Fractions
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Basic Operations with Fractions

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1) Adding fractions:  One easy way to add two fraction is to use the formula below:

This formula will work for any fractions and you don’t have to find a least common denominator! The formula uses the product of the original denominators as a common denominator, which works just as well as the least common denominator except that it is more likely you will have to reduce the answer to lowest terms. But so what! That's easy!  
Example:

 

2) Subtracting fractions: Subtracting two fractions can be accomplished by a very similar formula: 

Notice that the only difference is that subtraction is used in numerator in place of addition.
Example:

3) Multiplying fractions:  To multiply two fractions simply multiply the numerators and denominators of the fractions together.  It's much easier than adding and subtracting fractions!  It looks like this: 

Example:

The arithmetic may often be simplified by canceling common factors as the following example shows:

4) Dividing fractions: To divide two fractions simply switch around the numerator and denominator of the second fraction and then multiply them.  In math terminology: to divide two fractions you multiply the dividend by the reciprocal of the divisor.  Whew!  Lets stick with English!  Here's what it looks like:

Example:

Make sure you don’t cancel out common factors until the second fraction has been inverted! You’ll get the wrong answer if you do!

For any of the four operations, if whole numbers are involved, simply make the whole number into a fraction by placing it over 1 and proceed in the same way.
Example:

 

Designed by John Neely, Math Center Coordinator, University of Northern Iowa, Spring 2004
Last revised 1/31/06
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