Proportions Chapter 7 Section 7.2

Objective Students will solve problems using proportions

Vocabulary Proportions Extremes Means

Concept An equation that states that two ratios are equal is called a proportion. Usually you write a proportion in one of two ways: 2 : 3 = 4 : 6 or 2 / 3 = 4 / 6 Both can be read as “2 is to 3 as 4 is to 6.”

Concept In the proportion a:b = c:d, a and d are called the extremes, and b and c are called the means. You can use the multiplication property of equality to show that in any proportion the product of the extremes equals the product of the means.

Concept If a / b = c / d, then ad = bc You can use this fact to solve proportions Cross multiply, then divide

Example 3 / x = 5 / 4

Example 4 / 21 = -2 / 15a

Example 3 / n = 8

Example (x-4) / 3 = 2 / 15

Example (2n-3) / 5 = (n+2) / 6

Concept You can also use proportions to help you solve word problems. The key to solving these problems is that you must set up your proportion correct. However you set up the first ratio, you must set up the second ratio the exact same way.

Example With a 5 lb bag of flour the cooking class can make 120 date-nut muffins. How many muffins can they make with a 2 lb bag of flour?

Example About 8 gal of gas filled the tank after Greg drove 224 mi. How many miles can he expect to drive on a full tank of about 13 gal?

Questions

Assignment Worksheet