# Spectrum Math Grade 7 Chapter 2 Lesson 7 Answer Key Multiplying and Dividing Using Mathematical Properties

This handy Spectrum Math Grade 7 Answer Key Chapter 2 Lesson 2.7 Multiplying and Dividing Using Mathematical Properties provides detailed answers for the workbook questions.

## Spectrum Math Grade 7 Chapter 2 Lesson 2.7 Multiplying and Dividing Using Mathematical Properties Answers Key

Commutative Property: The order in which numbers are multiplied does not change the product.
a × b = b × a
Associative Property: The grouping of factors does not change the product.
a × (b × c) = (a × b) × c
Identity Property: The product of a factor and 1 is the factor.
a × 1 = a
Properties of Zero: The product of a factor and 0 is 0. The quotient of the dividend 0 and any divisor is 0.
a × 0 = 0 a × 0 ÷ a = 0

Write the name of the property shown by each equation.

Question 1.
a. 3 × (2 × r) = (3 × 2) × r
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3 × (2 × r) = (3 × 2) × r =  Associative Property
According to the associative principle of multiplication, when multiplying three integers, the outcome will always be the same regardless of how the numbers are grouped. If there are three numbers, x, y and z, the associative property of multiplication implies that x × (y × z) = (x × y) × z

b. 15 × 1 = 15
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15 × 1 = 15 = Identity Property
According to the identity property of multiplication, if a number is multiplied by 1 (one), the result will be the original number. This property is applied when numbers are multiplied by 1. If there is a number, x then the identity property implies that x × 1 = x.

Question 2.
a. 12 × p = p × 12
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12 × p = p × 12 = Commutative Property
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product. If there are two numbers, x and y, the commutative property of multiplication implies that x × y = y × x.

b. 35 × 0 = 0
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35 × 0 = 0 = Properties of Zero
According to the zero property of multiplication, if a number is multiplied by 0 (zero), the result will be zero. This property is applied when numbers are multiplied by 0. If there is a number, x then the identity property implies that x × 0 = 0.

Question 3.
a. 0 ÷ 76 = 0
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0 ÷ 76 = 0 = Properties of Zero
According to the zero property of division, if 0(zero) is divided by any other number, the result will be zero. If there is a number, x then the zero property of division implies that 0 ÷ x = 0.

b. (8 × 9) × 12 = 8 × (9 × 12)
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(8 × 9) × 12 = 8 × (9 × 12)  = Associative Property
According to the associative principle of multiplication, when multiplying three integers, the outcome will always be the same regardless of how the numbers are grouped. If there are three numbers, x, y and z, the associative property of multiplication implies that x × (y × z) = (x × y) × z.

Rewrite each expression using the property indicated.

Question 4.
a. commutative: 15 × z
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15 × z = z × 15
The above expression is the example for commutative property
According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product. If there are two numbers, x and y, the commutative property of multiplication implies that x × y = y × x.

b. zero: 16 × 0
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16 × 0 = 0
The above expression is the example for zero property.
According to the zero property of multiplication, if a number is multiplied by 0 (zero), the result will be zero. This property is applied when numbers are multiplied by 0. If there is a number, x then the identity property implies that x × 0 = 0.

Question 5.
a. identity: 12a × 1

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12a × 1 = 12a
The above expression is the example for identity property.
According to the identity property of multiplication, if a number is multiplied by 1 (one), the result will be the original number. This property is applied when numbers are multiplied by 1. If there is a number, x then the identity property implies that x × 1 = x.

b. associative: 14 × (3 × p)
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Answer: (14 × 3) × p
14 × (3 × p) = (14 × 3) × p
The above expression is the example for associative property.
According to the associative principle of multiplication, when multiplying three integers, the outcome will always be the same regardless of how the numbers are grouped. If there are three numbers, x, y and z, the associative property of multiplication implies that x × (y × z) = (x × y) × z.

Question 6.
a. zero: 0 ÷ 68
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