How to subtract fractions with different denominators?

If you have fraction a/b and you want to subtract c/d this can only be done if the denominators are equal. You can get to a common denominator b*d by multiplying a/b by d (numerator and denominator) and c/d likewise by b.

Then you get

ad/bd - bc/bd = (ad-bc) / bd

example:

1/2 - 1/3 = (1*3) / (2*3) - (1*2) / (3*2) = 3/6 - 2/6 = 1/6

Sometimes the denominator can get large using this trick. Then it is better to find some common multiple of both denominators. For example, if the denominators are 6 and 9, you could go to 6*9=54, but 18 is much closer by and can be achieved by mulitplying by 3 and 2 respectively.

Example:

1/6 - 1/9 = 3/18 - 2/18 = 1/18

(=9/54 - 6/54 = 3/54 = 1/18)