# What are equivalent fractions for 2/7?

##### 1 Answer
Mar 28, 2016

Any of the following:

$\frac{4}{14}$, $\frac{6}{21}$, ... , $\frac{285714}{999999}$

#### Explanation:

To construct an equivalent fraction, just multiply both the numerator and denominator by the same number.

For example:

$\frac{2 \cdot 2}{2 \cdot 7} = \frac{4}{14}$

$\frac{3 \cdot 2}{3 \cdot 7} = \frac{6}{21}$

$\frac{142857 \cdot 2}{142857 \cdot 7} = \frac{285714}{999999}$

The last example is interesting in that it tells you the repeating decimal representation of $\frac{2}{7}$:

$\frac{2}{7} = 0.285714285714285714 \ldots$

A shorthand way of representing a repeating decimal expansion like this is:

$\frac{2}{7} = 0. \overline{285714}$