Ratio is a concept that you have probably encountered in other math classes. It is a comparison of sizes.

## Ratio

The **ratio** of two numbers *a* and *b* is the fraction , usually expressed in reduced form. An alternative form involves a colon. The colon form is most frequently used when comparing three or more numbers to each other. See Table

**Example 1**: A classroom has 25 boys and 15 girls. What is the ratio of boys to girls?

The ratio of boys to girls is 5 to 3, or 5/3, or 5 : 3.

**Example 2:** The ratio of two supplementary angles is 2 to 3. Find the measure of each angle.

- The angles have measures of 72° and 108°.

- 2
*x*to 3*x*reduces to 2 to 3.

- 2
*x*+ 3*x*= 180° (The sum of supplementary angles is 180°.)

- 5
*x*= 180°

*x*= 36°

- Then, 2
*x*= 2(36°) and 3*x*= 3(36°).

- So, 2
*x*= 72° and 3*x*= 108°

- The angles have measures of 72° and 108°.

**Example 3:** A triangle has angle measures of 40°, 50°, and 90°. In simplest form, what is the ratio of these angles to each other?

- 40 : 50 : 90 = 4 : 5 : 9 (10 is a common divisor)

This means that:

1. The ratio of the first to the second is 4 to 5.

2. The ratio of the first to the third is 4 to 9.

3. The ratio of the second to the third is 5 to 9.

**Example 4:** A 50‐inch segment is divided into three parts whose lengths have the ratio 2 : 3 : 5. What is the length of the longest part?

The longest part has a measure of 25 inches.

## Proportion

A **proportion** is an equation stating that two ratios are equal.

## Means and extremes

The extremes are the terms in a proportion that are the farthest apart when the proportion is written in colon form ( *a:b* = *c:d*). In the foregoing, *a* and *d* are extremes. The means are the two terms closest to each other.

In the preceding proportion, the values *a* and *d* are called extremes of the proportion; the values *b* and *c* are called the means of the proportion.