# How do you find the reciprocal of -1/5?

May 24, 2017

The reciprocal of $- \frac{1}{5}$ is $- \frac{5}{1}$

#### Explanation:

The reciprocal of a number ($x$) is also known as the multiplicative inverse:
'the multiplying opposite'. (This means just invert it.)

It comes from $\frac{1}{x}$

The reciprocal of $\frac{a}{b}$ would be $\frac{1}{\frac{a}{b}}$ which is $\frac{b}{a}$.

The reciprocal of of $- \frac{m}{n}$ is $- \frac{n}{m}$

The product of a number and its reciprocal is always $+ 1$.

$\frac{a}{b} \times \frac{b}{a} = 1 \text{ and } - \frac{m}{n} \times - \frac{n}{m} = 1$

The reciprocal of $- \frac{1}{5}$ is $- \frac{5}{1} = - 5$

May 24, 2017

$- 5$
$\text{the reciprocal of a number n, is} \frac{1}{n}$
$\Rightarrow \text{reciprocal of } - \frac{1}{5} = \frac{1}{- \frac{1}{5}} = - 5$