# Fraction Calculator with Step by Step Details

## Add, Subtract, Multiply, and Divide Fractions

Enter your fraction, using a slash (/) symbol as the separator, then select your math operator.

 + - × ÷

## Solution

 2 3
+
 3 4
=1
 5 12

$$Find the least common denominator so that all of the denominators matchThe least common denominator of 3 and 4 is 12Find the multiple for each fraction that can be multiplied by the denominator to get the least common denominatorFind the multiple by dividing the least common denominator by each fractions denominatorFraction 1 Multiple: 12 ÷ 3 = 4Fraction 2 Multiple: 12 ÷ 4 = 3Multiply each fractions numerator and denominator by the multiple2 × 43 × 4+3 × 34 × 3=812+912Now that the denominators of each fraction are the same, simply add the numerators8 + 912=1712Reduce the fraction by finding the greatest common factor. The greatest common factor of 17 and 12 is 1Divide the numerator and denominator by the greatest common factor (1)17 ÷ 112 ÷ 1=1712Convert the fraction to a mixed fraction by finding the whole number and remainder17÷12=1R51712=1512$$

## Using the Fraction Calculator

Enter your fractions in the fields above and select the appropriate operator to add, subtract, multiply, or divide the fractions. The calculator will show it’s work and provide a detailed explanation of how it arrived at the answer. If you’re adding inch fractions see our inch fraction calculator. Also see our complete suite of fraction math tools.

There are 3 steps to adding fractions. In this example we will add 1/3 and 1/4.

### Find the Lowest Common Denominator

Find the lowest common denominator for both fractions denominators. The lowest common denominator is the smallest number that both denominators can be divided into evenly. For example, the common denominator of 3 and 4 is 12. Use our lowest common denominator calculator to find the common denominator for a set of fractions.

Find the multiple for each denominator that can be multiplied to reach the common denominator. This can be found by dividing the common denominator by each denominator. For example, if the denominator is 3 and the common denominator is 12, find the multiple like this: 12/3 = 4. If the denominator is 4 and the common denominator is 12, find the multiple like this: 12/4 = 3.

Multiply both the numerator and denominator by the multiple. For example, if the fraction is 1/3 and the multiple is 4, multiply the numerator by 4 and the denominator by 4, eg. 1 × 4 = 4 and 3 × 4 = 12. The fraction will be 4/12.

Once the denominators are all the same, simply add the numerators together and put them over the common denominator. For example, 4/12 + 3/12 = 7/12.

### Simplify the Fraction

The final step is to simplify the fraction. Start by finding the greatest common factor of both the numerator and the denominator. Learn more about finding the greatest common factor or use our factors calculator. Divide both the numerator and denominator by the common factor to reduce. Use our reduce fraction calculator to simplify a fraction and show the work needed to do so. Also see our equivalent fractions chart which shows the simplified fractions for common fractions. The greatest common factor of both 7 and 12 is 1, so the denominator cannot be simplified in the example above. The final result is 7/12.

## Subtracting Fractions

The steps to subtracting fractions are nearly identical to adding them. The only difference is that when subtracting you will subtract the numerators in step 2 above instead of adding them.

## Multiplying Fractions

There are 2 steps to multiplying fractions.

### Multiply the Numerators and Denominators

The first step is to multiply the numerators together and multiply the denominators together. For example, 2/3 × 3/4 = (2 × 3) / (3 × 4) = 6/12.

### Simplify the Fraction

As with adding and subtracting, the final step is to simplify the fraction. The greatest common factor of 6 and 12 is 6. Divide both the numerator and denominator by the greatest common factor. For example, to simplify 6/12: (6 ÷ 6) / (12 ÷ 6) = 1/2.

## Dividing Fractions

There are 2 steps to dividing fractions.

### Multiply the Numerators by the Denominators

The first step is to multiply the first numerator with the second denominator and multiply the second numerator by the first denominator. For example, 2/3 ÷ 3/4 = (2 × 4) / (3 × 3) = 8/9.

### Simplify the Fraction

As above, simplify the fraction by finding the greatest common factor and dividing the numerator and denominator by the common factor. In this example, 8/9 cannot be simplified.