# What are the equivalent fractions to 3/7?

Apr 7, 2016

They can be: $\frac{6}{14}$, $\frac{9}{21}$, $\frac{12}{28}$ and so on.

#### Explanation:

If you have a fraction $\frac{a}{b}$ then any fraction $\frac{k a}{k b}$ for a natural number $k$ is equivalent to $\frac{a}{b}$, because it can be reduced by $k$.

Example:

$\frac{3}{7} = \frac{3 \cdot 2}{7 \cdot 2} = \frac{6}{14}$

$\frac{3}{7} = \frac{3 \cdot 3}{7 \cdot 3} = \frac{9}{21}$

Also if $a$ and $b$ have any common factors greater than $1$ you can get other equivalent fractions by reducing original fraction by the factors. For example:

$\frac{9}{12} = \frac{3 \cdot 3}{3 \cdot 4} = \frac{3}{4}$.

So $\frac{3}{4}$ is equivalent to $\frac{9}{12}$