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

Jun 18, 2018

See a solution process below:

#### Explanation:

First, we need to convert the mixed number into an improper fraction:

$3 \frac{3}{4} = 3 + \frac{3}{4} = \left(\frac{4}{4} \times 3\right) + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$

The reciprocal of a number when multiplied by itself is equal to $1$

So we can write and solve for $r$:

$\frac{15}{4} \times r = 1$

$\frac{\frac{15}{4} \times r}{\textcolor{red}{\frac{15}{4}}} = \frac{1}{\textcolor{red}{\frac{15}{4}}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\frac{15}{4}}}} \times r}{\cancel{\textcolor{red}{\frac{15}{4}}}} = \frac{4}{15}$

$r = \frac{4}{15}$

$\frac{15}{4} \times \frac{4}{15} = \frac{15 \times 4}{4 \times 15} = \frac{60}{60} = 1$

Any easy way to remember this is to just flip the fraction to get the reciprocal:

$\frac{\textcolor{red}{15}}{\textcolor{b l u e}{4}} \to \frac{\textcolor{b l u e}{4}}{\textcolor{red}{15}}$

If the number is an integer and not a fraction, say $7$, we can write $7$ as $\frac{7}{1}$ to turn it into a fraction and apply the same rule:

$\frac{\textcolor{red}{7}}{\textcolor{b l u e}{1}} \to \frac{\textcolor{b l u e}{1}}{\textcolor{red}{7}}$

Jun 18, 2018

$\frac{4}{15}$

#### Explanation:

$\text{first express "3 3/4" as an improper fraction}$

$3 \frac{3}{4} = \frac{4 \times 3 + 3}{4} = \frac{15}{4}$

$\text{the reciprocal of any number "n" is } \frac{1}{n}$

$\text{the reciprocal of "15/4" is } \frac{1}{\frac{15}{4}} = \frac{4}{15}$