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.
- \(\text-22 + 5\)
- \(\text-22 -(\text-5)\)
- \((\text-22) (\text-5)\)
- \(\text-22 \div 5\)
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
- 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?
Solution
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(From Unit 4, Lesson 3.)