Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign and click Calculate. This fraction calculator includes steps shown in the answer.

If you have a whole number in front of your fraction you have a mixed number. To do math with mixed numbers use the CalculatorSoup® Mixed Numbers Calculator.

Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you would solve 1/3 × 3/8.

There are many ways to think about fractions. Commonly a fraction is explained as a part of a whole. If you had a dozen eggs and a recipe called for 5 eggs, you could say that you used 5/12 of a dozen eggs in the recipe.

Fractions can also be used to represent quantities between 2 whole numbers. Maybe your favorite restaurant is 5.3 miles away from your house. It's more than 5 miles, but it's not quite 6 miles away.

The 0.3 extra distance past the 5-mile mark is a fraction of a mile. You can say it's "point 3" miles more than 5 miles. You could also say the restaurant is "5 and 3 tenths miles" from your house.

For negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

Remember these guidelines when you have negative fractions:

A negative sign in the numerator or the denominator make a fraction negative

A negative sign in the numerator and in the denominator cancel each other out and make a fraction positive

This is similar to the regular rules for doing math with negative numbers. If you have two like signs, the number is positive. If you have one positive sign and one negative sign, the number is negative.

There are 2 cases where you need to know if your fractions have different denominators:

if you are adding fractions

if you are subtracting fractions

If your fractions have different denominators you'll need to find the least common denominator. This is the smallest number that is a multiple of all denominators.

You can use the LCD Calculator to find the least common denominator for a set of fractions

For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator

Multiply the numerator and denominator of your first fraction by that number

Repeat Steps 3 and 4 for each fraction

For addition equations, add the fraction numerators

For subtraction equations, subtract the fraction numerators

Convert improper fractions to mixed numbers

Reduce the fraction to lowest terms

Visit the CalculatorSoup® Channel on YouTube to watch these helpful video demos on adding and subtracting fractions.

Jump to the below to see how you can add fractions without finding the LCD.

Jump to the below to see how you can subtract fractions without finding the LCD.

Multiply all numerators together

Multiply all denominators together

Reduce the result to lowest terms

Watch the CalculatorSoup video How to Multiply Fractions on YouTube!

See the below for an example of multiplying fractions by hand.

Rewrite the equation as in "Keep, Change, Flip"

Keep the first fraction

Change the division sign to multiplication

Flip the second fraction by switching the top and bottom numbers

Multiply all numerators together

Multiply all denominators together

Reduce the result to lowest terms

Watch the CalculatorSoup video How to Divide Fractions on YouTube!

See the below for an example of dividing fractions by hand.

There is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below.

You may find that it is easier to use these formulas than to do the math to find the least common denominator.

The formulas for multiplying and dividing fractions follow the same process as described above.

The formula for adding fractions is:

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

Example steps:

\( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \)

\( = \dfrac{14}{24} = \dfrac {7}{12} \)

The formula for subtracting fractions is:

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

Example steps:

\( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

The formula for multiplying fractions is:

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

Example steps:

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

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

The formula for dividing fractions is:

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

Example steps:

\( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \)

\( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \)

To perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator. Be sure to check out the CalculatorSoup® YouTube channel to see a video on How to Simplify Fractions.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.