# Word Problems – Ratios

A ratio is a comparison of two numbers. It can be written with a colon (1:5), or using the word "to" (1 to 5), or as a fraction:

Example 1:

A backyard pond has 12 sunfish and 30 rainbow shiners. Write the ratio of sunfish to rainbow shiners in simplest form.

Write the ratio as a fraction.

So the ratio of sunfish to rainbow shiners is 2:5.

(Note that the ratio of rainbow shiners to sunfish is the reciprocal: or 5:2.)

Read word problems carefully to check whether the ratio you're being asked for is a fraction of the total or the ratio of one part to another part .

Example 2:

Ms. Ekpebe's class has 32 students, of which 20 are girls. Write the ratio of girls to boys.

Careful! Don't write 20/32... that's the fraction of the total number of students that are girls. We want the ratio of girls to boys.

Subtract 20 from 32 to find the number of boys in the class.

32 – 20 = 12

There are 12 boys in the class. So, ratio of girls to boys is 20:12.

You can reduce this ratio, the same way you reduce a fraction. Both numbers have a common fact of 4, so divide both by 4.

In simplest form , this ratio is 4:3.

Some ratio word problems require you to solve a proportion .

Example 3:

A recipe calls for butter and sugar in the ratio 2:3. If you're using 6 cups of butter, how many cups of sugar should you use?

The ratio 2:3 means that for every 2 cups of butter, you should use 3 cups of sugar.

Here you're using 6 cups of butter, or 3 times as much.

So you need to multiply the amount of sugar by 3.

So, you need to use 9 cups of sugar.

You can think of this in terms of equivalent fractions :