Find the Reciprocal 4/12-8/25

$\frac{4}{12} - \frac{8}{25}$

Step 1

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

$\frac{1}{\frac{4}{12} - \frac{8}{25}}$

Step 2

Simplify.

Cancel the common factor of $4$ and $12$ .

Factor $4$ out of $4$ .

$\frac{1}{\frac{4 (1)}{12} - \frac{8}{25}}$

Cancel the common factors.

Factor $4$ out of $12$ .

$\frac{1}{\frac{4 \cdot 1}{4 \cdot 3} - \frac{8}{25}}$

Cancel the common factor.

$\frac{1}{\frac{4 \cdot 1}{4 \cdot 3} - \frac{8}{25}}$

Rewrite the expression.

$\frac{1}{\frac{1}{3} - \frac{8}{25}}$

Simplify the denominator.

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{1}{\frac{1}{3} \cdot \frac{25}{25} - \frac{8}{25}}$

To write $- \frac{8}{25}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{\frac{1}{3} \cdot \frac{25}{25} - \frac{8}{25} \cdot \frac{3}{3}}$

Write each expression with a common denominator of $75$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{25}{25}$ .

$\frac{1}{\frac{25}{3 \cdot 25} - \frac{8}{25} \cdot \frac{3}{3}}$

Multiply $3$ by $25$ .

$\frac{1}{\frac{25}{75} - \frac{8}{25} \cdot \frac{3}{3}}$

Multiply $\frac{8}{25}$ by $\frac{3}{3}$ .

$\frac{1}{\frac{25}{75} - \frac{8 \cdot 3}{25 \cdot 3}}$

Multiply $25$ by $3$ .

$\frac{1}{\frac{25}{75} - \frac{8 \cdot 3}{75}}$

Combine the numerators over the common denominator.

$\frac{1}{\frac{25 - 8 \cdot 3}{75}}$

Simplify the numerator.

Multiply $- 8$ by $3$ .

$\frac{1}{\frac{25 - 24}{75}}$

Subtract $24$ from $25$ .

$\frac{1}{\frac{1}{75}}$

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 75$

Multiply $75$ by $1$ .

$75$