Basic Math and Pre-Algebra For Dummies (36 page)

These fractions are equal to
, but their terms (the numerator and denominator) are different. In this section, I show you how to both increase and reduce the terms of a fraction without changing its value.

 To increase the terms of a fraction by a certain number, multiply both the numerator and the denominator by that number.

For example, to increase the terms of the fraction
by 2, multiply both the numerator and the denominator by 2:

Similarly, to increase the terms of the fraction
by 7, multiply both the numerator and the denominator by 7:

 Increasing the terms of a fraction doesn't change its value. Because you're multiplying the numerator and denominator by the same number, you're essentially multiplying the fraction by a fraction that equals 1.

One key point to know is how to increase the terms of a fraction so that the denominator becomes a preset number. Here's how you do it:

1. Divide the new denominator by the old denominator.
   

   To keep the fractions equal, you have to multiply the numerator and denominator of the old fraction by the same number. This first step tells you what the old denominator was multiplied by to get the new one.
   

   For example, suppose you want to raise the terms of the fraction
   so that the denominator is 35. You're trying to fill in the question mark here:
   

   

   Divide 35 by 7, which tells you that the denominator was multiplied by 5.
   

2. Multiply this result by the old numerator to get the new numerator.
   

   You now know how the two denominators are related. The numerators need to have the same relationship, so multiply the old numerator by the number you found in Step 1.
   

   Multiply 5 by 4, which gives you 20. So here's the answer:
   

   

Reducing fractions is similar to increasing fractions, except that it involves division rather than multiplication. But because you can't always divide, reducing takes a bit more finesse.

In practice, reducing fractions is similar to factoring numbers. For this reason, if you're not up on factoring, you may want to review this topic in Chapter
8
.

In this section, I show you the formal way to reduce fractions, which works in all cases. Then I show you a more informal way you can use when you're more comfortable.

Reducing fractions the formal way relies on understanding how to break down a number into its prime factors. I discuss this in detail in Chapter
8
, so if you're shaky on this concept, you may want to review it first.

Here's how to reduce a fraction:

1. Break down both the numerator (top number) and the denominator (bottom number) into their prime factors.
   

   For example, suppose you want to reduce the fraction
   . Break down both 12 and 30 into their prime factors:
   

   

2. Cross out any common factors.
   

   As you can see, I cross out a 2 and a 3 because they're common factors — that is, they appear in both the numerator and the denominator:
   

   

3. Multiply the remaining numbers to get the reduced numerator and denominator.
   

   You can see now that the fraction
   reduces to
   :