# Fractions Calculator – Multiply, Divide, Add, and Subtract

Written by:
PK

This page contains a fractions calculator. Enter two fractions and choose whether to add, subtract, multiple, or divide the fractions. We'll perform your choice of math and let the tool return you the simplest fraction form.

## What are Fractions?

Fractions are two numbers expressed as a part of a whole. They consist of a top number (numerator) and a bottom number (denominator) and imply division.

fraction\ form=\frac{numerator}{denominator}

## Fraction Arithmetic

For the four basic arithmetic functions – addition, subtraction, division, and multiplication – there are basic rules to follow when working with fractions. I'll walk you through each one and show an example.

1. First, convert both fractions to a common base by multiplying top and bottom by the same number to equal a base. (You can find the least common denominator, or lazily multiply all denominators together).
2. Add the two numerators, and place the result in a new numerator.
3. Add the two denominators and place the result in a new denominator.
4. (Optional) Find the reduced or simplest form of the fraction.

Let's add two fractions together: 3/9 and 1/7.

\frac{3}{9}+\frac{1}{7}\ common\ denominator\ = 21\\~\\\frac{3}{9}=\frac{1}{3}*\frac{7}{7}=\frac{7}{21}\\~\\\frac{1}{7}*\frac{3}{3}=\frac{3}{21}\\~\\\frac{7}{21}+\frac{3}{21}=\frac{10}{21}

### Subtracting Fractions

To subtract two fractions:

1. First, convert both fractions to a common base. You then need to multiply top and bottom numbers by the same number to equal a base. (Either find the least common denominator, or simply multiply the denominators together).
2. Subtract the second numerator from the first, placing the result in a new numerator.
3. Subtract the second denominator from the first, placing the result in a new denominator.
4. (Optional) Find the reduced or simplest fraction form.

#### Example Fraction Subtraction

Let's subtract the fraction 1/7 from 6/21.

\frac{6}{21}-\frac{1}{7}\ common\ denominator\ = 21\\~\\\frac{1}{7}*\frac{3}{3}=\frac{3}{21}\\~\\\frac{6}{21}-\frac{3}{21}=\frac{3}{21}\\~\\(reduced)=\frac{1}{7}

### Multiplying Fractions

Multiplying two fractions is the easiest one to remember – just multiply the numerator and denominator across:

1. Multiply the first numerator by the second and put it in a new numerator.
2. Multiply the first denominator by the second and put it in a new denominator.
3. (Optional) Find the reduced or simplest fraction form.

#### Example Fraction Multiplication

Let's multiply the fractions 3/9 and 1/7.

\frac{3}{9}*\frac{1}{7}=\frac{3}{63}\\~\\(reduced)=\frac{1}{21}

### Dividing Fractions

Dividing fractions is also relatively straightforward. We add one step to multiplication and invert or "flip" the second fraction.

1. Rewrite the second fraction to take its inverse, or put the denominator over the numerator.
2. Multiply the first numerator by the new numerator of the rewritten second and put it in a third numerator.
3. Multiply the first denominator by the new denominator of the rewritten second and put it in a third denominator.
4. (Optional) Find the reduced or simplest fraction form.

#### Example Fraction Division

Let's divide the fraction 1/7 by 1/3.

\frac{1}{7}\div\frac{1}{3}=\frac{1}{7}*(\frac{1}{3})^{-1}=\\~\\\frac{1}{7}*\frac{3}{1} =\frac{3}{7}

## How to Use the Fractions Calculator

You can use the fractions calculator without remembering all those arithmetic functions!

In the box for Fraction One, enter the numerator for the first fraction. In the box for Fraction Two, enter the numerator and denominator of the second fraction.

In the Operation menu, choose which function to perform – do you want to add (+), subtract (-), multiply (*) or divide (÷) the fractions? Choose your preference from the menu. Then hit the Perform Fractional Math button.

The automatically simplified answer will be listed in the Result box.

### PK

PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK is in his mid-30s and lives in New Hampshire with his wife, kids, and dog.

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