Find the Reciprocal 2 1/4

$2 \frac{1}{4}$

Step 1

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

$\frac{1}{2 \frac{1}{4}}$

Step 2

Simplify.

Convert $2 \frac{1}{4}$ to an improper fraction.

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

$\frac{1}{2 + \frac{1}{4}}$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{2 \cdot \frac{4}{4} + \frac{1}{4}}$

Combine $2$ and $\frac{4}{4}$ .

$\frac{1}{\frac{2 \cdot 4}{4} + \frac{1}{4}}$

Combine the numerators over the common denominator.

$\frac{1}{\frac{2 \cdot 4 + 1}{4}}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{1}{\frac{8 + 1}{4}}$

Add $8$ and $1$ .

$\frac{1}{\frac{9}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{4}{9})$

Multiply $\frac{4}{9}$ by $1$ .

$\frac{4}{9}$