# 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.

- The distance between the cities is 60 miles and the driver has driven \(\frac13\) of the way.
- How many miles has she driven?
- How many miles remain?

- She has driven \(\frac25\) of the way.
- How many miles has she driven?
- How many miles remain?

- The distance between the cities is 300 miles and she has driven \(\frac16\) of the way.
- How many miles has she driven?
- How many miles remain?

- 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!

- Explain why each pair of expressions is equal.
- \((1 - \frac15) \boldcdot 20\) and \(\frac45 \boldcdot 20\)
- \(24 - \frac13 \boldcdot 24\) and \(24(1 - \frac13)\)
- \(64 - \frac14 \boldcdot 64\) and \(\frac34 \boldcdot 64\)

- 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