section 5-5

Using Proportional Reasoning


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What You'll Learn

  1. To use unit rates to solve proportions
  2. To solve proportions involving variables

… And Why

To calculate a cost, as in Example 1

Solving Proportions Using Unit Rates

Reading Math

Sometimes mi/gal is written as mpg.

Suppose you know that your car gets 29 mi/gal and you have 10 gal of gas. You estimate that you can go 29 • 10, or 290, miles before you run out of gas. You are using a unit rate and multiplying.

You can use unit rates to solve a proportion. First find the unit rate. Then multiply to solve the problem.

Example 1 Using Unit Rates

Image of six oranges with price tag that reads 6 for $2.34.ShoppingUse the information at the right to find the cost in dollars of 8 oranges.

Solve the proportion 2.34 dollars over 6 oranges = x dollars over 8 oranges

  1. Find the unit price.

2.34 dollars over 6 oranges

Start with 2.34 dollars over 6 oranges. Divide to find the unit price, so that 2.34 dollars divided by 6 oranges is equal to 39 cents per orange.

  1. You know the cost of one orange. Multiply to find the cost of 8 oranges.

Multiply the unit rate by the number of oranges, so that 39 cents times 8 = 3 dollars and 12 cents.

The cost of 8 oranges is $3.12.

Course 2 iText


Chapter 5
Ratios, Rates, and Proportions