# Ratios: Definition & Sample Problems

By William Springer

What is a ratio, and how to we find one? Learn how to use ratios to solve simple math problems.

## What is a Ratio?

A ratio expresses a relationship between two (or more) numbers of the same type; as such, it is simply two numbers with no units. A ratio gives us an easy way to compare two numbers. For example, a tv or monitor will generally have a ratio of 4:3 (for an older display) or 16:9 (for a widescreen display). This means that a widescreen monitor has 16 horizontal units for every 9 vertical units (or, more simply stated, 16 units of width for every 9 units of height). Knowing how to find a ratio in math allows us to make important comparisons in everyday life.

In geometry, we say that two figures (usually triangles) are proportional if their sides are in the same ratio to each other. For example, one right triangle could have sides with lengths of 3, 4, and 5 inches, while another has sides with 6, 8, and 10 feet. Because both triangles are in a 3:4:5 ratio, they are proportional; they have the same shape.

## Sample Problems

Let's try a few sample problems; the answers will be in the next section.

1) John is considering buying one of two houses. The first house is 6 miles away from his job, and the second house is 9 miles away from his job. What is the ratio of the two distances, in lowest terms?

2) Mary made \$12 per hour at her old job. If she got a raise when she moved to her new job and now makes \$15 per hour, what is the ratio of her new salary to her old salary?

3) A right triangle has three sides with lengths x, y, and z, such that side z is the hypotenuse (the side opposite the right angle) and x2 + y2 = z2. Let triangle A have x=3 and y=4. If the ratio of triangle A to similar triangle B is 1:4, how long is the hypotenuse on triangle B?