 # Fractions Calculator

## Standard fractions

Add, subtract, multiply and divide fractions.

## Simplify a fraction

Find the common factor of a fraction and then simplify it to its lowest form.

Use this popular fractions calculator to add, subtract, multiply and divide fractions, including mixed number fractions. The calculator gives explanation of the working steps involved and simplifies the result using the greatest common denominator.

Disclaimer: Whilst every effort has been made in building this calculator, we are not to be held liable for any damages or monetary losses arising out of or in connection with the use of it. This tool is here purely as a service to you, please use it at your own risk. Full disclaimer. Do not use calculations for anything where loss of life, money, property, etc could result from inaccurate calculations.

1. Check whether your denominators (bottom numbers) match.
3. They don’t? OK. Multiply your differing denominators together…
4. …And adjust both your nominators (top numbers) proportionately. E.g. if you doubled the denominator, then double its numerator.
5. Add together the nominators, and put this total over the common denominator.
6. Simplify the fraction to the smallest possible denominator, with the nominator also reduced proportionately.

Quick formula

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

Example of how to add fractions

$$\dfrac{2}{3} + \dfrac{1}{4} = \dfrac{(2\times4) + (3\times1)}{3\times4} = \dfrac{11}{12}$$

## How to subtract fractions

1. Check whether your denominators (bottom numbers) match.
3. They don’t? OK. Multiply your differing denominators together…
4. …And adjust both your nominators (top numbers) proportionately. E.g. if you doubled the denominator, then double its numerator.
5. Subtract the second nominator from the first, and put this total over the common denominator.
6. Simplify the fraction to the smallest possible denominator, with the nominator also reduced proportionately.

Quick formula

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

Example of how to subtract fractions

$$\dfrac{2}{3} - \dfrac{1}{4} = \dfrac{(2\times4) - (3\times1)}{3\times4} = \dfrac{5}{12}$$

You can learn about how to add and subtract fractions in our article how to add, subtract, multiply and divide fractions.

## How to multiply fractions

1. Multiply the numerators (top numbers) together to get your numerator answer.
2. Multiply the denominators (bottom numbers) together to get your denominator answer.
3. Simplify the fraction to the smallest possible denominator, with the nominator also reduced proportionately.

Quick formula

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

Example of how to multiply fractions

$$\dfrac{2}{3} \times \dfrac{1}{4} = \dfrac{(2\times1)}{(3\times4)} = \dfrac{2}{12} = \dfrac{1}{6}$$

## How to divide fractions

1. Write out the whole sum, BUT replace the ÷ with an ×
2. Flip the second fraction upside down, switching the nominator (top number) and denominator’s (second number) places.
3. Complete the sum by multiplying the first fraction with the reversed second fraction.
4. Simplify the fraction to the smallest possible denominator, with the nominator also reduced proportionately.

Quick formula

$$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc}$$

Example of how to divide fractions

$$\dfrac{2}{3} \div \dfrac{1}{4} = \dfrac{(2\times4)}{(3\times1)} = \dfrac{8}{3}$$ If you would like help with converting between decimals and fractions, see our article how to convert a decimal to a fraction.

Should you wish to convert a decimal number to a fraction, give the decimal to fraction calculator a try.

When it comes to performing a mathematical calculation, it is important to carry out the operations in the correct order. This is where the order of operations comes in. Thankfully, there are a couple of mnemonics to assist us with remembering the order of operations. Read our article about PEMDAS.