Find the Reciprocal 4 3/5

$4 \frac{3}{5}$

Step 1

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

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

Step 2

Simplify.

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $5$ .

$\frac{1}{\frac{20 + 3}{5}}$

Add $20$ and $3$ .

$\frac{1}{\frac{23}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{5}{23})$

Multiply $\frac{5}{23}$ by $1$ .

$\frac{5}{23}$