Modified: 28th August 2011

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.



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".


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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.
Basic operation === apply to both Upper Portion (UP) and Lower Portion (LP)
=== Push Upward -- use Thumb
=== Push Downward -- use 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. (see examples below)

(5) Units Arrangement

(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

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

(1) 5 green beads Af LP - use forefinger



(2) 1 green bead Pt UP - use forefinger



(B) Ten units
(2 beads in UP = 10, 1 beads in LP in next column also = 10)

(1) C1: 2 green beads Af UP - use thumb



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



(C) Ten units
(2 beads in UP = 10 or 1 bead in Up and 5 beads in LP = 10)

(1) 15 brown beads



(2) === C1: 1 bead Af UP - use thumb, 5 bead Af LP - use forefinger

(3) === C2: 1 bead, Pt LP - use thumb





(7) Addition

(A) 3 + 1 = 4

Procedures:

(1)

C1: 3 brown beads - use thumb

(2)

C1: add 1

=== 1 red bead Pt LP - use thumb



Result = 4



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(B) 3 + 6 = 9

Procedures:

(1) C1: 3 brown beads - use thumb

(2) C1: add 6

=== 1 red bead Pt UP - use forefinger
=== 1 red bead Pt LP - use thumb




Result = 9



(C) 4 + 4 = 8

Procedures:

(1) C1: 4 brown beads - use thumb



(2) C1: add 4

=== 1 red bead Pt UP - use forefinger (= 5)
=== 1 red bead Af LP - use forefinger (subtract 1)



Result = 8





(D) 8 + 7 = 15

Procedures:

(1) C1: 8 brown beads



(2) C1: add 7

=== 2 red bead Pt LP - use thumb
=== 1 red bead Pt UP (= 5) - use forefinger, now C1 = 15



=== C1: 5 bead Af LP - use forefinger
=== C1: 1 bead Af UP - use thumb
=== C2: 1 bead, Pt LP - use thumb



Result = 15



(E) 91 + 5 = 96

Procedures:

(1) C2 = 9, C1 = 1

=== 91 brown beads



(2) C1: add 5

=== 1 bead Pt UP - use forefinger

Result = 96





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

Procedures:

(1) 5,628 brown beads



(2) Add 1,151

=== C4 add 1
=== C3 add 1
=== C2 add 5
=== C1 add 1



Result = 6,779



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

Procedures:

(1) 6,122 brown beads



(2) Add 1,758

C4 add 1 === 1 bead Pt LP
C3 add 7 === 1 bead Pt UP, 2 beads Pt LP
C2 add 5 === 1 bead Pt UP
C1 add 8 === 1 bead Pt UP, 3 beads Pt LP, now C1 = 10 units




(3) === C1: 5 beads Af LP, 1 bead Af UP

(4) === C2: 1 bead Pt LP

Result = 7,880





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

Procedures:

6,647 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 C4)



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



(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 C3)



=== C3: 1 bead Pt LP



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



(8) C1: add 8

=== 1 beads in Pt UP, 3 beads Pt LP





(9)

=== C1: 1bead Af UP, 5 beads Af LP, 1 bead Pt LP in C2



Result = 8,515



All procedures together



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(8) Subtraction

(A) 54 - 17 = 37

Procedures:

(1) C2: 5, C1: 4

54 brown beads 



(2) C2: 5 - 1 = 4

=== 1 bead Af UP



=== 4beads Pt LP



(3) C1: 4 - 7

=== 4 is not enough to subtract 7, hence borrow 1 unit (= 10) from C2



=== C1: = 14



=== 14 - 7 = 7



Result = 37



All procedures together



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(B) 94 - 28 = 66

Procedures:

(1) C2 = 9, C1 = 4

94 brown beads



(2) C2: 9 - 2 is 7



(3) C1: 4 - 8

=== 4 is not enough to subtract 8, hence borrow 1 unit (= 10) from C2

(4) === C2: 7 - 1 = 6

(5) === C1: 14 - 8 = 6



Result = 66





(C) 9,699 - 6,647 = 3,052

Procedures:

(1) C4 = 9
C3 = 6
C2 = 9
C1 = 9

9,699 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:


(1) 6 x 4 = 24

C2:

2 === 2 beads Pt LP

C1:

4 === 4 beads Pt LP



(2) 6 x 2 = 12

C3:

1 === 1 beads Pt LP

C2:

2 === 2 beads Pt LP



Result = 144



(B) 62 x 8 = 496

Procedures:


(1) 8 x 2 = 16

C2:

1 === 1 bead Pt LP

C1:

6 === 1 bead Pt UP, 1 bead Pt LP



(2) 8 x 6 = 48

C3:

4 === 4 beads Pt LP

C2:

8 === 3 beads Pt LP, 1 bead Pt UP



Result = 496





(C) 86 x 7 = 602

Procedures:


(1) 7 x 6 = 42

C2:

4 === 4 beads Pt LP

C1:

2 === 2 beads Pt LP



(2) 7 x 8 = 56

C3:

5 === 1 bead Pt UP

C2:

6 === 1 bead Pt LP,1 bead Pt UP



Final action

C2:

1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next column C3)

C3:

1 bead Pt LP



Result = 602



(D) 23 x 13 = 299

Procedures:


(1) 3 x 3 = 9

C1:

9 === 4 beads Pt LP, 1 bead Pt UP



(2) 3 x 2 = 6

C2:

6 === 1 bead Pt LP, 1 bead Pt UP



(3) 1 x 3 = 3

C2:

3 === 3 beads Pt LP



(4) 1 x 2 = 2

C3:

2 === 2 beads Pt LP



Result = 299



All procedures together



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(E) 46 x 75 = 3,450

Procedures:


(1) 5x6 = 30

C2:

3 === 3 beads Pt LP

C1:

0 === no action



(2) 5x4  = 20

C3:

2 === 2 beads Pt LP

C2:

0 === no action, remember that is the last digit



(3) 7 x 6 = 42

C3:

4 === 1 bead Pt UP, 1 bead Af LP

C2:

2 === 2 beads Pt LP, 1 bead Pt UP



=== C2: 5 beads Af LP, 1 bead Pt UP



(4) 7 x 4 = 28

C4:

2 === 2 beads Pt LP

C3:

8 === 3 beads Pt LP, 1 bead Pt UP



=== C3: 2 beads Af UP, 1 bead Pt LP in C4



Result = 3,450



All procedures together



(F) 123 x 246 = 30,258

Procedures:


(1) 6 X 3 = 18

C2:

1 === 1 bead Pt LP

C1:

8 === 1 bead Pt UP, 3 beads Pt LP



(2) 6 x 2 = 12

C3:

1 === 1 bead Pt LP

C2:

2 === 2 beads Pt LP



(3) 6 x 1 = 6

C3:

6 === 1 bead Pt LP, 1 bead Pt UP



(4) 4 x 3 = 12

C3:
C2:


1 === 1 bead Pt LP
2 === 2 beads Pt LP




=== C2: 5 beads Af LP, 1 bead Pt UP





(5) 4 x 2 = 8

C3:

8 === 1 bead Pt LP in C4, 2 beads Af LP in C3



(6) 4 x 1 = 4

C4:

4 === 4 beads Pt LP



=== 5 beads Af LP, 1 bead Pt UP





(7) 2 x 3 = 6

C3:

6 === 1 bead Pt LP, 1 bead Pt UP



=== 2 beads Af UP, 1 bead Pt LP in C4



(8) 2 x 2 = 4

C4:

4 === 4 beads Pt LP



=== 1 bead Af UP, 5 beads Af LP, 1 bead Pt LP in C5



(9) 2 x 1 = 2

C5:

2 === 2 beads Pt LP



Result = 30,258



All procedures together



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(G) 769 x 298 = 229,162

Procedures:


(1) 8 x 9 = 72

C2:

7 === 1 bead Pt UP, 2 beads Pt LP

C1:

2 === 2 beads Pt LP





(2) 8 x 6 = 48

C3:

4 === 4 beads Pt LP,

C2:

8 === 3 beads Pt LP, 1 bead Pt UP



=== C2: 5 beads Af LP, 1 bead Pt UP, 1 bead Pt LP in C3



=== C3: 5 beads Af LP, 1 bead Pt UP




(3) 8 x 7 = 56

C4:

5 === 1 bead Pt UP

C3:

6 === 1 bead Pt LP, 1 bead Pt UP



=== C3: 2 beads Af UP, 1 bead Pt LP in C4





(4) 9 x 9 = 81

C3:

8 === 1 bead Pt UP, 3 beads Pt LP

C2:

1 === 1 bead Pt LP



(5) 9 x 6 = 54

C4:

5 === 1 bead Pt UP

C3:

4 === 1 bead Pt UP, 1 bead Af LP



=== C3: 2 beads Af UP, 1 bead Pt LP in C4



=== C4: 2 beads Af UP, 1 bead Pt LP in C5



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(6) 9 x 7 = 63

C5:

6 === 1 bead Pt LP, 1 bead Pt UP

C4:

3 === 3 beads Pt LP 



=== C4: 5 beads Af LP, 1 bead Pt UP



(7) 2 x 9 = 18

C4:

1 === 1 bead Pt LP

C3:

8 === 2 beads Pt UP, 2 beads Af LP



=== C3: 2 beads Af UP, 1 bead Pt LP in C4



(8) 2 x 6 = 12

C5:

1 === 1 bead Pt LP

C4:

2 === 2 beads Pt LP





(9) 2 x 7 = 14

C6:

1 === 1 bead Pt LP

C5:

4 === 1 bead Pt UP, 1 bead Af LP



=== C5: 2 beads Af UP, 1 bead Pt LP in C6



Result = 229,162



All procedures together



Have Fun!



Modified: 28th August 2011

More information will be added in next update!

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