Find the Reciprocal 5 3/4

$5 \frac{3}{4}$

Step 1

To find the reciprocal, divide $1$ by the number given.

$\frac{1}{5 \frac{3}{4}}$

Step 2

Simplify.

Convert $5 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{1}{5 + \frac{3}{4}}$

Add $5$ and $\frac{3}{4}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{5 \cdot \frac{4}{4} + \frac{3}{4}}$

Combine $5$ and $\frac{4}{4}$ .

$\frac{1}{\frac{5 \cdot 4}{4} + \frac{3}{4}}$

Combine the numerators over the common denominator.

$\frac{1}{\frac{5 \cdot 4 + 3}{4}}$

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{1}{\frac{20 + 3}{4}}$

Add $20$ and $3$ .

$\frac{1}{\frac{23}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{4}{23})$

Multiply $\frac{4}{23}$ by $1$ .

$\frac{4}{23}$