Question

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

Answer 1

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.

Answer 2

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.