Arithmetic : Fractions

Addition and Subtraction of Fractions

When fractions have the same (like) denominator, add or subtract the numerators and place the result over the common denominator. Then simplify the new fraction if required.

Example
Dad gave Steve 8 boxes of chocolates. Steve ate 1¾ boxes in January, ¾ box in February, and 1¼ boxes in March. How many boxes of chocolates did Steve consume and how many boxes remain?
Solution. ¾ boxes, and 4¼ boxes remain. 

Thus, Steve consumed 3

When fractions do not have the same denominator, addition and subtraction are performed after each fraction is expressed as an equivalent fraction with the (least) common denominator given by the LCM of the denominators. Using the least common multiple (LCM) typically reduces the computational effort.
For example to determine 2/3 + 4/5 − 11/9, the common denominator used is 45 (which is the LCM of 3, 5 and 9) and not 135 (which is 3 × 5 × 9). Next, each fraction is expressed as follows: 2/3 = 30/45, 4/5 = 36/45, and 11/9 = 55/45. Finally, 2/3 + 4/5 − 11/9 = (30 + 36 − 55)/45 = 11/45.