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