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How to Reduce Fractions


Reducing fractions has a lot to do with finding a common factor. As a matter of fact, it has everything to do with finding a common factor (greatest common factor to be exact). If two numbers are given, their common factor is a number they both can be divided by. For instance: 6 and 63 have common factors (they both can be divided by): 1 and 3. Three is the greatest common factor. When reducing (which means simplifying) a fraction, you need to find the greatest common factor of numerator and denominator. More about it below.




If you are given a fraction, then to simplify (reduce) it you have to find common factors of numerator and denominator (as was mentioned in introduction). To reduce a fraction you have to divide numerator and denominator by the same number. Factor is a number that other number can be divided by (whole number), for instance: 5 is a factor of 20 (because 20 can be divided by 5).


Find factors of the numerator

Letís say the fraction we have to simplify is 9/12. We have to find the greatest common factor of 9 and 12. Letís find factors of 9 first. Any number has itself and 1 as factors i.e. any number has at least 2 factors. For 9 they are 1 and 9. To find other factors, start dividing 9 by other numbers starting with 2:

  • 9 canít be divided by 2, so 2 is not a factor.
  • 9 can be divided by 3 (we get 3), so 3 is a factor.
  • 9 canít be divided by 4, so 4 is not a factor.
  • a number (9) shouldnít be divided by numbers that are bigger than its half. Half of 9 is 4,5 which means we shouldnít divide it by anything bigger than 4,5 otherwise we will get number between 1 and 2, and we only need whole numbers.

So we got: factors 1, 3 and 9.


Simplify the fraction

9ís biggest factor is 9 so we can try and simplify fraction by 9. But you canít divide 12 by 9. The second biggest factor is 3. You actually can divide 12 by 3 which means 3 is the biggest common factor of 9 and 12. Divide numerator and denominator by 3 to reduce fraction:

9: 3 = 3

12: 3 = 4

9/12 = 3/4


  • Donít forget to check if you made all the calculations right.
  • Donít divide numerator and denominator by different numbers - it should always be the same number.
  • Donít forget that factors are always whole numbers.
  • Don't use online tools to simplify fractions: you will learn nothing that way.



If you are still having trouble reducing fractions, watch the video embedded above. Remember that you should always try to simplify fraction by numerator itself: if your fraction is 3/12 you can simplify it by 3 and get 1/4. If you canít divide denominator by numerator, then use our guidelines above and find the greatest common factor.

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