Basic Math and Pre-Algebra For Dummies (34 page)

Figure 
9-3
shows a few more examples of ways to represent parts of the whole with fractions.

In each case, the numerator tells you how many pieces are shaded, and the denominator tells how many pieces there are altogether.

The fraction bar can also mean a division sign. In other words,
signifies 3 ÷ 4. If you take three cakes and divide them among four people, each person gets
of a cake.

Fractions have their own special vocabulary and a few important properties that are worth knowing right from the start. When you know them, you find working with fractions a lot easier.

The top number in a fraction is called the
numerator,
and the bottom number is called the
denominator.
For example, look at the following fraction:

In this example, the number 3 is the numerator, and the number 4 is the denominator. Similarly, look at this fraction:

The number 55 is the numerator, and the number 89 is the denominator.

When you flip over a fraction, you get its reciprocal. For example, the following numbers are reciprocals:

is its own reciprocal

When the denominator (bottom number) of a fraction is 1, the fraction is equal to the numerator by itself. Conversely, you can turn any whole number into a fraction by drawing a line and placing the number 1 under it. For example,

 When the numerator and denominator match, the fraction equals 1. After all, if you cut a cake into eight pieces and you keep all eight of them, you have the entire cake. Here are some fractions that equal 1:

When the numerator of a fraction is 0, the fraction is equal to 0. For example,

 The denominator of a fraction can never be 0. Fractions with 0 in the denominator are
undefined
— that is, they have no mathematical meaning.