# What is the opposite and reciprocal of 2 1/2?

Jun 24, 2015

The opposite of $2 \frac{1}{2}$ is $- \frac{1}{2}$.

The reciprocal of $2 \frac{1}{2}$ is $\frac{2}{5}$.

#### Explanation:

The opposite of a number is its additive inverse, which means that its sign is reversed. A number and its additive inverse equal zero when added. The opposite of $2 \frac{1}{2}$ is $- 2 \frac{1}{2}$.

$2 \frac{1}{2} + \left(- 2 \frac{1}{2}\right) = 0$

In order to get the reciprocal of a mixed fraction, you must first convert it into an improper fraction. Then switch the numerator and denominator. The reciprocal of a number is its multiplicative inverse, which means that when they are multiplied, their product is $1$.

$2 \frac{1}{2} = \frac{5}{2}$

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

$\frac{5}{2} \cdot \frac{2}{5} = 1$