Complex Fraction
Pronunciation: /kəmˈplɛks ˈfræk ʃən/ ?
 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. (Accessed: 20100104). http://www.merriamwebster.com/dictionary/complex fraction.
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 4042. International Textbook Company, January 1963. (Accessed: 20100112). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.
 Rivenburg, Romeyn Henry. A Review of Algebra, pp 2122. American Book Company, 1914. (Accessed: 20100117). http://www.archive.org/stream/reviewofalgebra00riverich#page/21/mode/1up/search/complex.
 Manchester, Raymond. Brief Course in Algebra, pp 131132. C. W. Bardeen, 1915. (Accessed: 20100117). http://www.archive.org/stream/briefcourseinalg00mancrich#page/130/mode/2up/search/complex.
More Information
 McAdams, David. Reducing Fractions. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 20090312. http://www.allmathwords.org/article.aspx?lang=en&id=Reducing%20Fractions.
Cite this article as:
Complex Fraction. 20100104. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexfraction.html.
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20100117: Added "References" (
McAdams, David.)
20090115: Added 'Reducing Fractions' to 'More Information' (
McAdams, David.)
20081128: Initial version (
McAdams, David.)