Name: rebecca

Who is asking: Teacher
Level: Elementary

Question:
When we add fractions, we find a common denominator and add the numerators When we multiply fractions, we simply multiply both numerators and denominators with no regard to commonality.

1. Why do we not have to find a common denominator when multiplying?

2. Why do we multiply both numerators and denominators?

1. The general rule for adding is YOU MUST ADD LIKE QUANTITIES. You can't add "thirds" and "fifths" for the same reason you can't add "apples" and "elephants" -- it just doesn't make any sense. But the same fraction has many different names so that, unlike apples and elephants, you can change "thirds" and "fifths" to their equals that happen to have a common name such as "fifteenths" or "thirtieths".

2. If you want the product to make numerical sense you must do what the numbers tell you to do. "Two-thirds" of x means that you divide x into three equal pieces and take two of those pieces. If x happens to be 5/6 the instructions given by (2/3)*(5/6) are take your "five-sixths" and divide it into three equal pieces, each of size "five-eighteenths". Then 2 sets of 5 makes 10 "eighteenths".