Fraction (Lat. frangere, to break), in arithmetic and algebra, an expression for an unexecuted division, originally invented to represent a quantity less than a unit. Thus | originally signified three quarters of one, and afterward was used for the fourth part of three, these two quantities being identical. The dividend number is called the numerator, because in arithmetic it numbers how many parts are taken; and the divisor is called the denominator, because it names the parts. These terms are retained in algebra, where it is evident that their literal meaning is inapplicable. Fractions are also used to express the ratio of the numerator to the denominator. Thus the expression a+b / a-b may signify the ratio of the sum of the quantities a and b to their difference, or the quotient arising from the division of that sum by that difference. The propriety of indicating the quotient and the ratio by the same sign is evident from the consideration that the quotient bears the same ratio to unity that the dividend bears to the divisor. A decimal fraction is one whose denominator consists of 1 with zeros annexed, in which case the denominator is not written, but is understood from a point being prefixed, with zeros if necessary; thus, .371 means 371/1000; .0371, 371/10,000, and so on.

A continued fraction is a fraction whose numerator is 1, and whose denominator is a whole number plus a fraction whose numerator is 1 and denominator a whole number plus a fraction, etc.