The Fundamental Operations in Bead Arithmetic - How to Use the Chinese Abacus

The Fundamental Operation In

Bead Arithmetic

INTRODUCTION

Definition of Bead Arithmetic. Bead Arithmetic is a certain method of reckoning, in which numbers are represented by wooden beads. these beads are systematically arranged on a frame known as the Chinese abacus. The term Bead arithmetic is used to distinguish it from the other form of arithmetic in which written figures are used. It may be called a science of numbers but, since it is used in daily business life, it is more appropriate to speak of it as an art of reckoning.

History. The history of this subject is very meagre. "For reckoning the ancient Chinese used bamboo tallies or chips; the modern Chinese use the abacus. There is no record of who invented the frame, nor is the time known at which this ingenious contrivance made its first appearance. In Dao Nan Tsang’s Cease Farming Sketch Book, the terms movable beads frame and sliding beads frame were casually mentioned." (Chinese Cyclopedia.) As this book was written during the Yuan Dynasty (which was ruling in the fourteenth century) it is clear that the abacus was in common use more than six hundred years ago.

Merits of the Abacus. In solving any problem in arithmetic, however simple it may be, two parts of our mental powers must be used, namely, the faculties of computation and of memory. We employe them when we add one and two; for in adding we must first retain the number one in our mind, then we fix our attention upon the other number, two, and finally we compute how much one and two are. With very small numbers these are very simple operations. But as the problems become more complex we soon reach the limit of our mental capacity. In dealing with difficult problems we must find some means by which the memory is relieved of the strain of computation. Fortunate are we that some wise men of past generations did find such means for us. We now merely need to learn how to use them. Among such devices are the bamboo tallies or counters used in ancient times and the Chinese Abacus. It is not an automatic machine such as the standard adding machines (in many respects it is superior to such machines) but even so it tenders no little service to us as a memorizing agent in computation. By using this instrument we can devote our entire attention to accuracy in computing and leave the memory work to the frame.

Advantages and Disadvantages of Bead Arithmetic as Compared with Written Arithmetic. Upon comparison, both the Bead and written or Pen Arithmetic, as it is called in China, have their weak as well as their strong points. In dealing with intricate problems the Pen Arithmetic is indeed more serviceable, but for most of the daily business transactions, Bead Arithmetic is far better suited. Its chief advantage over the pen arithmetic is the economy of time. It is quite safe to say that to solve any problem in the fundamental operations of arithmetic by using the abacus, it takes at most half the time that is needed when the written numerals are used. This is especially true in addition. For example, if two men were to solve the same problem in this process, beginning at the same time but using different methods, the result would no