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# Fractions Study Guide: GED Math (page 2)

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Updated on Mar 23, 2011

### Raising Fractions to Higher Terms

You raise a fraction to higher terms by multiplying both the numerator and the denominator by the same number. For example, if you multiply by , you will get .

Both and have the same value; they are equal fractions. You sometimes need to raise a fraction to higher terms when you are comparing fractions. You will also have to raise fractions to higher terms when you are adding and subtracting fractions that have different denominators.

When raising a fraction to higher terms, you will usually need to find an equal fraction with a specific denominator. Here's how to raise a fraction to higher terms with a specific denominator.

Step 1   Divide the denominator of the fraction into the new denominator.

Step 2   Multiply the quotient, or the answer to step 1, by the numerator.

Step 3   Write the product, or the answer to step 2, over the new denominator.

Example

This problem asks you to raise to 9ths.

Divide the denominator into the new denominator, which is 9: 9 ÷ 3 = 3.

Multiply 3 by the numerator: 3 × 1 = 3.

Write 3 over the new denominator: .

### Comparing Fractions

Sometimes you will be asked to compare two or more fractions. You might be asked which of two fractions is larger, for example. Or you could be asked if two fractions are equal. If the two fractions have the same denominator, you simply compare the numerators; the number with the higher numerator is larger.

Example

Which fraction is larger, or ?

You know that 8 is larger than 5, so is larger than .

What if the fractions do not have the same denominator? One way to answer this type of question is to convert both fractions so that they have the same denominator. This is called finding a common denominator. If the two fractions have the same denominator, you can compare their numerators.

Example

Which fraction is larger, or ?

To answer this question, you can raise both fractions to higher terms with a common denominator. First, you need to find a denominator that both 6 and 4 can divide into. You could choose 24 (6 × 4 = 24), but 12 is the least common denominator (LCD). Then raise each fraction to higher terms with the same denominator.

Then compare the numerators of the two fractions. Because 10 is greater than 9, you know that is larger than . This means that is larger than .

Practice problems for these concepts can be found at:

Fractions and Decimals Practice Problems: GED Math