### Topic Page: Complex Fraction

**fraction**

*The Penguin Dictionary of Mathematics*

A quotient of one number (or a expression) by another, indicated by a/b (or a/b). The dividend a is the numerator and the nonzero divisor b is the denominator. Fractions are classified as:

Common (or simple or vulgar) fraction - the numerator and denominator are both integers.

Complex fraction - the numerator and denominator are themselves fractions. Proper fraction - the numerator is less than the denominator, as in 7/8. Improper fraction - the numerator is greater than the denominator, as in 8/7. Mixed fraction - an integer together with a proper fraction, as in 1½.

Rules for combining fractions are:

Addition. The fractions are put in a form in which their denominators are equal. For example, to add ½ and 1/3, write ½ = 3/6 and 1/3 = 2/6 (6 is the lowest common denominator of the two fractions). Then,

Subtraction. The same method as addition, except that the numerators are subtracted rather than added.

Multiplication. The numerators are multiplied and the denominators are also multiplied. For example,

Division. The divisor is inverted and the two fractions are then multiplied. Thus

See also continued fraction; decimal; partial fraction; reducible fraction.

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