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.