How to Subtract Fractions

PDF download Download Article
PDF download Download Article

Subtracting fractions may look a little confusing at first but with some basic multiplication and division, you'll be ready for simple subtraction. If the fractions are proper, ensure that the denominators are the same before you subtract the numerators. If the fractions are mixed and you have whole numbers, turn them into improper fractions. You'll also need to make sure the denominators are the same before subtracting the numerators.

Things You Should Know

  • First, find a common denominator for both fractions. Then, adjust the numerators as needed.
  • For example: 3/4 and 1/3 have a common denominator of 12. The fractions would then become 9/12 and 4/12.
  • Now, subtract (but only the numerators). So 9/12 - 4/12 = 5/12.
Method 1
Method 1 of 2:

Finding the Least Common Multiple and Subtracting

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/c\/cc\/Subtract-Fractions-Step-1-Version-3.jpg\/v4-460px-Subtract-Fractions-Step-1-Version-3.jpg","bigUrl":"\/images\/thumb\/c\/cc\/Subtract-Fractions-Step-1-Version-3.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-1-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    List multiples of the denominators if necessary. If the denominators of your fractions aren't the same, you'll need to make them the same. List the multiples of each denominator so you can find a number that both denominators have in common. For example, if you're doing 1/4 - 1/5, list all the multiples of 4 and 5 to find 20. [1]
    • Since the multiples of 4 include 4, 8, 12, 16, 20 and the multiples of 5 include 5, 10, 15, and 20, 20 is the lowest number they have in common.
    • If the denominators are already the same, you can skip straight to subtracting the numerators.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a1\/Subtract-Fractions-Step-2-Version-3.jpg\/v4-460px-Subtract-Fractions-Step-2-Version-3.jpg","bigUrl":"\/images\/thumb\/a\/a1\/Subtract-Fractions-Step-2-Version-3.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-2-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Once you've found the lowest common multiple for your unlike fractions, multiply the fraction so the denominator becomes the least common multiple. [2]
    • For example, multiply 1/4 by 5 to get a denominator of 20. You'll also need to multiply the numerator by 5, so 1/4 becomes 5/20.
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/af\/Subtract-Fractions-Step-3-Version-3.jpg\/v4-460px-Subtract-Fractions-Step-3-Version-3.jpg","bigUrl":"\/images\/thumb\/a\/af\/Subtract-Fractions-Step-3-Version-3.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-3-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Keep in mind that if you adjust 1 of the fractions in the problem, you'll need to adjust all of the fractions so they're equivalent. [3]
    • For example, if you've adjusted 1/4 to become 5/20, multiply the 1/5 by 4 to get 4/20. The original problem 1/4 - 1/5 becomes 5/20 - 4/20.
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/9f\/Subtract-Fractions-Step-4-Version-3.jpg\/v4-460px-Subtract-Fractions-Step-4-Version-3.jpg","bigUrl":"\/images\/thumb\/9\/9f\/Subtract-Fractions-Step-4-Version-3.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-4-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Subtract the numerators and keep the denominator the same. If you started with denominators that were the same or you made equivalent fractions with the same denominator, subtract the numerators. Write the answer and then write the denominator underneath it. [4]
    • Remember not to subtract the denominators as well.
    • For example, 5/20 - 4/20 = 1/20.
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f1\/Subtract-Fractions-Step-5-Version-3.jpg\/v4-460px-Subtract-Fractions-Step-5-Version-3.jpg","bigUrl":"\/images\/thumb\/f\/f1\/Subtract-Fractions-Step-5-Version-3.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-5-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Once you have your answer, check to see if you can simplify it. Find the greatest common factor of the numerator and denominator and divide both numbers by it. For example, if you had an answer of 24/32, the greatest common factor is 8. Divide both numbers by 8 to get 3/4. [5]
    • Depending on your answer, you may not be able to simplify it. For example, 1/20 can't be reduced further.
    EXPERT TIP

    Joseph Meyer

    Math Teacher
    Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
    Joseph Meyer
    Math Teacher

    Simplifying a fraction just changes the way the fraction is written. To simplify a fraction, you can cancel out the greatest common factor from the numerator and denominator or convert an improper fraction to a mixed number. This doesn't change the inherent value of the fraction.

    6. Advertisement
Method 2
Method 2 of 2:

Subtracting Mixed Numbers

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/63\/Subtract-Fractions-Step-6-Version-3.jpg\/v4-460px-Subtract-Fractions-Step-6-Version-3.jpg","bigUrl":"\/images\/thumb\/6\/63\/Subtract-Fractions-Step-6-Version-3.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-6-Version-3.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Change the mixed numbers into improper fractions. Mixed numbers are whole numbers with fractions. To make it easier to subtract, turn the whole numbers into fractions. This will mean that the numerator will be larger than the denominator. [6]
    • For example, 2 3/4 - 1 1/7 will become 11/4 - 8/7.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2c\/Subtract-Fractions-Step-7-Version-2.jpg\/v4-460px-Subtract-Fractions-Step-7-Version-2.jpg","bigUrl":"\/images\/thumb\/2\/2c\/Subtract-Fractions-Step-7-Version-2.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-7-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Find the lowest common multiple of both denominators so you can make a like denominator for the fractions. For example, if you're doing 11/4 - 8/7, list all the multiples of 4 and 7 to find 28. [7]
    • Since the multiples of 4 include 4, 8, 12, 16, 20, 24, 28 and the multiples of 7 include 7, 14, 21, and 28, 28 is the lowest number they have in common.
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/39\/Subtract-Fractions-Step-8-Version-2.jpg\/v4-460px-Subtract-Fractions-Step-8-Version-2.jpg","bigUrl":"\/images\/thumb\/3\/39\/Subtract-Fractions-Step-8-Version-2.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-8-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    You'll need to make denominators become the lowest common multiple. To do this, multiply the entire fraction. [8]
    • For example, to make the denominator for 11/4 become 28, multiply the fraction by 7. The fraction will become 77/28.
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/c\/c1\/Subtract-Fractions-Step-9-Version-2.jpg\/v4-460px-Subtract-Fractions-Step-9-Version-2.jpg","bigUrl":"\/images\/thumb\/c\/c1\/Subtract-Fractions-Step-9-Version-2.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-9-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    If you've changed the denominator for 1 of the fractions in your problem, you'll need to adjust the other fractions so their ratios are still equal to the original problem. [9]
    • For example, if you've adjusted 11/4 to become 77/28, multiply the 8/7 by 4 to get 32/28. The problem 11/4 - 8/7 becomes 77/28 - 32/28.
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/78\/Subtract-Fractions-Step-10-Version-2.jpg\/v4-460px-Subtract-Fractions-Step-10-Version-2.jpg","bigUrl":"\/images\/thumb\/7\/78\/Subtract-Fractions-Step-10-Version-2.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-10-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    If the denominators were the same to begin with or you've made equivalent fractions, you can now subtract the numerators. Write the answer and place it over the denominator. Remember not to subtract the denominator. [10]
    • For example, 77/28 - 32/28 = 45/28.
  6. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a1\/Subtract-Fractions-Step-11-Version-2.jpg\/v4-460px-Subtract-Fractions-Step-11-Version-2.jpg","bigUrl":"\/images\/thumb\/a\/a1\/Subtract-Fractions-Step-11-Version-2.jpg\/aid2169629-v4-728px-Subtract-Fractions-Step-11-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>\u00a9 2024 wikiHow, Inc. All rights reserved. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This image is <b>not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. This image may not be used by other entities without the express written consent of wikiHow, Inc.<br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    You'll probably need to change the answer into a mixed number . Start by dividing the numerator by the denominator to get a whole number. Then write how many parts you have left. This number will be the numerator. Place the numerator over the same denominator. Reduce this fraction if you can. [11]
    • For example, 45/28 becomes 1 17/28 because 28 goes into 45 1 time and has 17 parts of 28 left over.
    7. Advertisement

Practice Problems and Answers

Community Q&A

Search
Add New Question
  • Question
    How do I subtract a fraction from a whole number?
    Community Answer
    Take the LCM of denominator of both the fractions (the denominator of whole number is one). Then, in both the numbers divide the LCM by the denominator and multiply the result by the numerator. Subtract the numbers in numerators and you will get your answer.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 30 Helpful 54
  • Question
    Can you help me solve 1/4 - 5/6 please?
    Community Answer
    1/4 - 5/6 = -7/12. That is a negative number.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 78 Helpful 124
  • Question
    How can I learn to subtract a mixed fractions?
    JulyAtNight
    Community Answer
    Turn them into improper fractions. Then you can make the denominator the same to subtract them. Don't forget to simplify if necessary.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 34 Helpful 54
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      Tips

      • If you prefer, you can work mixed numbers without turning them into improper fractions. Subtract the integers and then subtract the numerators from the fractions if they have like denominators.
        Thanks
      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Submit
      Thanks for submitting a tip for review!
      Advertisement

      You Might Also Like

      How Do I Measure ¾ Cup?
      Easy-to-Follow Methods for Adding Fractions
      How to
      Type Fractions
      How to
      Multiply Fractions With Whole Numbers
      How to
      Solve Fraction Questions in Math
      How to
      Add Fractions With Unlike Denominators
      How to
      Divide Mixed Fractions
      How to
      Order Fractions From Least to Greatest
      How to
      Find the Least Common Denominator
      How to
      Calculate Fractions
      How to
      Divide Fractions by a Whole Number
      How to
      Divide a Whole Number by a Fraction
      How to
      Divide Fractions by Fractions
      How to
      Do Fractions
      Advertisement

      References

      1. ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Proper_Fractions.pdf
      2. ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Proper_Fractions.pdf
      3. ↑ https://www.mathsisfun.com/fractions_subtraction.html
      4. ↑ https://www.mathsisfun.com/fractions_subtraction.html
      5. ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Proper_Fractions.pdf
      6. ↑ https://www.mathsisfun.com/numbers/fractions-mixed-addition.html
      7. ↑ https://www.mathsisfun.com/numbers/fractions-mixed-addition.html
      8. ↑ https://www.mathsisfun.com/equivalent_fractions.html
      9. ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Mixed_Numbers_and_Improper_Fractions.pdf
      1. ↑ https://www.mathsisfun.com/numbers/fractions-mixed-addition.html
      2. ↑ https://www.georgebrown.ca/sites/default/files/uploadedfiles/tlc/_documents/Adding_and_Subtracting_Mixed_Numbers_and_Improper_Fractions.pdf

      About This Article

      Article Summary X

      To subtract fractions, first make sure the denominators are the same. If they're not, find the least common multiple of the 2 denominators. Then, multiply each denominator so that it equals the least common multiple. Next, multiply the numerator by the same number you multiplied the denominator by. Finally, subtract the numerators and leave the denominator as the least common multiple. To learn how to subtract mixed numbers, scroll down!

      Did this summary help you?
      In other languages
      Thanks to all authors for creating a page that has been read 684,139 times.

      Reader Success Stories

      • Miss anomonus Unnone

        Sep 18, 2020

        "wikiHow has helped me in school, fashion, and everything else. I am forever grateful, thanks wikiHow."
      More reader stories Hide reader stories
      Share your story

      Did this article help you?

      Advertisement