How to Cancel Fractions

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Cancelling fractions is also called simplifying fractions. Basically, a fraction can be made simpler by dividing the top and bottom by the same number. Both the top and bottom must divide evenly for you to simplify the fraction. You can either find the greatest common factor to simplify the fraction or start simplifying by using prime numbers.

Method 1
Method 1 of 3:

Finding the Greatest Common Factor

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  1. A factor is one of the numbers that can be multiplied evenly by another number to get the third number. For instance, a factor of 6 is 2 because 2 times 3 equals 6. [1]
  2. The easiest way to write out all the factors is to begin with 1 and the number. [2]
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  3. [3] For instance, say the fraction is 14/28. The first two factors for 14 are 1 and 14. Place them an inch or so apart on a line. Connect them with an arch, so that you know that those two multiply together to make 14.
    • Move inward, making a factor rainbow by making an arch with each set of factors.
    • Divide by 2 next, which divides evenly because 2 multiplied by 7 equals 14. Therefore, the next two factors are 2 and 7. Connect those with an arch.
    • However, 3 does not divide into 14 evenly, and neither does 4 or 5. At this point, you've reached the middle of the factor rainbow, so the factors are 1, 2, 7, and 14.
  4. [4] The first two factors for 28 are 1 and 28; connect those two with an arch.
    • The next two are 2 and 14. Three does not divide evenly into 28. However, 4 does, so the next factors are 4 and 7. Neither 5 nor 6 divide evenly into 28, so you've reached the end of your factor rainbow for 28. Your factors are 1, 2, 4, 7, 14, and 28.
  5. The greatest common factor is the largest factor that both numbers share. For instance, in the two sets of factors you just found, 14 is shared between both sets, so it is the greatest common factor. [5]
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Method 2
Method 2 of 3:

Simplifying the Fraction

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  1. Place the 14 over the 28 with a line in between.
  2. Place a division side to the right of each number. To the right of the division signs, place a 14 for each number. Put an equal sign to the right of the equation. [6]
  3. Divide both 14 and 28 by 14. Fourteen divided by 14 is 1. Twenty-eight divided by 14 is 2. [7]
  4. To the right of the equal sign, right 1 above 2 with a line in between. Your final answer is 1/2. [8]
  5. Multiply 1/2 by 14 on top and bottom to see if you get 14/28. One times 14 is 14, and 2 times 14 is 28. Your answer is correct.
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Method 3
Method 3 of 3:

Guessing at Factors

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  1. For instance, you can choose 2 if both numbers are even. [9] Three is a good choice if you can add the digits together to a number divisible by three. For instance, 39 is divisible by 3 because 3 plus 9 equals 12, a number divisible by 3.
    • Try only using prime numbers, such as 2, 3, 5, 7, and so on, and moving from the smallest to the largest. [10]
  2. Say the fraction is 18/63. Eighteen is divisible by 2, but 63 is not. You need to move to the next prime, 3. Both 18 and 63 are divisible by 3. Divide 3 into both numbers; 18 divided by 3 is 6, while 63 divided by 3 is 21. Therefore, your new fraction 6/21. [11]
  3. Often, with this method, you'll need to simplify the fraction some more. Because 6/21 does not seem simplified, try dividing into it again. Both numbers are divisible by the same factor, 3. Six divided by 3 is 2, while 21 divided by 3 is 7. Your new fraction is 2/7. [12]
  4. The factors of 2 are just 1 and 2. The factors of 7 are 1 and 7. Therefore, the numbers do not share any more common factors. [13]
  5. You used the factors 3 and 3. Multiply them together to get the greatest common factor for the original fraction, 9. Now, check your answer by multiplying each number in your final fraction by 9. Two times 9 is 18, while 7 times 9 is 63, making the fraction 18/63. Your answer checks out.
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Expert Q&A

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  • Question
    How do I explain to my students what canceling or simplifying numbers in fractions are?
    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
    Expert Answer
    When discussing the concept of simplifying fractions by canceling out numbers, it's crucial to clarify its true meaning. Instead of merely instructing students to multiply by the denominator for elimination, we delve into the idea of reversing division. Take, for instance, a fraction like 5x divided by 6. If the objective is to isolate x, the approach involves undoing the division by multiplying it by 6. By highlighting the reciprocal relationship between multiplication and division, students come to understand that the actions of multiplying by 6 and dividing by 6 effectively negate each other, resulting in a simplified fraction equivalent to 1. This instructional method focuses on imparting fundamental concepts rather than relying solely on memorized rules. While providing practical procedures for struggling students, the ultimate aim is to cultivate a more profound comprehension of how mathematical operations interact and interconnect.
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  • Question
    What is 1/2 divided by 5/6?
    Community Answer
    1/2 divided by 5/6 is the same as 1/2 multiplied by 6/5, which is 6/10 or 3/5.
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  • Question
    What if it is 6/1 divided by 6/12?
    Ruby
    Top Answerer
    You can simplify 6/12 to 1/2, which makes the sum easier. From there you multiply by the inverse, in this case 6/1 × 2/1, which is 12/1 or just 12.
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      References

      1. ↑ https://www.mathsisfun.com/greatest-common-factor.html
      2. ↑ https://www.mathsisfun.com/greatest-common-factor.html
      3. ↑ https://www.khanacademy.org/math/cc-fourth-grade-math/imp-factors-multiples-and-patterns/imp-factors-and-multiples/v/finding-factors-of-a-number
      4. ↑ https://www.youtube.com/watch?v=vqYhXDFuF0M
      5. ↑ https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-gcf/v/greatest-common-divisor
      6. ↑ https://www.mathsisfun.com/simplifying-fractions.html
      7. ↑ https://www.mathsisfun.com/simplifying-fractions.html
      8. ↑ https://www.mathsisfun.com/simplifying-fractions.html
      9. ↑ https://www.youtube.com/watch?v=usxTJbQbAIg
      1. ↑ http://www.mathsisfun.com/simplifying-fractions.html
      2. ↑ https://www.khanacademy.org/math/cc-fourth-grade-math/imp-factors-multiples-and-patterns/imp-prime-and-composite-numbers/v/prime-numbers
      3. ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut34_complex.htm
      4. ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut7_factor.htm

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