# Lesson 13

Expressions with Rational Numbers

### Problem 1

The value of $$x$$ is $$\frac {\text{-}1}{4}$$. Order these expressions from least to greatest:

$$x$$

$$1-x$$

$$x-1$$

$$\text-1\div x$$

### Solution

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### Problem 2

Here are four expressions that have the value $$\frac {\text{-}1}{2}$$:

$$\frac {\text{-}1}{4} + \left(\frac {\text{-}1}{4}\right)$$

$$\frac12 - 1$$

$$\text-2 \boldcdot \frac14$$

$$\text-1 \div 2$$

Write five expressions: a sum, a difference, a product, a quotient, and one that involves at least two operations that have the value $$\frac {\text{-}3}{4}$$.

### Solution

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### Problem 3

Find the value of each expression.

1. $$\text-22 + 5$$
2. $$\text-22 -(\text-5)$$
3. $$(\text-22) (\text-5)$$
4. $$\text-22 \div 5$$

### Solution

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### Problem 4

The price of an ice cream cone is $3.25, but it costs$3.51 with tax. What is the sales tax rate?

### Solution

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(From Unit 4, Lesson 10.)

### Problem 5

Two students are both working on the same problem: A box of laundry soap has 25% more soap in its new box. The new box holds 2 kg. How much soap did the old box hold?

• Here is how Jada set up her double number line.
• Here is how Lin set up her double number line.

Do you agree with either of them? Explain or show your reasoning.

### Solution

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(From Unit 4, Lesson 7.)

### Problem 6

1. A coffee maker’s directions say to use 2 tablespoons of ground coffee for every 6 ounces of water. How much coffee should you use for 33 ounces of water?
2. A runner is running a 10 km race. It takes her 17.5 minutes to reach the 2.5 km mark. At that rate, how long will it take her to run the whole race?

### Solution

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(From Unit 4, Lesson 3.)