ABACUS: MYSTERY OF THE BEAD

The Bead Unbaffled - An Abacus Manual

Multiplication and DecimalsThe 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 = 2.41893 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

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)

Step 2:

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 8Step 2a 2 6 0 0 9 0 0 7 8 0 0 0 0

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

Step 3:

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 4Step 3a 2 6 0 0 0 2 4 1 8 0 0 0 0

PROBLEM: 2 6.0005 x .036 = 0.2160186.0005 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....

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

Step 1:

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

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

Step 2:

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 0Step 2a 0 3 6 0 0 6 0 0 0 0 1 8 0

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

Step 3:

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 6Step 3a 0 3 6 0 0 0 2 1 6 0 1 8 0

- Totton

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Abacus: Mystery of the Bead

▪Advanced Abacus Techniques© July, 2004

Totton Heffelfinger Toronto Ontario Canada

totton[at]idirect[dot]com