# 9.6 Proportion

In this section, we consider two important types of relationships that occur frequently in real life: direct and inverse proportion.

## Direct Proportion

The first type of relationship is known as direct proportion. Two quantities are said to be directly proportional to each other if when one doubles, triples, and quadruples, the other also doubles, triples, and quadruples. For example, if you buy three times as many items as usual, you would expect to have to pay three times as much money (unless there were some special offer available) because the price is directly proportional to the number of items bought.

## Activity: Directly Proportional Relationships

Which of the following quantities are in direct proportion?

Select the two correct answers from the following:

a.

(a) The number of kilometers and the equivalent number of miles.

b.

(b) The number of euros that are exchanged for dollars.

c.

(c) The monthly cost of a cell phone and the minutes used for talking in Section 9.3.3.

The correct answers are a and b.

If you triple the number of dollars you exchange, you would expect to get three times as many euros. However, part (c) is not a directly proportional relationship. If you use 30 minutes, the charge is $25. But if you double the time used to 60 minutes, the charge is$31, and the price has not doubled.