Find the Reciprocal 5 3/7

$5 \frac{3}{7}$

Step 1

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

$\frac{1}{5 \frac{3}{7}}$

Step 2

Simplify.

Convert $5 \frac{3}{7}$ to an improper fraction.

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

$\frac{1}{5 + \frac{3}{7}}$

Add $5$ and $\frac{3}{7}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{5 \cdot \frac{7}{7} + \frac{3}{7}}$

Combine $5$ and $\frac{7}{7}$ .

$\frac{1}{\frac{5 \cdot 7}{7} + \frac{3}{7}}$

Combine the numerators over the common denominator.

$\frac{1}{\frac{5 \cdot 7 + 3}{7}}$

Simplify the numerator.

Multiply $5$ by $7$ .

$\frac{1}{\frac{35 + 3}{7}}$

Add $35$ and $3$ .

$\frac{1}{\frac{38}{7}}$

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{7}{38})$

Multiply $\frac{7}{38}$ by $1$ .

$\frac{7}{38}$