Basic Math and Pre-Algebra For Dummies (47 page)

Here's another example to work with:

This time, I put all the steps together:

With the problem set up like this, you just have to simplify the result:

In this case, you can reduce the fraction:

The easy way I show you in the preceding section works best when the numerators and denominators are small. When they're larger, you may be able to take a shortcut.

Before you subtract fractions with different denominators, check the denominators to see whether one is a multiple of the other (for more on multiples, see 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.
   

   For example, suppose you want to find
   . If you cross-multiply these fractions, your results are going to be much bigger than you want to work with. But fortunately, 80 is a multiple of 20, so you can use the quick way.
   

   First, increase the terms of
   so that the denominator is 80 (for more on increasing the terms of fractions, see Chapter
   9
   ):
   

   

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

   Here's the problem as a subtraction of fractions with the same denominator, which is much easier to solve:
   

   

   In this case, you don't have to reduce to lowest terms, although you may have to in other problems. (See Chapter
   9
   for more on reducing fractions.)
   

As I describe earlier in this chapter in “All Together Now: Adding Fractions,” you want to use the traditional way only as a last resort. I recommend that you use it only when the numerator and denominator are too large to use the easy way and when you can't use the quick trick.

To use the traditional way to subtract fractions with two different denominators, follow these steps:

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

   For example, suppose you want to subtract
   . Here's how to find the LCM of 8 and 14:
   

   

   So the LCM of 8 and 14 is 56.
   

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

   The denominators of both now are 56:
   

   

3. Substitute these two new fractions for the original ones and subtract as I show you earlier in “Subtracting fractions with the same denominator.”
   

   

   This time, you don't need to reduce because 5 is a prime number and 56 isn't divisible by 5. In some cases, however, you have to reduce the answer to lowest terms.