# Lesson 10

The Distributive Property, Part 2

### Problem 1

Here is a rectangle.

1. Explain why the area of the large rectangle is $$2a + 3a + 4a$$.
2. Explain why the area of the large rectangle is $$(2+3+4)a$$.

### Solution

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### Problem 2

Is the area of the shaded rectangle $$6(2-m)$$ or $$6(m-2)$$?

Explain how you know.

### Solution

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### Problem 3

Choose the expressions that do not represent the total area of the rectangle. Select all that apply.

A:

$$5t + 4t$$

B:

$$t + 5 + 4$$

C:

$$9t$$

D:

$$4 \boldcdot 5 \boldcdot t$$

E:

$$t(5+4)$$

### Solution

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### Problem 4

Evaluate each expression mentally.

1. $$35\boldcdot 91-35\boldcdot 89$$
2. $$22\boldcdot 87+22\boldcdot 13$$
3. $$\frac{9}{11}\boldcdot \frac{7}{10}-\frac{9}{11}\boldcdot \frac{3}{10}$$

### Solution

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(From Unit 6, Lesson 9.)

### Problem 5

Select all the expressions that are equivalent to $$4b$$.

A:

$$b+b+b+b$$

B:

$$b+4$$

C:

$$2b+2b$$

D:

$$b \boldcdot b \boldcdot b \boldcdot b$$

E:

$$b \div \frac{1}{4}$$

### Solution

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(From Unit 6, Lesson 8.)

### Problem 6

Solve each equation. Show your reasoning.

$$111=14a$$

$$13.65 = b + 4.88$$

$$c+ \frac{1}{3} = 5\frac{1}{8}$$

$$\frac{2}{5} d = \frac{17}{4}$$

$$5.16 = 4e$$

### Solution

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(From Unit 6, Lesson 4.)

### Problem 7

Andre ran $$5\frac{1}{2}$$ laps of a track in 8 minutes at a constant speed. It took Andre $$x$$ minutes to run each lap. Select all the equations that represent this situation.

A:

$$\left(5\frac{1}{2}\right)x = 8$$

B:

$$5 \frac{1}{2} + x = 8$$

C:

$$5 \frac{1}{2} - x = 8$$

D:

$$5 \frac{1}{2} \div x = 8$$

E:

$$x = 8 \div \left(5\frac{1}{2}\right)$$

F:

$$x = \left(5\frac{1}{2}\right) \div 8$$

### Solution

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(From Unit 6, Lesson 2.)