Fractions

It seems from the earliest observable records the Chinese were happy and accustomed to deal with fractions and like most cultures, like all numbers they were initially written in words. Addition, subtraction, division and multiplication were familiar from the early Han (206 B.C. to A.D. 220) onwards.

The following methods were obtained from Needham (1959) pages 94-95:

In division by a fraction both numbers were multiplied by the denominator of the fraction and then rules similar to those of today were used. For example in division of 119 000 by 182 5/8 both were multiplied by 8 first.

In adding fractions each numerator was multiplied by the denominators of the other fractions and then all the denominators multiplied by one another. The numerators were then added. This is very similar to the method we use today (when doing such calculations by hand) except we try to find the lowest common denominator (a number which each fraction denominator can divide evenly into) to make things easier.

Subtraction was carried out by multiplying the numerators by the alternate denominator, subtracting the smaller of the two products from the greater and dividing the remainder by the product of the denominators.

NOTE: with this method of subtraction you will always end up with a positive result.

The use of a bar to separate the numerator and denominator was not introduced into China until the late 17th century, a late occurrence. On the other hand they were thinking of proper fractions at an early stage as they refered to the numerator as 'son' and denominator as 'mother'. Therefore the lower figure would be larger (ie. pregnant as it were).

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