Complex Fraction
Pronunciation: /kəmˈplɛks ˈfræk ʃən/ Explain
 Figure 1: Complex fraction. 
 Figure 2: Complex fraction. 

A complex fraction is a
fraction
that has at least one other fraction in the numerator or denominator.^{[1]}
A complex fraction can also
be called a compound fraction.

Simplifying a Complex Fraction
To simplify a complex fraction, combine fractions in the
numerator
and the
denominator.
Then combine the numerator and denominator.
Example 1
Step  Equation  Description 
1   This is the fraction to simplify. 
2   Find the common denominator of . Change both terms to fractions using the common denominator: . 
3   Add the fraction(s) with the common denominator together: . 
4   Use the definition of a fraction to turn the fraction into a multiplication problem: . 
5   Multiply the fractions: . 
6   The original fraction and the simplified fraction are equivalent. 
Table 1 
Example 2
Step  Equation  Description 
1   This is the fraction to simplify. 
2   Find the common denominator of . The common denominator is . Change both terms to fractions using the common denominator: and . 
3   Add the fraction(s) with the common denominator together: . 
4   Use the definition of a fraction to turn the fraction into a multiplication problem: . 
5   Multiply the products: . 
6   The original fraction and the simplified fraction are equivalent. 
Table 2 
References
 complex fraction. merriamwebster.com. Encyclopedia Britannica. MerriamWebster. Last Accessed 8/6/2018. http://www.merriamwebster.com/dictionary/complex fraction.
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 4042. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/6/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
 Rivenburg, Romeyn Henry. A Review of Algebra. pp 2122. www.archive.org. American Book Company. 1914. Last Accessed 8/6/2018. http://www.archive.org/stream/reviewofalgebra00riverich#page/21/mode/1up/search/complex. Buy the book
 Manchester, Raymond. Brief Course in Algebra. pp 131132. www.archive.org. C. W. Bardeen. 1915. Last Accessed 8/6/2018. http://www.archive.org/stream/briefcourseinalg00mancrich#page/130/mode/2up/search/complex. Buy the book
More Information
 McAdams, David E.. Reducing Fractions. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/r/reducingfractions.html.
Cite this article as:
McAdams, David E. Complex Fraction. 6/25/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexfraction.html.
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Revision History
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (
McAdams, David E.)
1/17/2010: Added "References". (
McAdams, David E.)
1/15/2009: Added 'Reducing Fractions' to 'More Information'. (
McAdams, David E.)
11/28/2008: Initial version. (
McAdams, David E.)