Lesson 18
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 6, Lesson 7.)Problem 5
Here are 4 points on a coordinate plane.
![Coordinate plane, origin O, x and y axes marked by ones. Point K is three left, 3 up. Point X is 3 right, 2 up. Point M is 5 left, 4 down. Point Y is 2 right, 3 down.](https://cms-im.s3.amazonaws.com/geMRWSrPnp1WVBK777TC4zkZ?response-content-disposition=inline%3B%20filename%3D%226-6.7.new.PP.image.10.png%22%3B%20filename%2A%3DUTF-8%27%276-6.7.new.PP.image.10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T110140Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0901253580edb39a167f5cd4b09a4ef7ac6ef9527273dba595ca14293a6996a6)
- Label each point with its coordinates.
- Plot a point that is 3 units from point \(K\). Label it \(P\).
- Plot a point that is 2 units from point \(M\). Label it \(W\).
Solution
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(From Unit 7, Lesson 13.)Problem 6
A furniture store pays a wholesale price for a mattress. Then, the store marks up the retail price to 150% of the wholesale price. Later, they put the mattress on sale for 50% off of the retail price. A customer just bought the mattress on sale and paid $1,200.
- What was the retail price of the mattress, before the discount?
- What was the wholesale price, before the markup?
Solution
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(From Unit 6, Lesson 8.)