How to Subtract, Add & Simplify Fractions

By Usha Dadighat; Updated April 24, 2017
Fractions show parts of a whole.

Working with fractions is a basic mathematical principle needed for understanding further math topics and real world applications. Adding and subtracting fractions work on the same principle. Simplifying fractions before completing any other operations makes the process easier and lets you see if you need to complete any further steps. The simplest form of a fraction is the standard form of the fraction used for both common fractions and mixed numbers.

Adding and Subtracting Fractions

Determine if the two fractions have a common denominator. For example, the fractions 1/3 and 2/3 have a common denominator and the fractions 1/14 and 1/5 do not.

Set both fractions to have a lowest common denominator. If adding or subtracting more than two fractions, complete the operation on two fractions at a time before moving on to the next fraction. The denominator is the lower number of a fraction. To find the lowest common denominator, multiply the denominators of both of the fractions together and set this number as the new denominator. Multiply the numerator, or top number, of the first fraction by the denominator of the second fraction and multiply the numerator of the second fraction by the denominator of the first fraction.

Add or subtract the numerators of the fractions together. Do not add or subtract the denominators. Simplify the fraction if needed.

Simplifying Fractions

Find a number that goes evenly into both the numerator and denominator of the fraction. For example, 5 goes into both the numerator and denominator of 15/20.

Divide both parts of the fraction separately by the common number, or factor. For example, you could divide both parts of 20/30 by 2 to get 10/15.

Repeat until the parts of the fraction cannot be divided by the same number. For example, divide 20/30 by 2 to get 10/15, then by 5 to get 2/3, which is the simplified version of the fraction.

About the Author

Usha Dadighat has been writing since 2008. She earned a Bachelor of Science in computer science and a minor in psychology from the Missouri University of Science and Technology in December 2010. She currently works as a software development engineer and has extensive technical writing experience.