Algebra Examples

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

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{3 \cdot \frac{5}{5} - \frac{1}{5}}$

Step 2.1.2

Combine $3$ and $\frac{5}{5}$ .

$\frac{1}{\frac{3 \cdot 5}{5} - \frac{1}{5}}$

Step 2.1.3

Combine the numerators over the common denominator.

$\frac{1}{\frac{3 \cdot 5 - 1}{5}}$

Step 2.1.4

Simplify the numerator.

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Step 2.1.4.1

Multiply $3$ by $5$ .

$\frac{1}{\frac{15 - 1}{5}}$

Step 2.1.4.2

Subtract $1$ from $15$ .

$\frac{1}{\frac{14}{5}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{5}{14})$

Step 2.3

Multiply $\frac{5}{14}$ by $1$ .

$\frac{5}{14}$