Q77. - Algebra 2

Question

Find the reciprocal of each number.

$2.5$

Step-by-Step Solution

Answer

The reciprocal of the $2.5$ is $0.4$.

Step 1- Given information

We have, a number $2.5$.

To find the reciprocal of the given number. 

Step 2- concept used

When we multiply by $x$ with the reciprocal or multiplicative inverse of a number $x$is the number 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 $2.5$ is$=x.$

So,

$\begin{array}{l}2.5\times x=1\\ \Rightarrow \frac{25}{10}\times x=1\\ \Rightarrow \frac{5}{2}\times x=1\\ \Rightarrow x=\frac{2}{5}\\ \Rightarrow x=0.4\end{array}$

Hence, the reciprocal of the $2.5$ is $0.4$.