# Fractions Calculator

Online fractions calculator. Add, subtract, divide, or multiply fractions.

Result:
Waiting for input...

To calculate the result, enter both fractions, choose whether you want the result of addition, subtraction, multiplication, or division, and press the = button. Apart from the result itself, the calculator should also generate detailed calculations with an optional, simplified result.

## Adding fractions

Formula for adding fractions:

$$\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \times d) + (c \times b)}{b \times d} = \dfrac{ad + bc}{bd}$$

Example:

$$\frac{6}{12} + \frac{3}{20} = \frac{(6 \times 5) + (3 \times 3)}{5 \times 3} = \frac{30 + 9}{60} = \frac{39}{60} = \frac{13}{20}$$

## Subtracting fractions

Formula for subtracting fractions:

$$\dfrac{a}{b} - \dfrac{c}{d} = \dfrac{(a \times d) - (c \times b)}{b \times d} = \dfrac{ad - bc}{bd}$$

Example:

$$\frac{10}{5} - \frac{2}{7} = \frac{(10 \times 7) - (2 \times 5)}{7 \times 5} = \frac{70 - 10}{35} = \frac{60}{35} = \frac{12}{7} = 1 \frac{5}{7}$$

## Multiplying fractions

Formula for multiplying fractions:

$$\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}$$

Example:

$$\frac{4}{10} \times \frac{5}{6} = \frac{4 \times 5}{10 \times 6} = \frac{20}{60} = \frac{1}{3}$$

## Dividing fractions

Formula for dividing fractions:

$$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c} = \dfrac{a \times d}{b \times c}$$

Example:

$$\frac{4}{9} \div \frac{4}{15} = \frac{4}{9} \times \frac{15}{4} = \frac{4 \times 15}{9 \times 4} = \frac{60}{36} = \frac{5}{3} = 1 \frac{2}{3}$$
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