Basic Math and Pre-Algebra For Dummies (37 page)

As another example, here's how you reduce the fraction
:

This time, cross out two 2s from both the top and the bottom as common factors. The remaining 2s on top and the 5s on the bottom aren't common factors. So the fraction
reduces to
.

Here's an easier way to reduce fractions when you get comfortable with the concept:

1. If the numerator (top number) and denominator (bottom number) are both divisible by 2 — that is, if they're both even — divide both by 2.
   

   For example, suppose you want to reduce the fraction
   . The numerator and the denominator are both even, so divide them both by 2:
   

   

2. Repeat Step 1 until the numerator or denominator (or both) is no longer divisible by 2.
   

   In the resulting fraction, both numbers are still even, so repeat the first step again:
   

   

3. Repeat Step 1 using the number 3, and then 5, and then 7, continuing testing prime numbers until you're sure that the numerator and denominator have no common factors.
   

   Now, the numerator and the denominator are both divisible by 3 (see Chapter
   7
   for easy ways to tell if one number is divisible by another), so divide both by 3:
   

   

   Neither the numerator nor the denominator is divisible by 3, so this step is complete. At this point, you can move on to test for divisibility by 5, 7, and so on, but you really don't need to. The numerator is 3, and
   it obviously isn't divisible by any larger number, so you know that the fraction
   reduces to
   .
   

In “Knowing the Fraction Facts of Life,” I tell you that any fraction whose numerator is greater than its denominator is an improper fraction. Improper fractions are useful and easy to work with, but for some reason, people just don't like them. (The word
improper
should've tipped you off.) Teachers especially don't like them, and they really don't like an improper fraction to appear as the answer to a problem. However, they love mixed numbers. One reason they love them is that estimating the approximate size of a mixed number is easy.

For example, if I tell you to put
of a gallon of gasoline in my car, you probably find it hard to estimate roughly how much that is: 5 gallons, 10 gallons, 20 gallons?

But if I tell you to get
gallons of gasoline, you know immediately that this amount is a little more than 10 but less than 11 gallons. Although
is the same as
, knowing the mixed number is a lot more helpful in practice. For this reason, you often have to convert improper fractions to mixed numbers.