Q: A beginning math student asked, "Why do you need a common denominator
when adding fraction but not when multiplying?"

A: Because when you add things, they must be of the same kind. For example,
apples can be added to apples to find a total number of apples.

When you multiply things they can be of different kinds, although different
rules apply. For example, the number of apples that fit in a crate can be
multiplied by the number of crates to get the total number of apples.

A "common denominator" follows similar rules. Some number of
twelfths is of the same kind as some other number of twelfths, so they can be
added. For example, 4/12 can be added to 3/12 to give 7/12. Do you see? Just as
you can add apples to apples to get a total number of apples, you can add
twelfths to twelfths to get a total number of twelfths.

### Related pages in this website

LCM and GCD - Least Common Multiple and
Greatest Common Divisor... A common denominator is a common multiple of
the original denominators, so the LCM is a good common denominator.

Word
Problems - Translating the English problem into mathematical notation,
substitution, percents, arithmetic using fractions, Distance = Rate * Time,
compound interest, "work" problems, "related rates" problems, linear
Programming, and more.

The webmaster and author of this Math Help site is
Graeme McRae.