How to Add and Subtract Fractions in Algebra
 
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How Proper Fractions Work

The simplest type of fraction is a proper fraction, which is always just part of one whole thing. In a proper fraction, the numerator is always smaller than the denominator, and its value is always less than 1. Because a proper fraction represents just part of a whole thing, the denominator is the number value of the "whole thing" while the numerator is the number value of the "part."

Take a look at these examples of proper fractions:

  • Cut a cake into six slices. Eat one piece, and you still have five pieces left. Lucky you! You can have your cake and eat it too!

    Because the whole cake equals 6 slices, 6 is the denominator. Because the part you have left is 5 pieces, 5 is the numerator, making the fraction = 5/6.

  • One pound of butter equals 16 ounces. Put one ounce of butter on your popcorn.

    Because an entire pound equals 16 ounces, the denominator is 16. Because the part you need to butter your popcorn is 1 ounce, 1 is the numerator, making the fraction = 1/16.

Now try turning the following examples into proper fractions:

  • One cup of oil is equal to 8 ounces. You need just 2 ounces to bake brownies. What part of the cup of oil do you need? The answer is 2/8.

  • A chocolate bar weighs 6 ounces, but someone ate 2 ounces, leaving 4 ounces. How much of the entire bar is left? The answer is 4/6.

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