped does not change the product.

(1.4 x 50) x 20 = 1.4 x ( 20 x 50)

7 x 50 = 1.4 x 1000

1400 = 1400

(1.4 × 50) × 20 = 1400 or 1.4 x ( 20 x 50) = 1400

**Mathematical PRACTICE** Use Algebra Find the unknown in each equation. Circle which property you used.

Question 8.

19.5 × = 19.5

= ____________

Commutative Property

Associative Property

Identity Property

Answer:

Explanation:

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

19.5 x 1 = 19.5

Question 9.

34 × 65 = 65 ×

= _____________

Commutative Property

Associative Property

Identity Property

Answer:

Explanation:

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

34 x 65 = 65 x 34

Question 10.

2.1 × = 4.3 × 2.1

= _____________

Commutative Property

Associative Property

Identity Property

Answer:

Explanation:

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

2.1 x 4.3 = 4.3 x 2.1

Question 11.

(17 × 2) × 5 = 17 × ( × 5)

= ______________

Commutative Property

Associative Property

Identity Property

Answer:

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

(17 × 2) × 5 = 17 × (2 × 5)

**Problem Solving**

Question 12.

Elijah and 2 of his friends are each paid $20 per afternoon for stuffing envelopes. If they work 5 afternoons, what is the total amount of their earnings?

Answer:

$300

Explanation:

Elijah and 2 of his friends are each paid $20 per afternoon for stuffing envelopes.

3 x $20 = $60

If they work 5 afternoons.

The total amount of their earnings,

(3 x 20) x 5

$60 x 5 = $300

Associative property is applied.

Question 13.

Replace the in (8.7 × ) × 5 with a number greater than 10 so that the product is easy to find mentally. Explain.

Answer:

20

Explanation:

20 is greater then 10.

So, that the product is easy to find mentally.

8.7 x 20 x 5

8.7 x (20 x 5) = 8.7 x 100 = 870

Question 14.

**Mathematical PRACTICE** Draw a Conclusion Each juice box contains 6.4 ounces. Each value pack of juice holds 10 juice boxes. If you have fifty value packs, how many ounces of juice do you have?

Answer:

3,200 ounces.

Explanation:

Each juice box contains 6.4 ounces.

Each value pack of juice holds 10 juice boxes.

6.4 x 10 = 64 ounces.

If you have fifty value packs,

50 x 64 = 3200 ounces.

**HOT Problems**

Question 15.

**Mathematical PRACTICE** Use Number Sense Which two properties can you use to find (3.4 × 4) × (25 × 1) mentally? Explain. Remember that the parentheses tell you which factors to multiply first.

Answer:

Associative Property and Identity Property.

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

(3.4 × 4) × (25 × 1)

13.6 x 25 = 340

Question 16.

**Building on the Essential Question** How do the multiplication properties help me to find products mentally?

Answer:

When two numbers are multiplied we get a product.

When the places of numbers are interchanged, their product remains the same,

i.e., 3 × 5 = 5 × 3 = 15.

The different types of properties are,

Commutative Property.

Associative Property.

Identity Property.

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

### McGraw Hill My Math Grade 5 Chapter 6 Lesson 8 My Homework Answer Key

**Practice**

**Use properties of multiplication to find each product mentally. Show your steps and identify the properties that you used.**

Question 1.

(1.6 × 2) × 5 = ____________

Answer:

16

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

(1.6 × 2) × 5

3.2 x 5 = 16

Question 2.

(27 × 2.5) × 4 = _____________

Answer:

270

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

(27 × 2.5) × 4

67.5 x 4 = 270

**Algebra Find each unknown.**

Question 3.

× 5.5 = 5.5

= ______________

Answer:

1

Explanation:

x × 5.5 = 5.5

x = 5.5 ÷ 5.5

x = 1

The Identity Property of Multiplication states that the product of any factor and 1 equals the factor.

Question 4.

49 × 201 = × 49

= ______________

Answer:

201

Explanation:

49 x 201 = x × 49

x = (49 x 201) ÷ 49

x = 201

The Commutative Property of Multiplication shows that the order in which factors are multiplied does not change the product.

**Problem Solving**

Question 5.

For a party, Shandra and James each bought 5 packages of hot dog buns that each cost $1.50. How much did the hot dog buns cost altogether?

Answer:

$7.5

Explanation:

Shandra and James each bought 5 packages of hot dog buns.

Each cost $1.50.

Total cost of hot dog buns, 5 x $1.50 = $7.5

Question 6.

Eva needs to find: (6 × 1.5) × 2. Give the product and name the property she could use.

Answer:

18

Associative Property.

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

(6 × 1.5) × 2

6 x 1.5 = 9

9 x 2 = 18

Question 7.

Write a multiplication sentence to show how the Associative Property can help you solve a problem mentally. Explain.

Answer:

(17 × 2) × 5 = 17 × (2 × 5)

The associative property of multiplication helps us to multiply numbers faster.

Instead of multiplying a list of numbers in the order in which they’re written,

group them differently to multiply in an order according to the convenient.

Explanation:

(17 × 2) × 5 = 17 × (2 × 5)

34 x 5 = 17 x 10

170 = 170

Question 8.

**Mathematical PRACTICE** Reason Without calculating, is the equation (1.8 × 3) × 2.1 = 3 × (1.8 × 2.1) true or false? Explain your reasoning.

Answer:

True.

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

(1.8 × 3) × 2.1 = 3 × (1.8 × 2.1)

5.4 x 2.1 = 3 x 3.78

11.34 = 11.34

**Test Practice**

Question 9.

Which multiplication property is shown in the equation below?

3.1 × (2 × 9) = (3.1 × 2) × 9

(A) Identity Property

(B) Commutative Property

(C) Zero Property

(D) Associative Property

Answer:

Option(D)

Explanation:

The Associative Property of Multiplication states that the way in which factors are grouped does not change the product.

3.1 × (2 × 9) = (3.1 × 2) × 9

3.1 x 18 = 6.2 x 9

55.8 = 55.8