Find the Reciprocal 6 4/5

$6 \frac{4}{5}$

Step 1

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

$\frac{1}{6 \frac{4}{5}}$

Step 2

Simplify.

Convert $6 \frac{4}{5}$ to an improper fraction.

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

$\frac{1}{6 + \frac{4}{5}}$

Add $6$ and $\frac{4}{5}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{6 \cdot \frac{5}{5} + \frac{4}{5}}$

Combine $6$ and $\frac{5}{5}$ .

$\frac{1}{\frac{6 \cdot 5}{5} + \frac{4}{5}}$

Combine the numerators over the common denominator.

$\frac{1}{\frac{6 \cdot 5 + 4}{5}}$

Simplify the numerator.

Multiply $6$ by $5$ .

$\frac{1}{\frac{30 + 4}{5}}$

Add $30$ and $4$ .

$\frac{1}{\frac{34}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{5}{34})$

Multiply $\frac{5}{34}$ by $1$ .

$\frac{5}{34}$