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# Fraction Review for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide (page 2)

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Updated on Jun 23, 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 50¢ in your pocket, you say that you have half a 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 two steps ; then . Or we could do it in a single step .

Shortcut: When the top and bottom numbers both end in zeroes, cross out the same number of zeroes in both numbers to begin the reducing process. For example reduces to when you cross out two zeroes in both numbers.

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 these fractions to lowest terms.

### 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.

If the fractions have the same bottom numbers, just add the top numbers together and write the total over the bottom number.

Examples:     Reduce the sum: .
.         Change the sum to a mixed number: ; then reduce: .
There are a few extra steps to add mixed numbers with the same bottom numbers, say :
2. Change the improper fraction into a mixed number:
3. Add the whole numbers:                                                             2 + 1 = 3
4. Add the results of steps 2 and 3:

### Finding the Least Common Denominator

If the fractions you want to add don't have the same bottom number, you will have to raise some or all of the fractions to higher terms so that they all have the same bottom number, called the common denominator. All of the original bottom numbers divide evenly into the common denominator. If it is the smallest number that they all divide evenly into, it is called the least common denominator (LCD).

Here are a few tips for finding the LCD, the smallest number that all the bottom numbers evenly divide into:
• See if all the bottom numbers divide evenly into the largest bottom number.
• Check out the multiplication table of the largest bottom number until you find a number that all the other bottom numbers evenly divide into.
• When all else fails, multiply all the bottom numbers together.
Example:
1. Find the LCD. Multiply the bottom numbers:           3 ×5 = 15
2. Raise each fraction to 15ths:
3.