# 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. 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
StepEquationDescription
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
StepEquationDescription
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
1. McAdams, David E.. All Math Words Dictionary, complex fraction. 2nd Classroom edition 20150108-4799968. pg 39. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. complex fraction. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/25/2018. http://www.merriam-webster.com/dictionary/complex fraction. Buy the book
3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 40-42. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/25/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
4. Rivenburg, Romeyn Henry. A Review of Algebra. pp 21-22. www.archive.org. American Book Company. 1914. Last Accessed 6/25/2018. http://www.archive.org/stream/reviewofalgebra00riverich#page/21/mode/1up/search/complex. Buy the book
5. Manchester, Raymond. Brief Course in Algebra. pp 131-132. www.archive.org. C. W. Bardeen. 1915. Last Accessed 6/25/2018. http://www.archive.org/stream/briefcourseinalg00mancrich#page/130/mode/2up/search/complex. Buy the book

• McAdams, David E.. Reducing Fractions. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/27/2018. https://www.allmathwords.org/en/r/reducingfractions.html.

McAdams, David E. Complex Fraction. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/complexfraction.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)