# 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"
$\left(1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{to}\text{\hspace{0.17em}}\text{\hspace{0.17em}}5\right)$
, 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.

$\frac{12}{30}$

Now reduce the fraction .

$\frac{2}{5}$

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 $3$ .

$3\times 3=9$

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

You can think of this in terms of equivalent fractions :

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