Basic Math and Pre-Algebra For Dummies (44 page)

This fraction can't be reduced further, so
is the final answer.

As you also discover in “Finding the sum of fractions with the same denominator,” sometimes when you add two proper fractions, your answer is an improper fraction:

If you have more work to do with this fraction, leave it as an improper fraction so that it's easier to work with. But if this is your final answer, you may need to turn it into a mixed number (see Chapter
9
for details).

 In some cases, you have to add more than one fraction. The method is similar, with one small tweak. For example, suppose you want to add
:

1. Start by multiplying the
   numerator
   of the first fraction by the
   denominators
   of all the other fractions.
   

   

2. Do the same with the second fraction, and add this value to the first.
   

   

3. Do the same with the remaining fraction(s).
   

   

   When you're done, you have the numerator of the answer.
   

4. To get the denominator, just multiply all the denominators together:
   

   

   As usual, you may need to reduce or change an improper fraction to a mixed number. In this example, you just need to change to a mixed number (see Chapter
   9
   for details):
   

   

I show you a way to add fractions with different denominators in the preceding section. It always works, and it's easy. So why do I want to show you another way? It feels like déjà vu.

In some cases, you can save yourself a lot of effort with a little bit of smart thinking. You can't always use this method, but you can use it when one denominator is a multiple of the other. (For more on multiples, see Chapter
8
.) Look at the following problem:

First, I solve it the way I show you in the preceding section:

Those numbers are pretty big, and I'm still not done because the numerator is larger than the denominator. The answer is an improper fraction. Worse yet, the numerator and denominator are both even numbers, so the answer still needs to be reduced.

With certain fraction addition problems, I can give you a smarter way to work. The trick is to turn a problem with different denominators into a much easier problem with the same denominator.