Computation: Chinese Counting Rods
The basic questions in the study of arithmetic in any civilization are: how did the people add, subtract, multiply, and divide, and what were the notations and media that were used to perform these operations.
The ancient Chinese used bamboo sticks or animal bones to count. The first five numbers were tallies in the following form:
The representations for six, seven, eight, and nine were as follows:
The horizontal rod represented the quantity five.
It is easy to imagine how these rod numerals were handled for the addition or subtraction of small numbers such as two plus five or nine minus two. In the case of the addition of, for example, six and seven, the three vertical rods were grouped together and the two horizontal rods representing two fives were replaced by a single rod positioned horizontally to the left of the three vertical rods. The sum, thirteen, was expressed in the following form:
In this manner, a place value notation was created; the tens’ place was to the left of the...
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