ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual
 

Multiplication and Decimals

The following is an example where one of our group was having difficulty getting the unit number in the product answer to fall on a predetermined unit rod. Since his rod calculations were correct, the problem was solved in Step 2 of the first example.

At 01:12 AM 7/20/2004 -0000, Mr. K wrote:
Here's what I did with 93 x .026, I don't understand why my  answer is wrong.

 93 = +2
.026 = -1
always add = +1

results start on rod +2 (rod E)

put 93 on E and *F*

 

Hi Mr. K,

Following the rules for setting problems onto the soroban so that the unit number in the product falls naturally on a predetermined unit rod, your calculations are absolutely correct. Set 93 on E and *F*


PROBLEM: 1   93 x .026 = 2.418

93 x .026...........N =  2  - 1  + 1 = 2

NUMBERS ON THE SOROBAN

----A----B----C----D----E---*F*---G----H----I----J----K----
...+6...+5...+4...+3...+2...+1....0...-1...-2...-3...-4....

 

Step 1: Set the multiplicand 93 on EF and and the multiplier 26 on BC. (Fig.1)

   Fig. 1

  
Step 1
A B C D E F G H I J K L M
    .     .     .     .  
2 6 0 0 9 3 0 0 0 0 0 0 0


Step 2:
Multiply the 3 on F by the 2 on A and add the product 06 to rods GH. (It's important to remember that when adding products to the soroban always think in terms of adding two numbers. For example 3 x 4 = 12 and 3 x 2 = 06)

2a: Multiply the 3 on F by the 6 on B and add the product 18 to HI. Clear the multiplicand 3 on F leaving 78 on rods HI. (Fig.2)

   Fig.2

  
Step 2
A B C D E F G H I J K L M
    .     .     .     .  
2 6 0 0 9 3 0 0 0 0 0 0 0
          + 0 6            Step 2
            + 1 8          Step 2a
2 6 0 0 9 0 0 7 8 0 0 0 0


Step 3:
Multiply the 9 on E by the 2 on A and add the product 18 to FG.

3a: Multiply the 9 on E by the 6 on B and add the product 54 to GH. Clear the multiplicand 9 on F leaving 2418 on rods FGHI. Because rod *F* is the unit rod the answer reads  2.418. (Fig.3)

   Fig.3

  
Step 3
A B C D E F G H I J K L M
    .     .     .     .  
2 6 0 0 9 0 0 7 8 0 0 0 0
        + 1 8              Step 3
          + 5 4            Step 3a
2 6 0 0 0 2 4 1 8 0 0 0 0

 

PROBLEM: 2   6.0005 x .036 = 0.216018

6.0005 x .036...........N =  1  - 1  + 1 = 1

NUMBERS ON THE SOROBAN

----A----B----C----D----E---*F*---G----H----I----J----K----
...+6...+5...+4...+3...+2...+1....0...-1...-2...-3...-4....


Step 1:
Set the multiplicand 60005 on FGHIJ and and the multiplier 36 on CD. (Fig.4)

   Fig.4

  
Step 1
A B C D E F G H I J K L M
    .     .     .     .  
0 3 6 0 0 6 0 0 0 5 0 0 0


Step 2:
Multiply the 5 on J by the 3 on C and add the product 15 to rods KL.

2a: Multiply the 5 on J by the 6 on D and add the product 30 to LM. Clear the multiplicand 5 on J leaving 180 on rods KLM. (Fig.5)

   Fig.5

  
Step 2
A B C D E F G H I J K L M
    .     .     .     .  
0 3 6 0 0 6 0 0 0 5 0 0 0
                  + 1 5    Step 2
                    + 3 0  Step 2a
0 3 6 0 0 6 0 0 0 0 1 8 0


Step 3:
Multiply the 6 on F by the 3 on C and add the product 18 to GH.

3a: Multiply the 6 on F by the 6 on D and add the product 36 to HI. Clear the multiplicand 6 on F leaving 216018 on rods GHIJKL. Because rod F is the unit rod the answer reads 0.216018. (Fig.6)

   Fig.6

  
Step 3
A B C D E F G H I J K L M
    .     .     .     .  
0 3 6 0 0 6 0 0 0 0 1 8 0
          + 1 8            Step 3
            + 3 6          Step 3a
0 3 6 0 0 0 2 1 6 0 1 8 0

 

- Totton

Abacus: Mystery of the Bead
Advanced Abacus Techniques

© July, 2004
Totton Heffelfinger   Toronto Ontario  Canada
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totton[at]idirect[dot]com