Word Problems: Ratios

A ratio is a comparison of two numbers. It can be written with a colon $\left(1:5\right)$ , or using the word "to" $\left(1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{to}\text{\hspace{0.17em}}\text{\hspace{0.17em}}5\right)$ , or as a fraction: $\frac{1}{5}$

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.

$\frac{12}{30}$

$\frac{2}{5}$

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

(Note that the ratio of rainbow shiners to sunfish is the reciprocal : $\frac{5}{2}$ 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 $\frac{20}{32}$ ... 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 $5:3$ .

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 $3$ .

$3×3=9$

So, you need to use $9$ cups of sugar.

You can think of this in terms of equivalent fractions :

$\frac{2}{3}=\frac{6}{9}$