Basic Math and Pre-Algebra For Dummies (43 page)

The numerator and the denominator are both even, so you know they can be reduced:

In other cases, the sum of two proper fractions is an improper fraction. You get a numerator that's larger than the denominator when the two fractions add up to more than 1, as in this case:

If you have more work to do with this fraction, leave it as an improper fraction so that it's easier to work with. But if this is your final answer, you may need to turn it into a mixed number (I cover mixed numbers in Chapter
9
):

 When two fractions have the same numerator, don't add them by adding the denominators and leaving the numerator unchanged.

When the fractions that you want to add have different denominators, adding them isn't quite as easy. At the same time, it doesn't have to be as hard as most teachers make it.

Now, I'm shimmying out onto a brittle limb here, but this needs to be said: Fractions can be added in a very simple way. It always works. It makes adding fractions only a little more difficult than multiplying them. And as you move up the math food chain into algebra, it becomes the most useful method.

So why doesn't anybody talk about it? I think it's a clear case of tradition being stronger than common sense. The traditional way to add fractions is more difficult, more time-consuming, and more likely to cause an error. But generation after generation has been taught that it's the right way to add fractions. It's a vicious cycle.

But in this book, I'm breaking with tradition. I first show you the easy way to add fractions. Then I show you a quick trick that works in a few special cases. Finally, I show you the traditional way to add fractions.

 At some point in your life, I bet some teacher somewhere told you these golden words of wisdom: “You can't add two fractions with different denominators.” Your teacher was wrong! Here's the way to do it:

1. Cross-multiply the two fractions and add the results together to get the numerator of the answer.
   

   Suppose you want to add the fractions
   and
   . To get the numerator of the answer, cross-multiply. In other words, multiply the numerator of each fraction by the denominator of the other:
   

   

   Add the results to get the numerator of the answer:
   

   • 5 + 6 = 11
     
2. Multiply the two denominators to get the denominator of the answer.
   

   To get the denominator, just multiply the denominators of the two fractions:
   

   

   The denominator of the answer is 15.
   

3. Write your answer as a fraction.
   

   

As you discover in the earlier section “Finding the sum of fractions with the same denominator,” when you add fractions, you sometimes need to reduce the answer you get. Here's an example:

Because the numerator and the denominator are both even numbers, you know that the fraction can be reduced. So try dividing both numbers by 2: