To understand proportions, you first need to have a handle on what a ratio is.

A ratio is a comparison of two numbers by division. The most common representation of a ratio is as a fraction in simplest form. For example, if a bike has a gear on the wheel with 16 teeth, or cogs, and a gear at the pedals with 40 teeth, the gear ratio would be 16 to 40. The fraction 16/40 can be simplified by dividing both the numerator and denominator by 8. Thus, an easier way to state this bike’s gear ratio would be the simplified ratio of 2/5.

Here are some other ways to write a ratio:

1:2 ½ 1 to 2 1 out of 2

When two ratios are equivalent, they are said to be in proportion.

Example: The ratio 6/8 is proportional to the ratio 9/12 because both ratios can be simplified to 3/4. Even though they may look different, 6/8, 9/12, and 3/4 are all expressing the exact same value!

A model of a car is built at 1/10th scale. Which of the following scales are equivalent to 1/10th?

a. 10/1000

b. 5/50

c. 100/200

d. 10/100

Answers b and d are equivalent to 1/10.