Complex Fraction

Pronunciation: /kəmˈplɛks ˈfræk ʃən/ ?
(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. (Accessed: 2010-01-04). http://www.merriam-webster.com/dictionary/complex fraction.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 40-42. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.
  3. Rivenburg, Romeyn Henry. A Review of Algebra, pp 21-22. American Book Company, 1914. (Accessed: 2010-01-17). http://www.archive.org/stream/reviewofalgebra00riverich#page/21/mode/1up/search/complex.
  4. Manchester, Raymond. Brief Course in Algebra, pp 131-132. C. W. Bardeen, 1915. (Accessed: 2010-01-17). 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. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Reducing%20Fractions.

Cite this article as:


Complex Fraction. 2010-01-04. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/complexfraction.html.

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2010-01-17: Added "References" (McAdams, David.)
2009-01-15: Added 'Reducing Fractions' to 'More Information' (McAdams, David.)
2008-11-28: Initial version (McAdams, David.)

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