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# Fractions for Firefighter Exam Study Guide (page 2)

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Updated on Jun 30, 2011

### Reducing Fractions

Reducing a fraction means writing it in lowest terms, that is, with smaller numbers. For instance, 50¢ is of a dollar, or of a dollar. In fact, if you have a 50¢ piece in your pocket, you say that you have a half dollar. Reducing a fraction does not change its value.

Follow these steps to reduce a fraction:
1. Find a whole number that divides evenly into both numbers that make up the fraction.
2. Divide that number into the top of the fraction, and replace the top of the fraction with the quotient (the answer you got when you divided).
3. Do the same thing to the bottom number.
4. Repeat the first 3 steps until you can't find a number that divides evenly into both numbers of the fraction.
For example, let's reduce We could do it in 2 steps: then Or we could do it in a single step:
Shortcut:When the top and bottom numbers both end in zeros, cross out the same number of zeros in both numbers to begin the reducing process. For example, reduces to when you cross out 2 zeros in both numbers. Also, remember that any number that ends with an even number (0, 2, 4, 6, or 8) can be divided by 2. Any fraction in which both the top and bottom numbers end with even numbers can be reduced

Whenever you do arithmetic with fractions, reduce your answer. On a multiple-choice test, don't panic if your answer isn't listed. Try to reduce it and then compare it to the choices. Reduce the following fractions to lowest terms. The answers appear at the end of this section on page 162.

### Raising Fractions to Higher Terms

Before you can add and subtract fractions, you have to know how to raise a fraction to higher terms. This is actually the opposite of reducing a fraction.

Follow these steps to raise to 24ths:
 1. Divide the old bottom number (3) into the new one (24): 2. Multiply the answer (8) by the old top number (2): 2 × 8 = 16 3. Put the answer (16) over the new bottom number (24): 4. Check: Reduce the new fraction to see if you get back the original one:
Raise these fractions to higher terms: