NUMBAT OER - Open Educational Resources

2.2 Subtracting fractions

The methods used to subtract fractions are the same as are used to add them together. If the denominator is the same for both fractions:

5  -  3  =  (5 - 3)  =  2  =  1
8 8 8 8 4

If the two fractions do not have an obvious common denominator, the two denominators are multiplied together:

12  -  11  =  (12 × 7)  -  (11 × 6)  =  (84 - 66)  =  18  =  3
6 7 (6 × 7) (7 × 6) 42 42 7

This is a slightly contrived example designed to yield an answer that simplifies easily. In this case it would have been simpler to have started by converting both fractions to mixed numbers:

12  -  11  = 2 - 1  4  = 1 4  =  3
6 7 7 7 7

The choice of whether to work with improper fractions or mixed numbers will be based on the sizes of numerators and denominators.