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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.
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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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Portion (UP): Two beads - represent FIVE each. Lower Portion (LP): Five beads - represent ONE each. |
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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 |
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(1)
Fingers to Use |
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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 |
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(2)
Action to Take |
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"Push to" (Pt) or "Away from" (Af) the horizontal
bar (B). |
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(3) Set up Position |
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Upper Portion (UP) and Lower Portion (LP),
all beads
"Away from" (Af) the horizontal bar (B).
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(4) Direction to work from |
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From Left to Right for addition and subtraction.
(see examples below) |
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(5) Units Arrangement |
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(Seventy-six thousand five hundred and twenty-one) |
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| C1 | Unit | C4 | Thousand | |||
| C2 | Ten units | C5 | Ten thousand | |||
| C3 | Hundred | C6 | Hundred thousand | |||
| and so on..................... |
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(6) Five units and Ten units |
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(A)
Five units
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(5 beads in LP = 1 bead in UP) |
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| (1) |
5 green beads Af LP - use forefinger |
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| (2) |
1 green bead Pt UP - use forefinger |
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(B) Ten units
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(2 beads in UP = 10, 1 beads in LP in next
column also = 10) |
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| (1) |
C1: 2 green beads Af UP - use thumb |
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| (2) |
C2: 1 red bead Pt LP - use thumb |
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| (C) Ten units | |||||
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(2 beads in UP = 10 or 1 bead
in Up and 5 beads in LP = 10) |
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| (1) |
15 brown beads |
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| (2) |
=== C1: 1 bead Af UP - use thumb, 5 bead
Af LP - use forefinger
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| (3) |
=== C2: 1 bead, Pt LP - use thumb |
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(7) Addition |
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(A)
3 + 1 = 4 |
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Procedures: |
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(1) |
C1: 3 brown beads - use thumb
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(2) |
C1: add 1 === 1 red bead Pt LP - use thumb |
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Result = 4![]() |
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(B)
3 + 6 = 9 |
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Procedures: |
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| (1) |
C1: 3 brown beads - use thumb
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| (2) |
C1: add 6 === 1 red bead Pt UP - use forefinger === 1 red bead Pt LP - use thumb |
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Result = 9![]() |
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(C)
4 + 4 = 8 |
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Procedures: |
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| (1) |
C1: 4 brown beads - use thumb |
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| (2) |
C1: add 4 === 1 red bead Pt UP - use forefinger (= 5) === 1 red bead Af LP - use forefinger (subtract 1) |
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Result = 8![]() |
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(D)
8 + 7 = 15 |
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Procedures: |
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| (1) |
C1: 8 brown beads
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| (2) |
C1: add 7 === 2 red bead Pt LP - use thumb === 1 red bead Pt UP (= 5) - use forefinger, now C1 = 15 ![]() |
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=== C1: 5 bead Af LP - use forefinger === C1: 1 bead Af UP - use thumb |
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=== C2: 1 bead, Pt LP - use thumb |
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Result = 15![]() |
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(E)
91 + 5 = 96 |
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Procedures: |
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| (1) |
C2 = 9, C1 = 1
=== 91 brown beads ![]() |
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| (2) |
C1: add 5 === 1 bead Pt UP - use forefinger |
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Result = 96![]() |
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(F)
5,628 + 1,151 = 6,779 |
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Procedures: |
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| (1) |
5,628 brown beads![]() |
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| (2) |
Add 1,151 === C4 add 1 === C3 add 1 === C2 add 5 === C1 add 1 ![]() |
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Result = 6,779![]() |
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(G)
6,122 + 1,758 = 7,880 |
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Procedures: |
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| (1) |
6,122 brown beads![]() |
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| (2) |
Add 1,758
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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 ![]() |
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| (3) |
=== C1: 5 beads Af LP, 1 bead Af UP
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| (4) |
=== C2: 1 bead Pt LP |
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Result = 7,880![]() |
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(H)
6,647 + 1,868 = 8,515 |
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Procedures: |
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6,647 brown beads![]() |
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| (1) |
C4: add 1
=== 1 bead Pt LP ![]() |
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| (2) |
C3: add 8 === 1 bead Pt UP === 3 beads Pt LP ![]() |
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| (3) |
=== C3: 2 beads (= 10 units) Af UP (10 units = 1 LP bead in next
column C4)![]() |
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| (4) |
=== C4: 1 bead Pt LP![]() |
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| (5) |
C2: add 6 === 1 bead Pt UP, 1 bead Pt LP ![]() |
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| (6) |
=== C2: 1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next
column C3)![]() |
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=== C3: 1 bead Pt LP![]() |
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| (7) |
=== C3: 5 beads Af LP, 1 bead Pt UP (5 units in LP = 1 unit in
UP)![]() |
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| (8) |
C1: add 8 === 1 beads in Pt UP, 3 beads Pt LP ![]() ![]() |
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(9) |
=== C1: 1bead Af UP, 5 beads Af LP, 1 bead Pt LP in C2![]() |
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Result = 8,515![]() |
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All procedures together![]() |
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(8) Subtraction |
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(A) 54 - 17 = 37 |
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Procedures: |
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| (1) |
C2: 5, C1: 4 54 brown beads ![]() |
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C2: 5 - 1 = 4 === 1 bead Af UP ![]() === 4beads Pt LP ![]() |
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| (3) |
C1: 4 - 7 === 4 is not enough to subtract 7, hence borrow 1 unit (= 10) from C2 ![]() |
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=== C1: = 14![]() === 14 - 7 = 7 ![]() |
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Result = 37![]() |
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All procedures together![]() |
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(B)
94 - 28 = 66 |
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Procedures:
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| (1) |
C2 = 9, C1 = 4 94 brown beads ![]() |
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| (2) |
C2: 9 - 2 is 7
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| (3) |
C1: 4 - 8 === 4 is not enough to subtract 8, hence borrow 1 unit (= 10) from C2 |
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| (4) |
=== C2: 7 - 1 = 6 |
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| (5) |
=== C1: 14 - 8 = 6![]() |
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Result = 66![]() |
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(C)
9,699 - 6,647 = 3,052 |
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Procedures: |
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| (1) |
C4 = 9 C3 = 6 C2 = 9 C1 = 9 9,699 brown beads ![]() |
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| (2) |
C4: 9 Subtract 6 = 3
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| (3) |
C3: 6 Subtract 6 = 0
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| (4) |
C2: 9 Subtract 4 = 5
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| (5) |
C1: 9 Subtract 7 = 2 |
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Result = 3,052![]() |
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(9) Multiplication |
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(A)
24 x 6 = 144 |
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Procedures: ![]() |
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(1) 6 x 4 = 24
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C2: |
2 === 2 beads Pt LP | ||||
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C1: |
4 === 4 beads Pt LP
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(2) 6
x 2 = 12
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C3: |
1 === 1 beads Pt LP | ||||
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C2: |
2 === 2 beads Pt LP![]() |
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Result = 144![]() |
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(B)
62 x 8 = 496 |
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Procedures:![]() |
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(1) 8
x 2 = 16
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C2: |
1 === 1 bead Pt LP | ||||
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C1: |
6 === 1 bead Pt UP, 1 bead Pt LP![]() |
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(2) 8
x 6 = 48
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C3: |
4 === 4 beads Pt LP | ||||
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C2: |
8 === 3 beads Pt LP, 1 bead Pt UP
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Result = 496
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(C)
86 x 7 = 602 |
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Procedures:![]() |
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(1) 7
x 6 = 42
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C2: |
4 === 4 beads Pt LP | ||||
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C1: |
2 === 2 beads Pt LP![]() |
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(2) 7 x 8 = 56
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C3: |
5 === 1 bead Pt UP | ||||
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C2: |
6 === 1 bead Pt LP,1 bead Pt UP![]() |
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Final action
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C2: |
1 bead Af UP, 5 beads Af LP (10 units = 1 LP bead in next column C3) | ||||
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C3: |
1 bead Pt LP
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Result = 602![]() |
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(D)
23 x 13 = 299 |
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Procedures:![]() |
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(1) 3
x 3 = 9
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C1: |
9 === 4 beads Pt LP, 1 bead Pt UP
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(2) 3 x 2 = 6
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C2: |
6 === 1 bead Pt LP, 1 bead Pt UP![]() |
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(3) 1 x 3 = 3
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C2: |
3 === 3 beads Pt LP![]() |
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(4) 1 x 2 = 2
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C3: |
2 === 2 beads Pt LP
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Result = 299
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All procedures together![]() |
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(E)
46 x 75 = 3,450 |
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Procedures:![]() |
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(1) 5x6 = 30
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C2: |
3 === 3 beads Pt LP | ||||
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C1: |
0 === no action![]() |
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(2) 5x4 = 20
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C3: |
2 === 2 beads Pt LP | ||||
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C2: |
0 === no action, remember that is the last digit![]() |
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(3) 7 x 6 = 42
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C3: |
4 === 1 bead Pt UP, 1 bead Af LP | ||||
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C2: |
2 === 2 beads Pt LP, 1 bead Pt UP
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=== C2: 5 beads Af LP, 1 bead Pt UP
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(4) 7 x 4 = 28
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C4: |
2 === 2 beads Pt LP | ||||
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C3: |
8 === 3 beads Pt LP, 1 bead Pt UP
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=== C3: 2 beads Af UP, 1 bead Pt LP in C4![]() |
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Result = 3,450
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All procedures together![]() |
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(F)
123 x 246 = 30,258 |
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Procedures:![]() |
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(1)
6 X 3 = 18 |
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C2: |
1 === 1 bead Pt LP | ||||
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C1: |
8 === 1 bead Pt UP, 3 beads Pt LP![]() |
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(2) 6 x 2 = 12 |
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C3: |
1 === 1 bead Pt LP | ||||
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C2: |
2 === 2 beads Pt LP
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(3) 6 x 1 = 6
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C3: |
6 === 1 bead Pt LP, 1 bead Pt UP |
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(4) 4 x 3 = 12
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C3: |
1 === 1 bead Pt LP 2 === 2 beads Pt LP ![]() === C2: 5 beads Af LP, 1 bead Pt UP ![]() |
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(5) 4 x 2 = 8
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C3: |
8 === 1 bead Pt LP in C4, 2 beads Af LP in C3![]() |
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(6) 4 x 1 = 4
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C4: |
4 === 4 beads Pt LP
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![]() === 5 beads Af LP, 1 bead Pt UP ![]() |
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(7) 2 x 3 = 6
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C3: |
6 === 1 bead Pt LP, 1 bead Pt UP![]() === 2 beads Af UP, 1 bead Pt LP in C4 ![]() |
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(8) 2 x 2 = 4
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C4: |
4 === 4 beads Pt LP![]() === 1 bead Af UP, 5 beads Af LP, 1 bead Pt LP in C5 ![]() |
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(9) 2 x 1 = 2
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C5: |
2 === 2 beads Pt LP![]() |
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Result = 30,258![]() |
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All procedures together![]() |
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(G)
769 x 298 = 229,162 |
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Procedures: |
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(1) 8 x 9 = 72
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C2: |
7 === 1 bead Pt UP, 2 beads Pt LP | ||||
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C1: |
2 === 2 beads Pt LP![]() |
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(2) 8 x 6 = 48
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C3: |
4 === 4 beads Pt LP, | ||||
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C2: |
8 === 3 beads Pt LP, 1 bead Pt UP
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![]() === C2: 5 beads Af LP, 1 bead Pt UP, 1 bead Pt LP in C3 ![]() === C3: 5 beads Af LP, 1 bead Pt UP ![]() |
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(3) 8 x 7 = 56
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C4: |
5 === 1 bead Pt UP | ||||
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C3: |
6 === 1 bead Pt LP, 1 bead Pt UP
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=== C3: 2 beads Af UP, 1 bead Pt LP in C4![]() |
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(4) 9 x 9 = 81
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C3: |
8 === 1 bead Pt UP, 3 beads Pt LP | ||||
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C2: |
1 === 1 bead Pt LP
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(5) 9 x 6 = 54
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C4: |
5 === 1 bead Pt UP | ||||
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C3: |
4 === 1 bead Pt UP, 1 bead Af LP
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(6) 9 x 7 = 63
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C5: |
6 === 1 bead Pt LP, 1 bead Pt UP | ||||
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C4: |
3 === 3 beads Pt LP
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![]() === C4: 5 beads Af LP, 1 bead Pt UP ![]() |
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(7) 2 x 9 = 18
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C4: |
1 === 1 bead Pt LP | ||||
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C3: |
8 === 2 beads Pt UP, 2 beads Af LP
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![]() === C3: 2 beads Af UP, 1 bead Pt LP in C4 ![]() |
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(8) 2 x 6 = 12
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C5: |
1 === 1 bead Pt LP | ||||
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C4: |
2 === 2 beads Pt LP | ||||
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(9) 2 x 7 = 14
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C6: |
1 === 1 bead Pt LP | ||||
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C5: |
4 === 1 bead Pt UP, 1 bead Af LP
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![]() === C5: 2 beads Af UP, 1 bead Pt LP in C6 ![]() |
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Result = 229,162
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All procedures together![]() |
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Have Fun! |
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