Lesson 18

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.

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

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?

(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.
  1. Label each point with its coordinates.
  2. Plot a point that is 3 units from point \(K\). Label it \(P\).
  3. Plot a point that is 2 units from point \(M\). Label it \(W\).
(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.

  1. What was the retail price of the mattress, before the discount?
  2. What was the wholesale price, before the markup?
(From Unit 6, Lesson 8.)