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A rational number that represents a part, or several equal parts, of a whole; examples include one-half, two-thirds, and three-fifths. The word comes from the Latin frangere, meaning "to break." A simple, common, or vulgar fraction is of the form a/b, where a (the numerator) may be any integer and b (the denominator) may be any integer greater than 0. If a < b, the fraction is said to be proper ("bottom heavy"); otherwise it is improper ("top heavy"). A decimal fraction has a denominator of 10, 100, 1000, etc.

In an algebraic fraction, the denominator, or the numerator and denominator, are algebraic expressions, for example x/(x2 + 2). In a composite fraction, both the numerator and denominator are themselves fractions.

Two fractions a/b and c/d can be added, subtracted, multiplied, and divided according to the rules:
a/b + c/d = (ad + bc)/b/d
a/b - c/d = (ad - bc)/bd
a/b × c/d = ac/bd
a/b ÷ c/d = ad/bc

Related entry

   • continued fraction

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