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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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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. |
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| Upper
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. |
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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 | |||
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. |
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| (5)
Units Arrangement
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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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| (1) | Five
units (5 beads in LP = 1 bead in UP) |
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(a) 5 green beads Af LP - use forefinger |
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(b)1 green bead Pt UP - use forefinger |
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| (2) | Ten
units (2 beads in UP = 1 beads in LP in next column) |
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(a) C1: 2 green beads Af UP - use forefinger |
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(b) C2: 1 red bead Pt LP - use thumb |
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| (3) | Ten
units |
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(a) 15 brown beads |
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(b) C1: 1 bead Af UP - use forefinger, 5 bead Af LP - use forefinger (c) C2: 1 bead, Pt LP - use thumb |
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| (7) Addition
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| (A) | 3
+ 1 = 3 |
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(a) C1: 3 brown beads (b) C1: add 1 -- 1 red bead Pt LP - use thumb |
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| (B) | 3
+ 6 = 9 |
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(a) C1: 3 brown beads (b) C1: add 6 -- 1 red bead Pt LP - use thumb, 1 red bead Pt UP - use forefinger |
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| (C) | 4 + 4 =
8 |
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(a) C1: 4 brown beads |
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(b) C1: add 4 -- 1 red bead Pt UP - use forefinger, 1 red bead, Af LP - use thumb |
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| (D) | 8
+ 7 = 15 |
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(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 |
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| (E) | 91 + 5
= 96 |
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(a) C2 C1: 91 brown beads |
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(b) C1: add 5 -- 1 red bead, Pt UP - use thumb Result = 96 |
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| (F) | 5,628 +
1,151 = 6,779 |
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(a) 5,628 -- brown beads (b) Add 1,151 - start from left hand side |
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| (G) | 6,122 +
1,758 = 7,880 |
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(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 |
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| (H) | 6,647 + 1,868
= 8,515
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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 |
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| (8) Subtraction
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(A) |
54 - 17 = 37
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| 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 |
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| (B) |
94 - 28 = 66
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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 |
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| (C) |
9699 - 6647 = 3,052
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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 |
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| (9)
Multiplication
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(A) |
24 x 6 = 144
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| 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 | |||||
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C1: 4 = 4 beads Pt LP
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(B) |
62 x 8 = 496
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| 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 | ||||
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C1: 6 = 1 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: | |||||
| 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
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(D) |
23 x 13 = 299
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| 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 | |||
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C2: 3 = 3 beads Pt LP
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| Result = 299
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| (E) | 46
x 75 = 3,450
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| 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
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(F) | 123
x246 = 30,258
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| 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
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| 1) | 1 X 6 = 6
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| C3: 6 = 1 bead
Pt UP, 1 bead Pt LP |
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| 2) | 2 x 6 = 12![]() |
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| C3: 1 = 1 bead Pt LP | |||||
| C2: 2 = 2 beads
Pt LP |
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| 3) | 3 x 6 = 18![]() |
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| C2: 1 = 1 bead Pt LP | |||||
| C1: 8 = 1 bead Pt
UP, 3 beads Pt LP |
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| 4) | 1 x 4 = 4![]() |
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| C4: 4 = 4 bead Pt
LP |
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| 5) | 2 x 4 = 8 | ||||
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| 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
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| 6) | 3 x 4 = 12 | ||||
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| 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
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| 7) | 1 x 2 = 2 | ||||
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| C5: 2 = 2 beads Pt
LP
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| 8) | 2 x 2 = 4 | ||||
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| C4: 2 = 4 beads Pt
LP
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| 9) | 3 x 2 = 6 | ||||
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| 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
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(F) | 769
x 298 = 229,162
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| 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
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| 1) | 7
x 8 = 56
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| C4: 5 = 1 bead Pt UP | |||||
| C3: 6 = 1 bead
Pt UP, 1 bead Pt LP
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| 2) | 6
x 8 = 48
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| 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
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| 3) | 9
x 8 = 72
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| 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
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| 4) | 7
x 9 = 63
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| C5: 6 = 1 beads Pt
LP, 1 bead Pt UP
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| 5) | 6
x 9 = 54
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| 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
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| 6) | 9
x 9 = 81
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| 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
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| C2 : 1 = 1 bead Pt
LP
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| 7) | 7
x 2 = 14
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| 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
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| 8) | 6
x 2 = 12
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| C5: 1 = 1 bead Pt LP | |||||
| C4: 2 = 2 bead Pt
LP
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| 9) | 9
x 2 = 18
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| C4: 1 = 1 bead Pt LP | |||||
| C3: 2 = 2 beads Pt
LP, 5 beads Af LP, 1 bead Pt UP
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Have
Fun!
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