Write and Solve Proportions

Honors Math – Grade 6

Problem of the Day

Ellen uses 9 gallons of gas when she drives 225 miles on the highway. Lori uses 7 gal of gas when she drives 175 miles on the highway. Is the average number of miles per gallon the same for Ellen's car as for Lori’s?

KEY CONCEPT Proportion

A proportion is an equation stating that two ratios or rates are equivalent.

To find out if the two average rates are the same, write two ratios and determine if they are equivalent—that is, if they form a proportion.

The middle terms, b and c, are called the means. The end terms, a and d, are called the extremes.

The Cross Products Rule (CPR) states the product of the means = the product of the extremes.

In a proportion, the order of the labels is both ratios needs to be the same.

To find if two ratios or rates form a proportion.

Method 1: CPR Method 2: Use Simplest Ratios

Determine if the ratios form a proportion.

56 :8=35 :5

1428

=1236

612

=1018

Determine if the ratios form a proportion.

1 .2:1.8=2.4 :3.6

3 .6 : 4.2=4.5 :5.6 412:9=

25:45

There are two ways to find the missing term of a proportion. The missing term can be located in any of the four positions.

Method 1: Use CPR

𝑛16

=1832

Method 2: Equivalent Fractions

𝑛16

=1832

Find the missing term in each proportion.

56=𝑛48

9𝑡=368

0.93.6

=1.2𝑦