How to Find the Perimeter With Fractions

By Hannah Richardson; Updated April 25, 2017
The perimeter is the total distance around a shape.

The perimeter of a shape is the total distance around it. To find the perimeter, add every side of the shape to find the total. If one or more sides are fractions, you will have to follow the rules for adding fractions to add each side and find the perimeter.

Identify All Sides

No matter what the shape is, add all sides to find the perimeter. If the shape has equal sides, there are formulas to simplify the process. To find the perimeter of an equilateral triangle, multiply the side length by 3. To find the perimeter of a square, multiply the side length by 4. If the shape is a rectangle, add the long side and the short side, and multiply that total by two: P = 2(x+y). These formulas still work with fractions. If your shape is a polygon with sides as fractions, follow the rules for adding fractions to find the perimeter.

Find the Common Denominator

Before you can add fractions, you must find a common denominator. The common denominator will be the Least Common Multiple (LCM): the smallest number that all of your denominators will divide into evenly. For example, if you have a 4-sided polygon with sides 1/2, 1/3, 3/4 and 5/6, you will have to change all of the denominators so they are all the same. Each of these denominators can divide evenly into 12, so 12 will be your new denominator. To change the fraction, multiply the numerator and denominator by the same number to keep the value the same. Multiply 1/2 by 6/6 to get 6/12. Multiply 1/3 by 4/4 to get 4/12. Multiply 2/4 by 3/3 to get 6/12. Multiply 5/6 by 2/2 to get 10/12. Now, every denominator is the same.

Use the Numerators

Once the denominators are the same, keep the denominator and only add the numerators. If your common denominator is 12, that will be the denominator of your answer. To add 6/12, 4/12, 6/12, and 10/12, add 6+4+6+10 and put the answer over 12. Your total, and your perimeter, will be 26/12.

If you have a shape with even sides and use a multiplication formula, only multiply the numerator. For example, to find the perimeter of a square with the formula P=4x, and your side length is 3/4, multiply 3x2 and put the product over 4. Your perimeter will be 6/4.

Simplify Your Results

After you find the perimeter, simplify your total fraction. If your total is an improper fraction, follow your directions to know whether to leave it as improper or turn it into a mixed number. To simply 26/12, for example, divide the numerator and denominator by the same number. Both 26 and 12 are divisible by 2, and after you divide, you will have 13/6. If your directions say to turn this into a mixed number, divide 6 into 13 and write your remainder as a fraction. Six will go into 13 two times with a remainder of 1. Put that remainder over your denominator for a final answer of 2 1/6.

About the Author

Hannah Richardson has a Master's degree in Special Education from Vanderbilt University and a Bacheor of Arts in English. She has been a writer since 2004 and wrote regularly for the sports and features sections of "The Technician" newspaper, as well as "Coastwach" magazine. Richardson also served as the co-editor-in-chief of "Windhover," an award-winning literary and arts magazine. She is currently teaching at a middle school.