Complex Fraction

Pronunciation: /kəmˈplɛks ˈfræk ʃən/ Explain
(1+3/4)/2
Figure 1: Complex fraction.
1/(1/(x+1)+1/(y-2))
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
StepEquationDescription
1(1+3/4)/2This is the fraction to simplify.
2(4/4+3/4)/2Find the common denominator of 1+3/4. Change both terms to fractions using the common denominator: 1+3/4 = 4/4+3/4.
3(7/4)/2Add the fraction(s) with the common denominator together: 4/4+3/4 = (4+3)/4 = 7/4.
4(7/4)*(1/2)Use the definition of a fraction to turn the fraction into a multiplication problem: a/b is defined as a divided by b implies (7/4)/2=(7/4)*(1/2).
57/8Multiply the fractions: (7/4)*(1/2)=(7*1)/(4*2)=7/2.
6(1+3/4)/2=7/8The original fraction and the simplified fraction are equivalent.
Table 1

Example 2
StepEquationDescription
11/(1/(x+1)+1/(y-2))This is the fraction to simplify.
21/((y-2)/((x+1)(y-2))+((x+1)/((x+1)(y-2))Find the common denominator of 1/(x+1) + 1/(y-2). The common denominator is (x+1)(y-2). Change both terms to fractions using the common denominator: 1/(x+1)*(y-2)/(y-2)=(y-2)/((x+1)(y-2)) and 1/(y-2)*(x+1)/(x+1)=(x+1)/((x+1)(y-2)).
31/((x-1+y)/((x+1)(y-2)))Add the fraction(s) with the common denominator together: (y-2)/((x+1)(y-2))+(x+1)/((x+1)(y-2))=(y-2+x+1)/(x+1)(y-2))=(x-1+y)/(x+1)(y-2)).
41*((x+1)(y-2))/(x-1+y)Use the definition of a fraction to turn the fraction into a multiplication problem: 1/((x-1+y)/((x+1)(y-2)))=1*((x+1)(y-2))/(x-1+y).
5(x-1+y)/((x+1)(y-2))Multiply the products: 1*(x-1+y)/((x+1)(y-2))=(x-1+y)/((x+1)(y-2)).
6/(1/(x+1)+1/(y-2))=(x-1+y)/((x+1)(y-2))The original fraction and the simplified fraction are equivalent.
Table 2

References

  1. complex fraction. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. http://www.merriam-webster.com/dictionary/complex fraction.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 40-42. 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
  3. Rivenburg, Romeyn Henry. A Review of Algebra. pp 21-22. 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
  4. Manchester, Raymond. Brief Course in Algebra. pp 131-132. 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.)

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