# What is the opposite and reciprocal of 2/5?

Jun 30, 2015

The opposite of $\frac{2}{5}$ is $- \frac{2}{5}$.

The reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$.

#### Explanation:

The opposite of a number is its additive inverse, which when added to the original number the result is zero.

$\frac{2}{5} + \left(- \frac{2}{5}\right) = 0$

The reciprocal of a number is its multiplicative inverse, which when multiplied times the original number the result is one.

$\frac{2}{5} \times \frac{5}{2} = \frac{10}{10} = {\cancel{10}}^{1} / {\cancel{10}}^{1} = 1$