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section 5-4
 

Proportions

 

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What You'll Learn

  1. To test if ratios can form a proportion
  2. To use cross products

… And Why

To compare answers to a survey, as in Example 1


Testing Ratios

You know that the ratios 6 over 8 and 9 over 12 are equal, since each ratio simplifies to 3 over 4.

You can write the equation 6 over 8 = 9 over 12.

Key ConceptsProportion

A proportion is an equation stating that two ratios are equal.

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You can test a pair of ratios to determine whether they can form a proportion. One method of testing ratios is to write both ratios in simplest form and see if they are equal.

Example 1 Writing Ratios in Simplest Form Real-World logo

SurveysThere are 24 students in class A and 60 students in class B. Ten students in class A saw a movie this weekend. Twenty-five students in class B saw a movie this weekend. For each class, look at the ratio of the number of students who saw a movie to the total number of students. Can the ratios form a proportion?

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Since both ratios are equal to 5 over 12, the ratios are proportional.



Another way to show that two ratios can form a proportion is to show that a common multiplier connects their numerators and denominators.

Example 2 Finding a Common Multiplier

Determine whether the ratios in each pair can form a proportion by finding a common multiplier.

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Interactivity icon Interactivity Proportions and common multipliers

Course 2 iText

Page

Chapter 5
Ratios, Rates, and Proportions