Q74. - Algebra 2

Question

Find the reciprocal of each number.

$-\frac{2}{3}$

Step-by-Step Solution

Answer

The reciprocal of the $-\frac{2}{3}$ is $-\frac{3}{2}$.

Step 1- Given information

We have, a number $-\frac{2}{3}$.

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 $-\frac{2}{3}$ is$=x.$

So,

$\begin{array}{l}-\frac{2}{3}\times x=1\\ \Rightarrow x=-\frac{3}{2}\end{array}$

Hence, the reciprocal of the$-\frac{2}{3}$is $-\frac{3}{2}$.