## Envision Math 6th Grade Textbook Answer Key Topic 2.4 The Distributive Property

**The Distributive Property**

How can you use the Distributive Property to evaluate expressions?

Answer:

The Distributive Property states that multiplying a sum (or difference) by a number gives the same result as multiplying each number in the sum

(or difference) by the number and adding (or subtracting) the products.

**Guided Practice**

**Do you know HOW?**

In 1 through 4, find each missing number.

Question 1.

8(7 + 23) = 8(7) + 8(☐)

Answer:

23

Explanation:

Question 2.

4(28) = 4(20) + 4 (☐)

Answer:

8

Explanation:

Question 3.

8(57) – 8(7) = 8(☐)

Answer:

50

Explanation:

Question 4.

5(26 – 3) = 5 (☐) – 5(3)

Answer:

26

Explanation:

Use mental math to evaluate 5 and 6.

Question 5.

6(32) = ☐

Answer:

192

Explanation:

Question 6.

20(5) – 20(2) = ☐

Answer:

60

Explanation:

**Do you UNDERSTAND?**

Question 7.

Why is it easier to evaluate 7 × 60 than to evaluate 7 × 55 + 7 × 5?

Answer:

See margin.

Explanation:

Question 8.

Tony read 22 pages in the morning and 28 pages in the afternoon for 5 days. Lois read 47 pages each day for 5 days. Explain howto use the Distributive Property to find how many pages each of them read.

Answer:

See margin.

Explanation:

**Independent Practice**

Leveled Practice In 9 through 16, find each missing number.

Question 9.

3(28) + (3)2 = ☐ (30)

Answer:

3

Explanation:

Question 10.

9(23) = 9(☐) + 9(3)

Answer:

20

Explanation:

Question 11.

6(46) – 6(6) = 6(☐)

Answer:

40

Explanation:

Question 12.

4(33) = 4(30) + 4(☐)

Answer:

3

Explanation:

Question 13.

30(22 – 10) = 30(22) – 30(☐)

Answer:

10

Explanation:

Question 14.

8(99) = 8(100) – 8(☐)

Answer:

1

Explanation:

Question 15.

20(33 – 5) = 20(☐)

Answer:

28

Explanation:

= 20(☐) + 20(8)

Answer:

20

Explanation:

Question 16.

5(42) + 5(5) = 5(☐)

Answer:

47

Explanation:

= 5(☐) + 5(7)

Answer:

40

Explanation:

Use the Distributive Property to break apart a number to find the product for 5 × 27.

5 × 27 ← Break 27 apart.

5(20) +5 (7) ← Multiply each addend.

100 + 35 ← Add.

135

5 × 27 = 135

Use the Distributive Property to join numbers together to find 8(32) – 8(2).

8(32) – 8(2)

8(32 — 2) ← Join factors.

8(30) ← Subtract.

240 ← Multiply.

8(32) – 8(2) = 240

**Independent Practice**

Use the Distributive Property and mental math to evaluate.

Tips: When doing mental math, choose to join or break apart based on which is easier.

Question 17.

7(29)

Answer:

203

Explanation:

Question 18.

6(21) + 6(31)

Answer:

312

Explanation:

Question 19.

5(22) + 5(8)

Answer:

150

Explanation:

Question 20.

8(47)

Answer:

376

Explanation:

Question 21.

6(41) + 6(9)

Answer:

300

Explanation:

Question 22.

30(3) + 30(5)

Answer:

240

Explanation:

Question 23.

3(21) – 3(11)

Answer:

30

Explanation:

Question 24.

5(25 – 3)

Answer:

110

Explanation:

**Problem Solving**

Question 25.

**Writing to Explain** The 6th graders ordered lunch from the Big Group Menu.They ordered 22 organic chilis and 8 veggie plates.Their order can be expressed as 6(22) + 6(8). Explain what mental math steps you would use to find the total cost of the order.

Answer:

See margin.

Question 26.

Using the Big Group Menu, write and solve a problem where you can use the Distributive Property.

Answer:

See margin.

Question 27.

**Writing to Explain** Jamal said that 9.45 is greater than 9.8 because 45 is greater than 8. Is he correct? Explain.

Answer:

No; sample answer: 0.8 = 0.80 and 80 > 45.

Explanation:

Question 28.

Hiroko put money in a savings account each week. After 9 weeks, there was $49.50 in the account. If Hiroko put the same amount in each week, how much did she save each week?

Answer:

$5.50

Explanation:

Question 29.

**Think About the Process** Which choice shows a problem with common factors that could be used for mental math?

A. 3(45) + 3(5)

B. 4(18) – 7(8)

C. 2(22) + 3(33)

D. 8(39) + 4(40)

Answer:

A. 3(45) + 3(5)