fraction
المؤلف:
Conway, J. H. and Guy, R. K.
المصدر:
The Book of Numbers. New York: Springer-Verlag
الجزء والصفحة:
...
24-10-2019
1016
fraction
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
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.
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