Question

Find the reciprocal of each number.

76. $3\frac{3}{4}$

Short answer

The reciprocal of the$3\frac{3}{4}$ is $\frac{4}{15}$.

Step-by-step solution

Step 1- Given information

We have, a number$3\frac{3}{4}$.

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 $3\frac{3}{4}$is$=x.$

So,

$\begin{array}{l}3\frac{3}{4}\times x=1\\ \Rightarrow \frac{15}{4}\times x=1\\ \Rightarrow x=\frac{4}{15}\end{array}$

Hence, the reciprocal of the$3\frac{3}{4}$ is $\frac{4}{15}$.