How to Subtract Fractions with Common Denominators

As with addition, subtracting fractions that have the same denominator (also called a common denominator) is very simple: Just subtract the second numerator from the first and keep the denominator the same. In some cases, you may have to reduce the answer to lowest terms.

Subtracting fractions that have different denominators takes a bit more work. You need to increase the terms of one or both fractions so both fractions have the same denominator. The easiest way to do this is to use cross-multiplication:

  1. Cross-multiply the two fractions and create two fractions that have a common denominator.

  2. Subtract the results from Step 1.

When one denominator is a factor of the other, you can use a quick trick to find a common denominator: Increase only the terms of the fraction with the lower denominator to make both denominators the same.

Sample questions

  1. Find

    image0.jpg image1.jpg

    The denominators are both 6, so subtract the numerators (5 and 1) to get the new numerator, and keep the denominator the same:

    image2.jpg

    The numerator and denominator are both even numbers, so you can reduce the fraction by a factor of 2:

    image3.jpg
  2. Find

    image4.jpg image5.jpg

    The denominators are different, but because 28 is a multiple of 7, you can use the quick trick described earlier. Increase the terms of 6/7 so that its denominator is 28; because 28 = 7 x 4, multiply both the numerator and denominator by 4:

    image6.jpg

    Now both fractions have the same denominator, so subtract the numerators and keep the same denominator:

    image7.jpg

    Both the numerator and denominator are divisible by 7, so you can reduce this fraction by a factor of 7:

    image8.jpg

Practice questions

  1. Subtract

    image9.jpg
  2. Find

    image10.jpg
  3. Solve

    image11.jpg

Following are answers to the practice questions:

  1. image12.jpg

    The denominators are the same, so subtract the numerators and keep the same denominator:

    image13.jpg

    The numerator and denominator are both even, so reduce this fraction by a factor of 2:

    image14.jpg
  2. image15.jpg

    The denominators are different, so change them to a common denominator by cross-multiplying. The new numerators are 4 x 3 = 12 and 1 x 5 = 5:

    image16.jpg

    The new denominators are 5 x 3 = 15:

    image17.jpg

    Now you can subtract:

    image18.jpg
  3. image19.jpg

    The denominators are different, but 6 is a factor of 12, so you can use the quick trick. Increase the terms of

    image20.jpg

    so that the denominator is 12, multiplying both the numerator and the denominator by 2:

    image21.jpg

    Now the two fractions have the same denominator, so you can subtract easily:

    image22.jpg

    The numerator and denominator are both divisible by 3, so reduce the fraction by a factor of 3:

    image23.jpg
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