HistoryAbacus (Suen Poon)Use of the AbacusNumbering SystemCalculation

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History

Abacus (Suen Poon) consists of a wooden frame with 13 sticks (some may have less) stretched vertically between the top and bottom, a wooden bar runs horizontally in the frame, two third of the way up the sticks. Two beads are strung on each stick above the horizontal bar and five beads below. The two beads represent five units each and the lower beads, single units of the order represented by the column.

Abacus (Suen Poon)



Many centuries ago, the abacus evolved independently in many countries throughout Europe, the Middle East and China. Its use is recorded in China as early as 6th century B.C., from where it found it's way to Korea and Japan.

Different styles of abacus were used in different countries, the Chinese version being known as a "Suen Poon" (abacus), use of the abacus in the Western world ceased many years ago but it is still in extensive use in Hong Kong and China.

Use of the Abacus

The Abacus (Suen Poon) is still in use and its distinctive noise can be heard in many small businesses and restaurants in Hong Kong and China.



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Experts use it to make long and complicated calculations faster than the same calculations made by using an electronic calculator. Indeed, competitions are regularly held in Hong Kong to determine which method is faster and the Abacus (Suen Poon) users inevitably win.

One mathematics teacher in Hong Kong has gone a step further; he teaches his pupils to calculate using a Abacus (Suen Poon) and when they are proficient, he removes the Abacus (Suen Poon). The pupils then solve complicated mathematical problems by moving their fingers as if using an imaginary Abacus (Suen Poon). They have been tested and have proved capable of making mental calculations quicker than using electronic calculators.

The first time, an IBM computer was put on display at the old Radio Show at Earls Court, a glass-fronted box containing an abacus (Suen Poon) was located on the wall next to the computer. Under the box was the message:


"IN CASE OF FAILURE, BREAK GLASS".

Numbering System



Upper Portion (UP): Two beads - represent FIVE each.
Lower Portion (LP): Five Beads - represent ONE each.

1) The first stick = 1
2) The second stick = 2
3) The third stick = 3
4) The fourth stick = 4 
5) The fifth stick = 5
6) The sixth stick = 6  ...and so on


Calculation

(1) Fingers to Use
Use the THUMB and the FOREFINGER.

(2) Action to Take
"Push to" (Pt) or "Away from" (Af) the horizontal bar (B).

(3) Set up Position
Upper Portion (UP) and Lower Portion (LP), all beads "Away from" (Af) the horizontal bar (B).



(4) Direction to work from
From Left to Right for addition and subtraction.

(5) Units Arrangement



Fig. 1
(Seventy-six thousand five hundred and twenty-one)

C1 Unit C4 Thousand
C2 Ten units C5 Ten thousand
C3 Hundred C6 Hundred thousand
and so on....

(6) Five units and Ten units

(1) Five units (5 beads in LP = 1 bead in UP)


(a) 5 green beads Af LP - use forefinger


(b)1 green bead Pt UP - use forefinger

(2) Ten units (2 beads in UP = 1 beads in LP in next column)


(a) C1: 2 green beads Af UP - use forefinger


(b) C2: 1 red bead Pt LP - use thumb

(3) Ten units


(a) 15 brown beads


(b) C1: 1 bead Af UP - use forefinger, 5 bead Af LP - use forefinger
(c) C2: 1 bead, Pt LP - use thumb


(7) Addition

(A) 3 + 1 = 3


(a) C1: 3 brown beads
(b) C1: add 1 -- 1 red bead Pt LP - use thumb


Result = 4

(B) 3 + 6 = 9


(a) C1: 3 brown beads
(b) C1: add 6 -- 1 red bead Pt LP - use thumb, 1 red bead Pt UP - use forefinger


Result = 9

(C) 4 + 4 = 8


(a) C1: 4 brown beads


(b) C1: add 4 -- 1 red bead Pt UP - use forefinger, 1 red bead, Af LP - use thumb


Result = 8

(D) 8 + 7 = 15


(a) C1: 8 brown beads
(b) C1: add 7 -- 2 red bead Pt LP - use thumb, 1 red bead Pt UP - use forefinger, now C1 = 15

(c) C1: 5 bead Af  LP - use forefinger, 1 bead Af UP - use forefinger
(d) C2: 1 bead, Pt LP - use thumb



Result = 15

(E) 91 + 5 = 96


(a) C2 C1: 91 brown beads


(b) C1: add 5 -- 1 red bead, Pt UP - use thumb

Result = 96

(F) 5,628 + 1,151 = 6,779


(a) 5,628 -- brown beads
(b) Add 1,151 - start from left hand side


Result = 6,779

(G) 6,122 + 1,758 = 7,880


(a) 6,122 -- brown beads
(b) Add 1,758 - start from left hand side......., 
(c) C1: add 8 = 1 bead Pt UP, 3 beads Pt LP, now C1 = 10 units
(d) C1: 5 beads Af LP, 1 bead Af UP
(e) C2: 1 bead Pt LP



Result = 7,880

(H) 6,647 + 1,868 = 8,515

Procedures:
6647 brown beads

1) C4: add 1, 1 bead Pt LP
2) C3: add 8, 1 bead Pt UP, 3 beads Pt LP
3) C3:  2 beads (=10 units) Af UP (10 units = 1 LP bead in next column)

4) C4: 1 bead Pt LP in 
5) C2: add 6, 1 bead Pt UP, 1 bead Pt LP
6) C2: 1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next column)

7) C3: 1 bead Pt LP
8) C3: 5 beads Af LP, 1 bead Pt UP (5 units in LP = 1 unit in UP)

9) C1: add 7, 1 beads in Pt UP, 2 beads Pt LP
10) C1: 1 bead Af UP, 5 beads Af LP, 1 bead Pt LP in C2


Result = 8,515

(8) Subtraction


(A) 54 - 17 = 37

Procedures:
1) 54 -- brown beads (C2 = 5 , C1 = 4)
2) C2 - 1 = 4, 1 bead Af UP, 4 beads Pt LP
3) C1: 4 is not enough to subtract 7, hence borrow 1 unit (= 10) from C2
4) C1: now is equal to 14, subtract 7 = 7

Result = 37

(B) 94 - 28 = 66

Procedures:
1) 94 -- brown beads (C2 = 9, C1 = 4)
2) C2: 9 - 2 is 7
3) C1: 4 is not enough to subtract 8, hence borrow 1 unit (= 10) from C2 
4) C2 equal to 6
5) C1: equal to 14 - 8 = 6

Result = 66

(C) 9699 - 6647 = 3,052

Procedures:
1) C4 = 9, C3 = 6, C2 = 9, C1 = 9 (brown beads)
2) C4:  9 Subtract 6 = 3
3) C3: 6 Subtract 6 = 0
4) C2: 9 Subtract 4 = 5
5) C1: 9 Subtract 7 = 2

Result = 3,052

(9) Multiplication


(A) 24 x 6 = 144

Procedures:
2 x 6 , 4 x 6; two operations
1) 2 x 6 = 12
C3: 1 = 1 beads Pt LP
C2: 2 = 2 beads Pt LP
2) 4 x 6 = 24
C2: 2 = 2 beads Pt LP
C1: 4 = 4 beads Pt LP


Result = 144


(B) 62 x 8 = 496

Procedures:
6 x 8 , 2 x 8; two operations
1) 6 x 8 = 48
C3: 4 = 4 bead Pt LP
C2: 8 = 3 beads Pt LP, 1 bead Pt UP (= 5 units)
2)  2 x 8 =16
C2: 1 = 1 beads Pt LP
C1: 6 = 1 beads Pt LP, 1 bead Pt UP

Result = 496


(C) 86 x 7 = 602

Procedures:
8 x 7 , 6 x 7; two operations
1) 8 x 7 = 56
C3: 5 = 1 bead Pt UP
C2: 6 = 1 bead Pt LP, 1 bead Pt Up
2) 6 x 7 = 42
C2: 4 = 4 beads Pt LP
C1: 2 = 2 beads Pt LP
3)  C2: 1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next column)
C3: 1 bead Pt LP


Result = 602


(D) 23 x 13 = 299

Procedures:
2 x 3 , 3 x 3, 2 x 1, 3 x 1, four operations
1) 2 x 3 = 6
C2: 6 = 1 bead Pt LP, 1 bead Pt UP
2)  3 x 3 = 9
C1: 9 = 4 beads Pt LP, 1 bead Pt UP
3) 2 x 1 = 2
C3: 2 = 2 beads Pt LP
4) 3 x 1 = 3
C2: 3 = 3 beads Pt LP

Result = 299

(E) 46 x 75 = 3,450

Procedures:
4 x 5, 6 x 5, 4 x 7, 6 x 7 four operations
1) 4 x 5 = 20
C3: 2 = 2 beads Pt LP, 
C2: 0 = no action
2) 6 x 5 = 30
C2: 3 = 3 beads Pt LP
C1: 0 = no action, but remember that is the last digit
3)  4 x 7 = 28
C4: 2 = 2 beads Pt LP
C3: 8 = 3 beads Pt LP, 1 bead Pt UP
C3: 1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next column)
C4: 1 bead Pt LP
4) 6 x 7 = 42
C3: 4 = 4 beads Pt LP
C2: 2 = 2 beads Pt LP
C2: 5 beads in LP now, 5 beads Af LP, 1 bead Pt UP


Result = 3,450


(F) 123 x246 = 30,258

Procedures:
1X 6, 2 x 6, 3 x 6; 1 x 4, 2 x 4, 3 x 4; 1 x 2, 2 x 2, 3 x 2 nine operations

1) 1 X 6 = 6
C3: 6 = 1 bead Pt UP, 1 bead Pt LP

2) 2 x 6 = 12
C3: 1 = 1 bead Pt LP
C2: 2 = 2 beads Pt LP

3) 3 x 6 = 18
C2: 1 = 1 bead Pt LP
C1: 8 = 1 bead Pt UP, 3 beads Pt LP

4) 1 x 4 = 4
C4: 4 = 4 bead Pt LP

5) 2 x 4 = 8
C3: 8 = 1 bead Pt UP, 3 beads Pt LP
C3: 1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next column)
C4: 1 bead Pt LP; 5 beads in LP now, 5 beads Af LP, 1 bead Pt UP

6) 3 x 4 = 12
C3: 1 = 1 bead Pt LP
C2: 2 = 2 beads Pt LP, 5 beads in LP now, 5 beads Af LP, 1 bead Pt UP

7) 1 x 2 = 2
C5: 2 = 2 beads Pt LP

8) 2 x 2 = 4
C4: 2 = 4 beads Pt LP

9) 3 x 2 = 6
C3: 6 = 1 bead Pt UP, 1 bead Pt LP
C3: 2 beads Af UP (10 units = 1 LP bead in next column)
C4: 1 bead Pt LP, 10 units in C4 now, 5 beads Af LP, 1 bead Pt UP, 1 bead Pt LP in C5


Result = 30,258


(F) 769 x 298 = 229,162

Procedures:
7 x 8, 6 x 8, 9 x 8; 7 x 9, 6 x 9, 9 x 9; 7 x 2, 6 x 2, 9 x 2, nine operations

1) 7 x 8 = 56
C4: 5 = 1 bead Pt UP
C3: 6 = 1 bead Pt UP, 1 bead Pt LP

2) 6 x 8 = 48
C3: 4 = 4 beads Pt LP, 10 units in C3 now, 5 beads Af LP, 1 bead Pt UP, 1 bead Pt LP in C4
C2: 8 = 3 beads Pt LP, 1 bead Pt UP

3) 9 x 8 = 72
C2: 7 = 2 beads Pt LP, 1 bead Pt UP, 10 units in C2 now, 5 beads Af LP, 1 bead Pt UP, 1 bead Pt LP in C3
C1: 2  = 2 beads Pt LP

4) 7 x 9 = 63
C5: 6 = 1 beads Pt LP, 1 bead Pt UP

5) 6 x 9 = 54
C4: 5 = 1 beads Pt UP,10 units in UP now, 2 beads Af UP, 1 bead Pt LP in C5
C3: 4 = 4 beads Pt LP, 5 beads Af LP, 1 bead Pt UP

6) 9 x 9 = 81
C3: 8 = 3 beads Pt LP, 1 bead Pt UP, 10 units in C3 UP now, 2 beads Af UP, 1 bead Pt LP in C4
C2 : 1 = 1 bead Pt LP

7) 7 x 2 = 14
C6: 1 = 1 bead Pt LP
C5: 1 bead Pt UP, 1 bead Af LP, 10 units in UP now, 2 beads Af UP, 1 bead Pt LP in C6

8) 6 x 2 = 12
C5: 1 = 1 bead Pt LP
C4: 2 = 2 bead Pt LP

9) 9 x 2 = 18
C4: 1 = 1 bead Pt LP
C3: 2 = 2 beads Pt LP, 5 beads Af LP, 1 bead Pt UP


Result = 226,162

Have Fun!



Modified: 27th May 2010

More information will be added in next update!

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