Basic Math and Pre-Algebra For Dummies (42 page)

Dividing fractions is just as easy as multiplying them. In fact, when you divide fractions, you really turn the problem into multiplication.

 To divide one fraction by another, multiply the first fraction by the reciprocal of the second. (As I discuss in Chapter
9
, the
reciprocal
of a fraction is simply that fraction turned upside down.)

For example, here's how you turn fraction division into multiplication:

As you can see, I turn
into its reciprocal —
— and change the division sign to a multiplication sign. After that, just multiply the fractions as I describe in “Multiplying numerators and denominators straight across”:

 As with multiplication, in some cases, you may have to reduce your result at the end. But you can also make your job easier by canceling out equal factors. (See the preceding section.)

When you add fractions, one important item to notice is whether their denominators (the numbers on the bottom) are the same. If they're the same — woo-hoo! Adding fractions that have the same denominator is a walk in the park. But when fractions have different denominators, adding them becomes a tad more complex.

To make matters worse, many teachers make adding fractions even more difficult by requiring you to use a long and complicated method when, in many cases, a short and easy one will do.

In this section, I first show you how to add fractions with the same denominator. Then I show you a foolproof method for adding fractions when the denominators are different. It always works, and it's usually the simplest way to go. After that, I show you a quick method that you can use only for certain problems. Finally, I show you the longer, more complicated way to add fractions that usually gets taught.

 To add two fractions that have the same denominator (bottom number), add the numerators (top numbers) and leave the denominator unchanged.

For example, consider the following problem:

As you can see, to add these two fractions, you add the numerators (1 + 2) and keep the denominator (5).

Why does this work? Chapter
9
tells you that you can think about fractions as pieces of cake. The denominator in this case tells you that the entire cake has been cut into five pieces. So when you add
, you're really adding one piece plus two pieces. The answer, of course, is three pieces — that is,
.

Even if you have to add more than two fractions, as long as the denominators are all the same, you just add the numerators and leave the denominator unchanged:

Sometimes when you add fractions with the same denominator, you have to reduce it to lowest terms (to find out more about reducing, flip to Chapter
9
). Take this problem, for example: