Q75. - Algebra 2

Question

Find the reciprocal of each number.

$-\frac{1}{5}$

Step-by-Step Solution

Answer

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

Step 1- Given information

We have, a number $-\frac{1}{5}$.

To find the reciprocal of the given number.

Step 2- concept used

The reciprocal or multiplicative inverse of a number $x$ is the number which, when multiplied by $x$ then gives $1$.

Such that    $x\times \frac{1}{x}=1$

Thus, $x$ is the reciprocal of $\frac{1}{x}$and $\frac{1}{x}$is the reciprocal of $x$.

Step 3- To find the reciprocal

Let the reciprocal of the given number $-\frac{1}{5}$ is$=x.$

So,

$\begin{array}{l}-\frac{1}{5}\times x=1\\ \Rightarrow \frac{1}{5}\times x=-1\\ \Rightarrow x=-5\end{array}$

Hence, the reciprocal of the$-\frac{1}{5}$ is $-5.$