# Lesson 13

Expressions with Rational Numbers

Let’s develop our signed number sense.

### Problem 1

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

\(x\)

\(1-x\)

\(x-1\)

\(\text-1\div x\)

### 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 \(\frac {\text{-}3}{4}\).

### Problem 3

Find the value of each expression.

- \(\text-22 + 5\)
- \(\text-22 -(\text-5)\)
- \((\text-22) (\text-5)\)
- \(\text-22 \div 5\)

### 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?

### 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.

### Problem 6

- 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?
- 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?