What You'll Learn
To compare answers to a survey, as in Example 1
You know that the ratios and are equal, since each ratio simplifies to .
You can write the equation = .
Ais an equation stating that two ratios are equal.
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.
Writing Ratios in Simplest Form
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?
Since both ratios are equal to , 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.
Finding a Common Multiplier
Determine whether the ratios in each pair can form a proportion by finding a common multiplier.
Interactivity Proportions and common multipliers