# Spectrum Math Grade 7 Chapter 2 Lesson 1 Answer Key Multiplying and the Distributive Property

This handy Spectrum Math Grade 7 Answer Key Chapter 2 Lesson 2.1 Multiplying and the Distributive Property provides detailed answers for the workbook questions.

## Spectrum Math Grade 7 Chapter 2 Lesson 2.1 Multiplying and the Distributive Property Answers Key

The distributive property combines multiplication with addition or subtraction. The property states:
a × (b + c) = (a × b) + [a × c)
a × (b – c) = (a × b) – (a × c)

3 × (6 + 4) = (3 × 6) + (3 × 4)
3 × (10) = (18) + (12)
30 = 30

Rewrite each expression using the distributive property.

Question 1.
a. (a × 4) + (a × 3) = ____
Answer: a ×  (4 + 3 )
(a × 4 ) + (a × 3) = a × ( 4 + 3)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. ___ × (6 + 12) = ____
Answer: (a × 6)  + (a × 12)
a × (6 + 12) = (a × 6)  + (a × 12)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 2.
a. 4 × (a + b) = ______
Answer: (4 × a ) + (4 × b)
4 × (a + b) = (4 × a) + (4 × b)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. (3 × a) + (3 × b) = _____
Answer: 3 × (a + b )
(3 × a) + (3 × b) = 3 × (a + b)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 3.
a. (d × 5) – (d × 2) = ____
Answer: d × ( 5 – 2)
(d × 5) – (d × 2) = d × (5 – 2) = d × 3
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. 5 × (8 + p) = _____
Answer: (5 × 8) + (5 × p)
= 40 + (5 × p)
5 × (8 + p) = (5 × 8 ) + (5 × p) = 40 + (5 × p)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 4.
a. d × (8 – h) = ____
Answer: (d × 8) – (d × h)
d × (8 – h) = (d × 8) – (d × h)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. 12 × (s – 10) = ____
Answer: (12 × s) – (12 × 10)
= (12 × s ) – 120
12 × (s – 10) = (12 × s) – (12 × 10) = (12 × s ) – 120
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 5.
a. r × (16 + s) = ____
Answer: (r × 16) + (r × s)
r × (16 + s) = (r  × 16) + (r × s)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. (35 × t) + (35 × y) = _____
Answer: 35 × (t + y)
(35 × t) + (35 × y) = 35 × (t + y)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 6.
a. (8 × a) + (b × 8) = _____
Answer: 8 ×( a + b)
(8 × a) + (b × 8) = 8 × (a + b)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. r × (q – s) = _____
Answer: (r × q) – (r × s)
r × (q – s) = (r × q) – (r × s)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 7.
a. (6 × 12) – (w × 6) = ____
Answer: 6 × (12 – w)
(6 × 12 ) – (w × 6) = 6 × (12 – w)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. p × (15 + z) = _____
Answer: (p × 15) + (p × z)
p × (15 + z) = (p × 15) + (p × z)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 8.
a. 15 × (y + 0) = ____
Answer: (15 × y) + (15 × 0)
= (15 × y ) + 0
= (15 × y)
15 × (y + 0) = (15 × y) + (15 × 0) = (15 × y)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. (d × d) + (d × b) = ____
Answer: d × (d + b)
(d × d) + (d × b ) = d × (d  + b)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 9.
a. (a × 2) + (a × 3) + (a × 4) = ____
Answer: a × (2 + 3 + 4)
(a × 2) + (a × 3) + (a × 4) = a × (2+ 3 + 4)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. p × (a + b + 4) = ____
Answer: (p × a) + (p × b) + (p × 4)
p × (a + b + 4) = (p × a) + (p × b) + (p × 4)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Question 10.
a. (a × b) + (a × c) – (a × d) = ____
Answer: a × (b + c – d)
(a × b) + (a × c) – (a × d) = a × (b + c – d)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

b. 8 × (a + b + c) = ____
Answer: (8 × a) + (8 × b) + (8 × c)
8 × (a + b + c) = (8 × a) + (8 × b) + (8 × c)
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.