Q30. - Algebra 1

Question

Name the reciprocal of the following number.

$3\frac{3}{4}$

Step-by-Step Solution

Answer

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

Step 1. Formula Used.

The rule for converting a mixed number into an improper fraction.

$a\frac{b}{c}=\frac{\left(a\times c\right)+b}{c}$

Step 2. Definition of reciprocal.

The product of any number and its reciprocal is 1.

Step 3. 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 4. 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:

$3\frac{3}{4}=\frac{\left(3\times 4\right)+3}{4}=\frac{15}{4}$

So, the reciprocal is given by

$\frac{1}{\left(\frac{15}{4}\right)}=\frac{4}{15}$

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