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.
Problems:

  • 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?

Solving Simple Proportions
Solving proportions
Solve proportions
Ratios and proportions and how to solve them
SOLVING PROPORTIONS EXAMPLES
Ratios and Proportions
Proportion word problems
Solve proportions: word problems
Proportion Worksheets
Writing proportions