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## Express Ratio as Fraction

#### Introduction

Ratios and Fractions both show the relationship between two values, and demonstrate the proportion of a quantity in terms of other numbers. For example, a ratio tells you how many boys and girls are in a class (5:7 - meaning that for every five boys, there are 7 girls); a fraction tells you how big a slice of cake is ($rac{1}{8}$ - meaning that if you were to cut the cake into 8 equal slices, this slice would be one of those.)

Because they do very similar things, you sometimes need to express ratios as fractions. For example, in the example above, you might want to know what fraction of the class is girls, and which fraction is boys.

## Lesson

To take a ratio and turn it into a fraction, you need to first work out the denominator. This is the number at the bottom of the fraction. In the fraction $rac{1}{3}$, 3 is the denominator.

To do this, you add the two numbers in the ratio together. Let's use the example from the introduction above, where we have a class with a ratio of 5:7 boys to girls (for every 5 boys, there are 7 girls).

We add the two numbers together:

$5 + 7 = 12$

Therefore, our denominator needs to be 12.

Then, we can just use the numbers from the ratio as our numerators (the top number of the fraction).

So $rac{5}{12}$ of the class are boys, and $rac{7}{12}$ are girls.

To test it, let's plug in some numbers. Let's imagine there is a total of 24 students in the class. To use the fractions, we would work out $rac{5}{12}$ of 24. That gives us 10 ($rac{5}{12} * 24 = 10$). To work out how many girls, we do $rac{7}{12} * 24$, which equals 14.

Since we have 10 boys and 14 girls the ratio is:

$10 : 14$

By making the ratio as simple as possible (dividing by 2), we get the ratio:

$5 : 7$

Therefore the fractions match the ratio and vice versa.

## Examples

$7:21$
To express the ratio '$7$ to $21$' as a fraction, place $7$ over $21$ and reduce
$\dfrac{7}{21}$ can be reduced, since $7$ is a factor of both $7$ and $21$:
$\dfrac{7}{21} \div \dfrac{7}{7} = \dfrac{1}{3}$
The fraction is now in lowest terms
$14:20$
To express the ratio '$14$ to $20$' as a fraction, place $14$ over $20$ and reduce
$\dfrac{14}{20}$ can be reduced, since $2$ is a factor of both $14$ and $20$:
$\dfrac{14}{20} \div \dfrac{2}{2} = \dfrac{7}{10}$
The fraction is now in lowest terms
$5:15$
To express the ratio '$5$ to $15$' as a fraction, place $5$ over $15$ and reduce
$\dfrac{5}{15}$ can be reduced, since $5$ is a factor of both $5$ and $15$:
$\dfrac{5}{15} \div \dfrac{5}{5} = \dfrac{1}{3}$
The fraction is now in lowest terms
$0.12:0.2$
To express the ratio '$0.12$ to $0.2$' as a fraction, place $0.12$ over $0.2$ and reduce
Multiply numerator and denominator by 100
$\dfrac{0.12}{0.2}$ * $\dfrac{100}{100}$ = $\dfrac{12}{20}$
$\dfrac{12}{20}$ can be reduced, since $4$ is a factor of both $12$ and $20$:
$\dfrac{12}{20} \div \dfrac{4}{4} = \dfrac{3}{5}$
The fraction is now in lowest terms