How to Simplify Fractions

By Hannah Richardson; Updated April 24, 2017
Reducing a fraction means dividing the numerator and denominator.

The directions of many worksheets, quizzes and tests will ask for fractions in their simplest form. To simplify a fraction, divide the top number, known as the numerator, and the bottom number, the denominator, by the greatest common factor. The GFC is the largest number that will divide into the numerator and denominator evenly.

Reducing Smaller Fractions

To reduce a smaller fraction, divide the numerator and the denominator by the GCF. If you have a pizza cut into 10 slices, and five of them were eaten, you only have one-half of a pizza left. To reduce 5/10, divide the numerator and the denominator by 5/5. Your final fraction will be 1/2. Five is the only number that will divide evenly into 5/10.

Reducing Larger Fractions

To divide the numerator and denominator by the GCF, you must know your multiplication tables, or start from the lowest numbers and work your way up. For example, if you have the fraction 36/60, you may know that 12 goes into both numbers evenly. If you divide 36 by 12, you get 3, and if you divide 60 by 12, you get 5. So, 36/60 reduced to its lowest form is 3/5.

Finding the GFC

If you do not recognize that 36 and 60 are divisible by 12, start with the lowest number you know goes into both and keep dividing until you can't divide anymore. Because 36 and 60 are even numbers, they are divisible by 2. If you divide 36/60 by 2/2, your newly reduced fraction is 18/30. Both of these numbers are even, so you can divide them, again, by 2. If you divide 18/30 by 2/2, the new fraction is 9/15. The fraction 9/15 has a numerator and denominator divisible by 3. If you divide 9/15 by 3/3, your final answer is 3/5.

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.