In order to solve problems involving ratios, you should be able to:

- work with fractions
- simplify fractions

A ratio is a way of expressing a relationship between two numbers that can be expressed in the following three common ways:

as a

** fraction**

with a

**colon (:)**using the word “

**to**”

Suppose we are told that there are three nurses for every ten patients at a hospital. The three ways this

ratio of nurses to patients can be written are:

- as a fraction:
- with a colon: 3:10
- with “to”: 3 to 10

Notice that in each case, the number of nurses is written first (or in the numerator of the fraction). This is because the problem stated that we were to express the

ratio of nurses to patients. Typically the first thing mentioned in a

ratio problem is what is listed first.

If the problem had asked us to express the number of patients to nurses, each of our ratios would be written in the opposite order:

- as a fraction:
- with a colon: 10:3
- with “to”: 10 to 3

When working with ratios, it is extremely important to pay attention to order. Read each problem carefully to find out what is being asked.