Fractions – Subtracting Mixed Numbers

By Stuart Ackerman

    When fractions are presented as mixed numbers such as 5½ and 3¼, it is easier to subtract them in two parts. 

     So when we subtract 5½ - 3¼, we start off by subtracting the whole numbers (or integers) 5-3=2.

     Then, we subtract the fractions.

½ - ¼ = ¼

     We combine the whole number 2, with the new fraction ¼, and the answer is 2¼.

     We can also change the mixed number into an improper fraction.

2¼ becomes

                4 x 2 = 8

               8 + 1 = 9

                9

           4

Let’s review the steps we took:

1.    First subtract the whole numbers (integers) in the mixed fractions.

2.    Subtract the fractions (you must know how to find a common denominator).

3.    Combine the new mixed number with the new fraction.

If you wish to convert the new mixed number into an improper fraction, you must:

1.    Multiply the denominator by the mixed number (e.g. 4 x the big 2)

2.    Add the result of the denominator x the mixed number (which was 8) to the numerator (little 1) to get 9.

3.    Present the fraction over the original denominator (4).

It is important for students to be proficient at finding common denominators and changing mixed numbers into improper fractions before learning to subtract mixed numbers.

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