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ABACUS Small and Handy but a remarkably efficient Chinese Calculator The Abacus

ABACUS Small and Handy but a remarkably efficient Chinese Calculator The Abacus, a sort of rectangular board with many beads -- somewhat similar to what children use at primary school to learn counting. Similar calculators (1) exist in several other countries, including Russia as well as Japan, but with differentiating variations. ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 1 of 23 15/7/2013 5:45 PM There is no doubt that it is one of the most prominent articles of business equipment in Chinese business offices today. There is not a home or office in Taiwan where an Abacus is not found. Its use is compulsory in all primary and business schools. Of late, many a foreigner is becoming interested in the use of the (2) Abacus in a increased number. Wherever a Chinese goes, be it New York, London, Bombay, Sidney or Buenos Aires, the Abacus goes with him. Chinese government officials, bankers, financiers, office clerks, junk dealers, and house wives depend largely upon it for their counting in the same manner, as a child depends on his mother. A Chinese is so dependent on the Abacus that he finds it awkward to make even simple calculations without one. (3) Naturally a great many expressions utilizing the name of Abacus has developed out of this national habit. Today, there are more than 100 different models of the Chinese Abacus varied in size and quality of the materials used, but only one type made of brass mounting on a marble base is the best. This Chinese dependence on the Abacus is under- (4) standable in the light of what this simple gadget can accomplish in the efficient calculations from the simplest to the most complex mathematical problems of addition, subtraction, multiplication and division. ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 2 of 23 15/7/2013 5:45 PM More briefly explained, the Abacus is an instrument to augment mental arithmetic. The mechanics of its use is simple, and its accuracy is assured by repetition and practice alone. (5) Many speed and accuracy contests have been staged between the Abacus and Calculating Machines. The small, insignificant and inexpensive Abacus has usually been the victor. It must be understood, how- ever, that while the Abacus outshines its mechanical brother in addition and subtraction, it faces some disadvantages in multiplication and division problems. (6) INTRODUCTION TO "ABACUS" Unit points on the crosspiece are usually placed (7) one every fifth upright. Unit points are use to indicate "ones", "thousands", "millions", "billions" and so on. How to manipulate your fingers. ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 3 of 23 15/7/2013 5:45 PM In pushing the counters, there are three ways. 1) Use only the forefinger. 2) Using the thumb and forefinger. 3) Using the thumb, forefinger and middle finger. (8) The third one is the method with the thumb. Of these three ways, the second one using the thumb and forefinger is recommended, it being the best and easiest. Thumb used to: "Put in" counters in the lower part. Forefinger used to: "Take off" the counters in the lower part. "Put in" a counter in the upper part. (9) "Take off" a counter in the upper part. Note: "Put in" means pushing the counters toward the crosspiece. "Take off" means pushing the counters away from the crosspiece. How to manipulate counters. the manipulation consists of the following six motions. 1) Putting in counters. (10) 2) Taking off counters. 3) Putting in five counter and taking off one-counter. 4) Putting in one-counter and taking off five counter. 5) Taking off counter of ones' place and putting in a counter of tens place. 6) Taking off a counters of tens' place and putting in counters of ones' place: Note: In order to indicate 10, a counter in the lower ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 4 of 23 15/7/2013 5:45 PM part on the next upright to the left is put in, (11) i.e. a counter in tens' place is put in. In illustrating the manipulations which ar most important in calculations, the following symbols are used to facilitate one's understanding of its manipu- lation. ^ Push up the counter with the thumb or fore finger. (In the case of taking off the counter in the upper part, push up the counter with the (12) forefinger. (subtraction) In the case of putting in the counter in the lower part, push up the counter with the thumb. (addition) Push down the counter with the forefinger. (means addition in the case of five counter) (means subtraction in the case of one counter) A counter already placed, i.e., a counter which has already been "put in" and which remains (13) either on the top or at the bottom. (*) A counter newly "put in". (/) A counter "taken off". Addition (A) 2 + 1 ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 5 of 23 15/7/2013 5:45 PM Answer: 3 In this case, first put in 2 with the thumb, second, put in 1 with thumb. (14) (B) 2 + 6 Answer: 8 In this case, put in 2 with the thumb first. Then put in 5 (upper part) with the forefinger, and simultaneously put in 1 (lower part) with the thumb. (15) (C) 2 + 4 Answer: 6 First, put in 2 with the thu- mb; Second, to add for put in ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 6 of 23 15/7/2013 5:45 PM 5 of the upper part and take off 1, of the lower part with the forefinger. (16) (D) 9 + 7 Answer: 16 First, put in 9 with the for- efinger and thumb. Then to add 7, take off 3 with the for- efinger, and put in 1 in place with the thumb, i.e., think 7 and 3 are 10. So take off 3 and carry the 1 ten which is put in the tens' the tens' place with thumb. (17) (E) 36 + 75 Answer: 111 To add two place numbers and above, always commence ad- ding from the left to the right. ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 7 of 23 15/7/2013 5:45 PM In this case put in 7 tens i.e., add 7 tens of 75 to 3 tens of 36 in the same method as in example D. Next add 5 ones to 6 ones in the following way. (18) Take off 5 (a five counter) with the forefinger, and simultaneously put in 1 ten in the tens' place with the thumb as in example D. [Other examples] 9 + 7 = 16 4 +27 = 31 3 + 8 = 11 7 + 5 = 12 23 +20 = 43 9 + 5 = 14 8 +13 = 21 2 + 8 = 10 21 + 8 = 29 50 +85 =135 6 + 9 = 15 76 +82 =158 6 + 7 = 13 31 + 7 = 38 8 + 6 = 14 25 +13 = 38 (19) Subtraction (F) 10 - 3 Answer: 7 In this case there are no ones. Consequently 1 ten is borrowed by taking off 1 ten with the forefinger and 3 ones are subtra- cted from it by putting in 7 ones, the remainder, with the forefinger and thumb. (20) ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 8 of 23 15/7/2013 5:45 PM (G) 12 - 6 Answer: 6 In the same there are not enou- gh) ones to subtract from. Cons- equently, as in example (F) 1 ten must be borrowed. With the forefinger 1 ten is taken off and the remainder 4 ones are put in by putting in a five counter and taking off a one counter in the ones' place. (21) (H) 100 - 58 Answer: 42 In subtraction involving two place, three place num- bers and above, always com- mence from the left to the right as in the case of addi- tion. In this case subtract 5 tens of the number 58 from the tens. However, as there are no tens, 1 hundred is borrowed in a same manner as in example F. Next, in subtracting 8 (22) ABACUS GUIDE BOOK http://www.tux.org/~bagleyd/AbacusGB.html 9 of 23 15/7/2013 5:45 PM ones, as there are no ones left, 1 ten must be borrowed. 8 is subtracted and 2 ones, the remainder, are put in by the same method as of example (F). [Other examples] 4 - 2 = 2 5 - 3 = 2 6 - 2 = 4 8 - 6 = 2 17 - 4 =13 11 - 6 = 5 15 - 6 = 9 12 - 6 = 6 88 -45 =43 40 -15 =25 30 -22 = 8 27 -12 =15 136 -74 =62 112 -50 =62 300 -126=174 10000-41=959 Exercise for addition and subtraction. (23) "How to exercise?" You need not care about the unit position. (1) 1 2 3 4 5 6 7 8 9 First of all, put in (2) 2 4 6 9 1 3 5 7 8 "123,456,789" on the (3) 3 7 0 3 7 0 3 6 7 "Abacus", and then (4) 4 9 3 8 2 7 1 5 6 put uploads/Finance/ abacus-guide-book.pdf