# What is absolute value reciprocal of 1 over 5?

Dec 7, 2017

5

#### Explanation:

A reciprocal number is a number by which a given number must be multiplied to get a result of one.

What this means is that a number multiplied by its reciprocal will always equal 1.

Usually what we do is simply flip the fraction over. So...

Flip $\frac{1}{5}$ over and we get $\frac{5}{1}$ or $5$. This makes sense because:

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

The absolute value of $\left\mid 5 \right\mid$ is simply $5$.
absolute value is asking us to make the number non-negative.

ALSO
We can solve for it.
$\frac{1}{5}$ times what equals 1?
We can right this as
$\frac{1}{5} \cdot x = 1$

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

$\textcolor{red}{5} \cdot \frac{1}{5} x = \textcolor{red}{5} \cdot 1$
$x = 5$