Practice questions available in **McGraw Hill Math Grade 6 Answer Key PDF** **Lesson 16.2 Commutative and Associative Properties **will engage students and is a great way of informal assessment.

## McGraw-Hill Math Grade 6 Answer Key Lesson 16.2 Commutative and Associative Properties

**Exercises**

**IDENTIFY THE PROPERTY
**Question 1.

3 × 4 × 2 = 2 × 4 × 3

Answer:

3 × 4 × 2 = 2 × 4 × 3 = 24.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

3 × 4 × 2 = 2 × 4 × 3

= 8 × 3

= 24.

Question 2.

1 + 9 + 22 = 22 + 9 + 1

Answer:

1 + 9 + 22 = 22 + 9 + 1 = 32.

Commutative property.

Explanation:

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

1 + 9 + 22 = 22 + 9 + 1

= 31 + 1

= 32.

Question 3.

2 + 3 + 3 + 2 = 2 + (3 + 3) + 2

Answer:

2 + 3 + 3 + 2 = 2 + (3 + 3) + 2 = 10.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

2 + 3 + 3 + 2 = 2 + (3 + 3) + 2

= 2 + 6 + 2

= 8 + 2

= 10.

Question 4.

4 × 2 + 2 × 3 = 2 × 4 + 3 × 2

Answer:

4 × 2 + 2 × 3 = 2 × 4 + 3 × 2 = 14.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

4 × 2 + 2 × 3 = 2 × 4 + 3 × 2

= 8 + 6

= 14.

Question 5.

7 × 2 × 7 = 7 × (2 × 7)

Answer:

7 × 2 × 7 = 7 × (2 × 7) = 98.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

7 × 2 × 7 = 7 × (2 × 7)

= 7 × 14

= 98.

Question 6.

7 × 7 × 8 × 7 = 8 × 7 × 7 × 7

Answer:

7 × 7 × 8 × 7 = 8 × 7 × 7 × 7 = 2,744.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

7 × 7 × 8 × 7 = 8 × 7 × 7 × 7

= 56 × 49

= 2,744.

Question 7.

(9 + 7) + 6 = 9 + (7 + 6)

Answer:

(9 + 7) + 6 = 9 + (7 + 6) = 22.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

(9 + 7) + 6 = 9 + (7 + 6)

= 9 + 13

= 22.

Question 8.

4 × 5 × 5 × 4 = 5 × 5 × 4 × 4

Answer:

4 × 5 × 5 × 4 = 5 × 5 × 4 × 4 = 400.

Commutative property.

Explanation:

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

4 × 5 × 5 × 4 = 5 × 5 × 4 × 4

= 25 × 16

= 400.

Question 9.

2 + 6 + 8 + 3 = 6 + 3 + 8 + 2

Answer:

2 + 6 + 8 + 3 = 6 + 3 + 8 + 2 = 19.

Commutative property.

Explanation:

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

2 + 6 + 8 + 3 = 6 + 3 + 8 + 2

= 9 + 8 + 2

= 17 + 2

= 19.

Question 10.

(6 × 4) × 2 = 6 × (4 × 2)

Answer:

(6 × 4) × 2 = 6 × (4 × 2) = 48.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

(6 × 4) × 2 = 6 × (4 × 2)

= 6 × 8

= 48.

Question 11.

12 + 13 + 13 + 12 = 12 + 12 + 13 + 13

Answer:

12 + 13 + 13 + 12 = 12 + 12 + 13 + 13 = 50.

Commutative property.

Explanation:

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.

12 + 13 + 13 + 12 = 12 + 12 + 13 + 13

= 24 + 13 + 13

= 37 + 13

= 50.

Question 12.

7 × 8 + 8 × 7 = 8 × 7 + 8 × 7

Answer:

7 × 8 + 8 × 7 = 8 × 7 + 8 × 7 = 112.

Associative property.

Explanation:

The associative property, in Math, states that while adding or multiplying numbers, the way in which numbers are grouped by brackets (parentheses), does not affect their sum or product.

7 × 8 + 8 × 7 = 8 × 7 + 8 × 7

= 56 + 56

= 112.