How to Subtract Fractions from Whole Numbers

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Subtracting fractions from whole numbers isn't as hard as it looks. There are two main ways to go about it: you can either convert the whole number into a fraction, or subtract 1 from that whole number and convert the 1 into a fraction with the same base as the fraction you're subtracting from it. Once you have two fractions with the same base, you can start to subtract. Both methods will help you.

Method 1
Method 1 of 2:

Subtracting Fractions from Whole Numbers

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  1. To do this, give the whole number a denominator of 1. [1]
    • Example:
  2. The original fraction's denominator is also the least common denominator (LCD) of the two fractions. Multiply the top and bottom of the "whole number fraction" by this number so the fractions have the same denominator. [2]
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  3. Now that the fractions have the same denominators, you can treat the numerators as a normal subtraction problem: [3]
    • =
  4. Convert to a mixed number (optional) . If your answer is an improper fraction, you may need to rewrite it as a mixed number: [4]
    • Example: Rewrite as a mixed number.
    • How many times does 5 fit evenly into 36? 5 x 7 = 35, so the whole number portion is 7 .
    • What's left over? The whole number portion is equivalent to , so solve - =
    • Combine the whole number and fraction: =
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Method 2
Method 2 of 2:

Alternate Method

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  1. Did you see how the method above converts the whole number into a fraction, then converts back to a mixed number at the end? This method lets you skip some of that so the fraction only involves smaller numbers.
  2. Convert improper fractions to mixed numbers . Skip this step if your fraction is not improper. (An improper fraction has a larger number on top than on bottom.) [5]
    • Example:
  3. For example, rewrite 5 as 4 + 1, or rewrite 22 as 21 + 1.
  4. At this point we're using the method above to solve the part of the problem in the form "1 - (fraction)". The other whole number will stay the same for the rest of the problem.
  5. As described above, multiply the top and bottom of your new fraction so it has the same denominator as the original fraction.
  6. Subtract the numerators to solve the fraction part of the equation.
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Practice Problems and Answers

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  • Question
    If the whole number is 1, then how am I supposed to make it into a fraction if 1/1 is 1 whole?
    Donagan
    Top Answerer
    As a simple example, let's say we're subtracting ¾ from 1. Convert 1 to 4/4. 4/4 - ¾ = ¼. If the whole number is something else, let's say 6, and you're subtracting ¾, convert the 6 to 24/4. 24/4 - ¾ = 21/4, or 5¼.
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    Not Helpful 32 Helpful 65
  • Question
    Can you help me with 5 5/6 - 2 2/3 step by step?
    WOOHP
    Community Answer
    1. 5 5/6 - 2 2/3 = 5 5/6 - 2 4/6 2. 5 5/6 - 2/4/6 = 3 1/6
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  • Question
    I'm confused. Can you please give an example?
    Karianna Wood
    Community Answer
    Take 3 - 2/7, for example. What over 7 is 3? 21, because 7 x 3 = 21. So 3 - 2/7 is the same as 21/7 - 2/7. What is 21/7 - 3/7? 21 - 3 = 18. So 21/7 - 3/7 = 18/7. (Optional) Simplify 18/7, which is 2 4/7. Does that help?
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      References

      1. ↑ https://virtualnerd.com/algebra-1/algebra-foundations/real-number-add-subtract/real-number-subtract/subtract-whole-number-from-fraction
      2. ↑ https://math.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Claassen_and_Ikeda)/10%3A_Appendix/10.02%3A_Fractions_and_Mixed_Numbers/10.2.03%3A_Adding_and_Subtracting_Fractions_and_Mixed_Numbers/10.2.3.02%3A_Subtracting_Fractions_and_Mixed_Numbers
      3. ↑ https://www.youtube.com/watch?v=RVMktMqUvn8
      4. ↑ https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/5.15/primary/lesson/improper-fractions-as-mixed-numbers-msm6/
      5. ↑ https://www.mathsisfun.com/improper-fractions.html

      About This Article

      Article Summary X

      To subtract a fraction from a whole number, start by converting the whole number to a fraction. Do this by giving the whole number a denominator of 1. For instance, if you’re subtracting 4/5 from 8, convert 8 into the fraction 8/1. Next, multiply the new fraction’s numerator and denominator by the denominator of the fraction that you’re subtracting. In our example, you’d multiply 8/1 by 5 to get 40/5. Now you have two like fractions—that is, two fractions that share the same denominator. Carry out the subtraction problem using just the numerators of the two fractions. In this example, 40-4 = 36. Write the difference between the two numerators over the common denominator to get 36/5. If you want to convert the answer to a mixed fraction, divide the numerator by the denominator. The quotient will become the new whole number, while the remainder will become the numerator of the new fraction. In this case, 36/5 = 7 with a remainder of 1, giving you the mixed fraction 7 and 1/5. For a trick to help subtract a fraction from a very large whole number, read on!

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