Basic Math and Pre-Algebra For Dummies (45 page)

 Before you add two fractions with different denominators, check the denominators to see whether one is a multiple of the other (for more on multiples, flip to Chapter
8
). If it is, you can use the quick trick:

1. Increase the terms of the fraction with the smaller denominator so that it has the larger denominator.
   

   Look at the earlier problem in this new way:
   

   

   As you can see, 12 divides into 24 without a remainder. In this case, you want to raise the terms of
   so that the denominator is 24:
   

   

   I show you how to do this kind of problem in Chapter
   9
   . To fill in the question mark, the trick is to divide 24 by 12 to find out how the denominators are related; then multiply the result by 11:
   

   

2. Rewrite the problem, substituting this increased version of the fraction, and add as I show you earlier in “Finding the sum of fractions with the same denominator.”
   

   Now you can rewrite the problem this way:
   

   

   As you can see, the numbers in this case are much smaller and easier to work with. The answer here is an improper fraction; changing it to a mixed number is easy:
   

   

In the two preceding sections, I show you two ways to add fractions with different denominators. They both work great, depending on the circumstances. So why do I want to show you yet a third way? It feels like déjà vu all over again.

The truth is that I don't want to show you this way. But they're
forcing
me to. And you know who
they
are, don't you? The man — the system — the powers that be. The ones who want to keep you down in the mud, groveling at their feet. Okay, so I'm exaggerating a little. But let me impress on you that you don't have to add fractions this way unless you really want to (or unless your teacher insists on it).

 Here's the traditional way to add fractions with two different denominators:

1. Find the least common multiple (LCM) of the two denominators (for more on finding the LCM of two numbers, see Chapter
   8
   ).
   

   Suppose you want to add the fractions
   . First find the LCM of the two denominators, 4 and 10. Here's how to find the LCM using the multiplication table method:
   

   • Multiples of 10:
     10, 20, 30, 40
     
   • Multiples of 4:
     4, 8, 12, 16, 20
     

   So the LCM of 4 and 10 is 20.
   

2. Increase the terms of each fraction so that the denominator of each equals the LCM (for more on how to do this, see Chapter
   9
   ).
   

   Increase each fraction to higher terms so that the denominator of each is 20.
   

   

3. Substitute these two new fractions for the original ones and add as I show you earlier in “Finding the sum of fractions with the same denominator.”
   

   At this point, you have two fractions that have the same denominator:
   

   

   When the answer is an improper fraction, you still need to change it to a mixed number: