Basic Math and Pre-Algebra For Dummies (35 page)

 Remember from earlier in this chapter that placing a number in the denominator is similar to cutting a cake into that number of pieces. You can cut a cake into two, or ten, or even a million pieces. You can even cut it into one piece (that is, don't cut it at all). But you can't cut a cake into zero pieces. For this reason, putting 0 in the denominator — much like lighting an entire book of matches on fire — is something you should never, never do.

A mixed number is a combination of a whole number and a proper fraction added together. Here are some examples:

A mixed number is always equal to the whole number plus the fraction attached to it. So
means
means
, and so on.

When the numerator (top number) is less than the denominator (bottom number), the fraction is less than 1:

Fractions like these are called are called
proper fractions.
Positive proper fractions are always between 0 and 1. However, when the numerator is greater than the denominator, the fraction is greater than 1. Take a look:

Any fraction that's greater than 1 is called an
improper fraction
. Converting an improper fraction to a mixed number is customary, especially when it's the final answer to a problem.

 An improper fraction is always top heavy, as if it's unstable and wants to fall over. To stabilize it, convert it to a mixed number. Proper fractions are always stable.

Later in this chapter, I discuss improper fractions in more detail when I show you how to convert between improper fractions and mixed numbers.

Take a look at these three fractions:

If you cut three cakes (as I do earlier in this chapter) into these three fractions (see Figure 
9-4
), exactly half of the cake will be shaded, just like in Figure 
9-1
, no matter how you slice it. (Get it? No matter how you slice it? You may as well laugh at the bad jokes, too — they're free.) The important point here isn't the humor, or the lack of it, but the idea about fractions.

The fractions
are all equal in value. In fact, you can write a lot of fractions that are also equal to these. As long as the numerator is exactly half the denominator, the fractions are all equal to
— for example,