# Lesson 4

Working with Fractions

• Let’s write equivalent expressions.

### 4.1: Math Talk: Subtracting from 1

Evaluate mentally:

$$1 - \frac12$$

$$1 - \frac{1}{10}$$

$$1-\frac{3}{10}$$

$$1-\frac{5}{17}$$

### 4.2: Partway There

Suppose a driver is traveling from one city to another. A diagram is provided to help with the first question. Create additional diagrams as needed. Be prepared to explain your reasoning.

1. The distance between the cities is 60 miles and the driver has driven $$\frac13$$ of the way.
1. How many miles has she driven?
2. How many miles remain?
2. She has driven $$\frac25$$ of the way.
1. How many miles has she driven?
2. How many miles remain?
3. The distance between the cities is 300 miles and she has driven $$\frac16$$ of the way.
1. How many miles has she driven?
2. How many miles remain?
4. A trip is $$x$$ miles long, and the driver has gone $$\frac14$$ of the way. Write an expression to represent how many miles remain in her trip.

### 4.3: Distribute and Subtract and Multiply!

1. Explain why each pair of expressions is equal.
1. $$(1 - \frac15) \boldcdot 20$$ and $$\frac45 \boldcdot 20$$
2. $$24 - \frac13 \boldcdot 24$$ and $$24(1 - \frac13)$$
3. $$64 - \frac14 \boldcdot 64$$ and $$\frac34 \boldcdot 64$$
2. Match each expression in List A with an equal expression in List B.

List A

$$\frac14 \boldcdot 80$$

$$\frac34 \boldcdot 80$$

$$80 \left(1 - \frac{5}{8}\right)$$

$$80 - \frac18 \boldcdot 80$$

$$\frac{3}{10} \boldcdot 80$$

$$\frac{7}{10} \boldcdot 80$$

$$80\left(\frac14\right)^2$$

$$80\left(\frac12\right)^3$$

$$80 \left(\frac34\right)^0$$

List B

$$80 - \frac58 \boldcdot 80$$

20

$$80 \boldcdot \left(\frac{1}{16}\right)$$

$$\left(1 - \frac14\right) \boldcdot 80$$

56

70

80

$$\left(1-\frac{7}{10}\right) \boldcdot 80$$

10