Brush up your maths: answer to adding and subtracting fractions exercise

Exercise:

Add 3/4 and 2/3 then subtract 1/6.

First we will do the addition. The highest common factor of 4 and 3 is 12, so the lowset common multiple is 4 × 3 = 12. This is the lowest common denominator.

      3       2           3 × 3       2 × 4           9       8             9 + 8           17
      –– + ––   =   ––––– + –––––   =   ––– + –––   =   –––––   =   –––
      4       3           4 × 3       3 × 4           12     12             12             12

Now we will subtract 1/6. The factors of 12 are 1, 2, 3, 4, 6, and 12, the factors of 6 are 1, 2, 3, and 6. The lowest common denominator is 6 × 2 = 12. So we have:

      17     1           17 × 1       1 × 2           17       2             17 – 2         15             5
      –– – ––   =   –––––– – –––––   =   ––– – ––––   =   –––––   =   –––   =   –––
      12     6           12 × 1       6 × 2           12     12               12             12             4

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Last updated: 13 January, 2012.

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