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McGraw-Hill Math Grade 7 Answer Key Lesson 4.2 Commutative and Associative Properties
Exercises Identify The Property
Question 1.
7 × 4 × 3 = 4 × 3 × 7
Answer:
The expression 7 × 4 × 3 = 4 × 3 × 7 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the factors are multiplied in any order without changing the product.
7 × 4 × 3 = 84
4 × 3 × 7 = 84
Question 2.
2 + 9 + 22 = 22 + 9 + 2
Answer:
The expression 2 + 9 + 22 = 22 + 9 + 2 is commutative property of addition.
Explanation:
The commutative property of addition states that the addends are added in any order without changing the sum.
2 + 9 + 22 = 33
22 + 9 + 2 = 33
Question 3.
3 × 4 × 4 × 2 = 3 × (4 × 4) × 2
Answer:
The expression 3 × 4 × 4 × 2 = 3 × (4 × 4) × 2 is Associative property of Multiplication.
Explanation:
The Associative property of multiplication states that the factors are grouped in any way without changing the product.
3 × 4 × 4 × 2 = 96
3 × (4 × 4) × 2 = 96
Question 4.
4 × 2 × 3 × 4 = 2 × 3 × 4 × 4
Answer:
The expression 4 × 2 × 3 × 4 = 2 × 3 × 4 × 4 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the factors are multiplied in any order without changing the product.
4 × 2 × 3 × 4 = 96
2 × 3 × 4 × 4 = 96
Question 5.
9 × 2 × 4 = 2 × 4 × 9
Answer:
The expression 9 × 2 × 4 = 2 × 4 × 9 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the factors are multiplied in any order without changing the product.
9 × 2 × 4 = 72
2 × 4 × 9 = 72
Question 6.
9 × 7 × 9 × 9 = (9 × 7) × (9 × 9)
Answer:
The expression 9 × 7 × 9 × 9 = (9 × 7) × (9 × 9) is Associative property of Multiplication.
Explanation:
The Associative property of multiplication states that the factors are grouped in any way without changing the product.
9 × 7 × 9 × 9 = 5,103
(9 × 7) × (9 × 9) = 63 x 81 = 5,103
Question 7.
9 + 7 + 1 = 7 + 9 + 1
Answer:
The expression 9 + 7 + 1 = 7 + 9 + 1 is commutative property of addition.
Explanation:
The commutative property of addition states that the addends are added in any order without changing the sum.
9 + 7 + 1 = 17
7 + 9 + 1 = 17
Question 8.
4 × 11 × 9 × 4 = 4 × 4 × 9 × 11
Answer:
The expression 4 × 11 × 9 × 4 = 4 × 4 × 9 × 11 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the factors are multiplied in any order without changing the product.
4 × 11 × 9 × 4 = 1,584
4 × 4 × 9 × 11 = 1,584Â
Question 9.
2 + 8 + 6 + 4 = (2 + 8) + (6 + 4)
Answer:
The expression 2 + 8 + 6 + 4 = (2 + 8) + (6 + 4) is Associative property of addition.
Explanation:
The Associative property of addition states that the addends are grouped in any way without changing the sum.
2 + 8 + 6 + 4 = 20
(2 + 8) + (6 + 4) = 10 + 10 = 20
Question 10.
6 × 4 × 2 = 4 × 2 × 6
Answer:
The expression 6 × 4 × 2 = 4 × 2 × 6 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the factors are multiplied in any order without changing the product.
6 × 4 × 2 = 48
4 × 2 × 6 = 48
Question 11.
22 + 21 + 24 + 22 = 22 + (21 + 24) + 22
Answer:
The expression 22 + 21 + 24 + 22 = 22 + (21 + 24) + 22 is Associative property of addition.
Explanation:
The Associative property of addition states that the addends are grouped in any way without changing the sum.
22 + 21 + 24 + 22 = 89
22 + (21 + 24) + 22 = 22 + 45 + 22 = 89
Question 12.
6 × 8 + 6 × 0 = 8 × 6 + 0 × 6
Answer:
The expression 6 × 8 + 6 × 0 = 8 × 6 + 0 × 6 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the factors are multiplied in any order without changing the product.
6 × 8 + 6 × 0 = 48 + 0 = 48
8 × 6 + 0 × 6 = 48 + 0 = 48