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.[3][4][5]
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
- 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
- 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
- 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
- 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
- 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
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. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexfraction.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
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.)