# How do you find the reciprocal of 4 1/3?

Jan 12, 2017

The reciprocal of $4 \frac{1}{3}$ is $\frac{3}{13}$

#### Explanation:

In general, the reciprocal of an improper fraction $\frac{a}{b}$ is $\frac{b}{a}$

In the case of $4 \frac{1}{3}$ we have a mixed fraction.

In order to find the reciprocal, we start by converting it into an improper fraction:

$4 \frac{1}{3} = 4 + \frac{1}{3} = \frac{4 \cdot 3}{3} + \frac{1}{3} = \frac{12}{3} + \frac{1}{3} = \frac{12 + 1}{3} = \frac{13}{3}$

So the reciprocal is $\frac{3}{13}$