Why must we find a common denominator when add/subtract fractions?

2 answers

If you have fractions with different denominators, thn it's kinda like comparing apples and oranges.

By finding a common denominator, you convert both fractions into something that can be compared.

e.g.

2/5 + 1/2
= 4/10 + 5/10
= 9/10

Without finding that common denominator, you wouldn't be able to add the numbers together.
If you don't, it is like trying to add or subtract apples and oranges... Or monkeys and kideny beans.

Suppose you cut a pizza into 8 pieces. Each piece is an "eighth" of a pizza. If you add two pieces to one piece, you have three-eigths of the pizza. You cannot add 1/8 and 2/8 and get 3/16. Only the numerators get added, and the denominators must be the same when you do this.