How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

  2. Find

    How to add and subtract fractions with the same denominator

    How to add and subtract fractions with the same denominator

    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:

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

Practice questions

  1. Subtract

    How to add and subtract fractions with the same denominator

  2. Find

    How to add and subtract fractions with the same denominator

  3. Solve

    How to add and subtract fractions with the same denominator

Following are answers to the practice questions:

  1. How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

  2. How to add and subtract fractions with the same denominator

    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:

    How to add and subtract fractions with the same denominator

    The new denominators are 5 x 3 = 15:

    How to add and subtract fractions with the same denominator

    Now you can subtract:

    How to add and subtract fractions with the same denominator

  3. How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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

    How to add and subtract fractions with the same denominator

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