OpenStax-CNX module: m34943
1
Addition and Subtraction of
Fractions, Comparing Fractions,
and Complex Fractions: Summary of
∗
Key Concepts
Wade Ellis
Denny Burzynski
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0†
Abstract
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This
module reviews the key concepts from the chapter "Addition and Subtraction of Fractions, Comparing
Fractions, and Complex Fractions."
1 Summary of Key Concepts
Addition and Subtraction of Fractions with Like Denominators ()
To add or subtract two fractions that have the same denominators, add or subtract the numerators and
place the resulting sum or dierence over the common denominator. Reduce, if necessary. Do not add or
subtract the denominators.
1
8
+
5
8
=
1+5
8
=
6
8
=
3
4
Basic Rule for Adding and Subtracting Fractions ()
Fractions can be added or subtracted conveniently only if they have like denominators.
Addition and Subtraction of Fractions with Unlike Denominators ()
To add or subtract fractions having unlike denominators, convert each fraction to an equivalent fraction
having as denominator the LCD of the original denominators.
Addition and Subtraction of Mixed Numbers ()
1. To add or subtract mixed numbers, convert each mixed number to an improper fraction, then add or
subtract the fractions.
Ordered Number System ()
Our number system is ordered because the numbers in the system can be placed in order from smaller to
larger.
∗ Version
1.2: Aug 18, 2010 8:07 pm -0500
† http://creativecommons.org/licenses/by/3.0/
http://cnx.org/content/m34943/1.2/
OpenStax-CNX module: m34943
2
Inequality Symbols ()
> represents the phrase "greater than."
< represents the phrase "less than."
Comparing Fractions ()
If two fractions have the same denominators, the fraction with the larger numerator is the larger fraction.
5
8
>
3
8
Simple Fractions ()
A simple fraction is any fraction in which the numerator is any whole number and the denominator is any
nonzero whole number.
Complex Fractions ()
A complex fraction is any fraction in which the numerator and/or the denominator is a fraction.
Complex fractions can be converted to simple fractions by employing the methods of adding, subtracting,
multiplying, and dividing fractions.
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