Q28. - Algebra 1

Question

Name the reciprocal of the following number.

$2\frac{3}{4}$

Step-by-Step Solution

Answer

The reciprocal of $2\frac{3}{4}$ is $\frac{4}{11}$.

Step 1. Definition of reciprocal.

The product of any number and its reciprocal is 1.

Step 2. Example:

Let a be any number then its reciprocal is given by

$a·\frac{1}{a}=1$

Hence, reciprocal of a is $\frac{1}{a}$.

Step 3. Find the reciprocal of the given number.

First, simplify mixed number to an improper fraction and then divide 1 by the improper fraction and simplify further as follows:

$2\frac{3}{4}=\frac{11}{4}$

So, the reciprocal is

$\frac{1}{\left(\frac{11}{4}\right)}=\frac{4}{11}$

The reciprocal of $2\frac{3}{4}=\frac{11}{4}$ is $\frac{4}{11}$.