A rational number expressed in the form  (in-line notation) or  (traditional "display" notation), where  is called the numerator and  is called the denominator. When written in-line, the slash "/" between numerator and denominator is called a solidus.

A mathematical joke states that 4/3 of people don't understand fractions.

A proper fraction is a fraction such that , and a reduced fraction is a fraction with common terms canceled out of the numerator and denominator.

The Egyptians expressed their fractions as sums (and differences) of unit fractions. Conway and Guy (1996) give a table of Roman notation for fractions, in which multiples of 1/12 (the uncia) were given separate names.

The rules for the algebraic combination of fractions are given by

			(1)
			(2)
			(3)
			(4)

Note however that the above results will not necessarily be reduced fractions.

REFERENCES:

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 22-23, 1996.

Courant, R. and Robbins, H. "Decimal Fractions. Infinite Decimals." §2.2.2 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 61-63, 1996.