Solving Proportions

Have you ever played dominoes? In the standard set of dominoes,
7 out of 28 tiles, or one-fourth of the tiles, are doubles.

The ratios \(\frac{7}{28}\) and \(\frac{1}{4}\) are equivalent.
That is \(\frac{7}{28}\) = \(\frac{1}{4}\).
The equation \(\frac{7}{28}\) = \(\frac{1}{4}\) is an example of a proportion.

A proportion is an equation that shows that two ratios are equivalent.
One way to determine whether two ratios form a proportion is to find their If the cross products of two ratios are equal, then the ratios form a proportion. In the proportion shown, notice that the cross products, 6 x 3 and 9 x 2, are equal.
Use cross products to determine whether each pair of ratios forms a proportion. \(\frac{6}{15}\) , \(\frac{4}{10}\) ;
\(\frac{12}{20}\) , \(\frac{9}{18}\)

If one value in a proportion is unknown, you can use cross products to solve the proportion.
Solve the proportion: \(\frac{12}{30}\) = \(\frac{x}{10}\)

Explain, in your own words, the meaning of proportion.
Tell how you can determine whether two ratios form a proportion.
Use pattern blocks to build a proportion. Draw a picture of your model and explain why the two ratios are proportional.

  • If a room contains 42 people who are married and 30 people who are single, what is the ratio of married people to single people?
  • Karina earned $32,000 last year and Tamara earned $42,000. What is the ratio of Karina’s earnings to Tamara’s?
  • A runner ran 4.9 miles yesterday and 7.7 miles today. What is the ratio of the distance she ran yesterday to the distance she ran today?
  • A political organization has a 7:1 ratio of members who are registered to vote to members who aren’t registered. If the organization has 28 registered members, how many nonregistered members does it have?
  • A house has a 9:2 ratio of windows to doors. If it has four doors, how many windows does it have?
  • Suppose that a store expects a 3 to 10 ratio of people who make a purchase to the number of people who enter the store. If 120 customers entered the store on a busy Saturday, how many made purchases?