Basic Math and Pre-Algebra For Dummies (46 page)

As another example, suppose you want to add the numbers
.

1. Find the LCM of 6, 10, and 15.
   

   This time, I use the prime factorization method (see Chapter
   8
   for details on how to do this). Start by decomposing the three denominators to their prime factors:
   

   

   These denominators have a total of three different prime factors — 2, 3, and 5. Each prime factor appears only once in any decomposition, so the LCM of 6, 10, and 15 is
   

   

2. You need to increase the terms of all three fractions so that their denominators are 30:
   

   

3. Simply add the three new fractions:
   

   

   Again, you need to change this improper fraction to a mixed number:
   

   

   Because both numbers are divisible by 2, you can reduce the fraction:
   

   

As I say earlier in this chapter, I think the traditional way to add fractions is more difficult than either the easy way or the quick trick. Your teacher may require you to use the traditional way, and after you get the hang of it, you'll get good at it. But given the choice, here's my recommendation:

• Use the easy way when the numerators and denominators are small (say, 15 or under).
  
• Use the quick trick with larger numerators and denominators when one denominator is a multiple of the other.
  
• Use the traditional way only when you can't use either of the other methods (or when you know the LCM just by looking at the denominators).
  

Subtracting fractions isn't really much different than adding them. As with addition, when the denominators are the same, subtraction is easy. And when the denominators are different, the methods I show you for adding fractions can be tweaked for subtracting them.

So to figure out how to subtract fractions, you can read the section “All Together Now: Adding Fractions” and substitute a minus sign (–) for every plus sign (+). But it'd be just a little chintzy if I expected you to do that. So in this section, I show you four ways to subtract fractions that mirror what I discuss earlier in this chapter about adding them.

As with addition, subtracting fractions with the same denominator is always easy. When the denominators are the same, you can just think of the fractions as pieces of cake.

To subtract one fraction from another when they both have the same denominator (bottom number), subtract the numerator (top number) of the second from the numerator of the first and keep the denominator the same. For example:

Sometimes, as when you add fractions, you have to reduce:

Because the numerator and denominator are both even, you can reduce this fraction by a factor of 2:

Unlike addition, when you subtract one proper fraction from another, you never get an improper fraction.

Just as with addition, you have a choice of methods when subtracting fractions. These three methods are similar to the methods I show you for adding fractions: the easy way, the quick trick, and the traditional way.

The easy way always works, and I recommend this method for most of your fraction subtracting needs. The quick trick is a great timesaver, so use it when you can. And as for the traditional way — well, even if I don't like it, your teacher and other math purists probably do.

This way of subtracting fractions works in all cases, and it's easy. (In the next section, I show you a quick way to subtract fractions when one denominator is a multiple of the other.) Here's the easy way to subtract fractions that have different denominators:

1. Cross-multiply the two fractions and subtract the second number from the first to get the numerator of the answer.
   

   For example, suppose you want to subtract
   . To get the numerator, cross-multiply the two fractions and then subtract the second number from the first number (see Chapter
   9
   for info on cross-multiplication):
   

   

   After you cross-multiply, be sure to subtract in the correct order. (The first number is the numerator of the first fraction times the denominator of the second.)
   

2. Multiply the two denominators to get the denominator of the answer.
   

   

3. Putting the numerator over the denominator gives you your answer.