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

  Patterns in Kojima's Method for Multiplication
 

An abacus is not a calculator. Rather, it's a tool for recording answers. This becomes particularly evident when doing problems of multiplication. Once learned, the technique of recording answers onto the correct rods makes doing multiplication virtually foolproof.

Kojima's technique is so effective in part  because we're taught to place product answers right next to the numbers in the multiplicand. This ensures that the correct numbers are always added to the correct rods.

Kojima always sets the multiplier to the left of the multiplicand. I will do the same in each example.

Example: ab * c = xxx

c * ab

c *  b|xx       c * b = xx, clear b
c * a|xx        c * a = xx
ans: |xxx


Example: ab * cd = xxxx

cd * ab 

c  *  b|xx      c * b = xx
 d *  b| xx     d * b = xx
       |xxx     interim answer, clear b
c  * a|xx       c * a = xx
 d * a| xx      d * a = xx
ans:  |xxxx


Example: abc * de = xxxxx

de * abc 

d  *   c|xx       c * c = xx
 e *   c| xx      d * c = xx
        |xxx      interim answer, clear c
d  *  b|xx        c * b = xx
 e *  b| xx       d * b = xx
       |xxxx      interim answer, clear b
d  * a|xx         c * a = xx
 e * a| xx        d * a = xx
ans:  |xxxxx


Example: abc * def = xxxxxx

def * abc 

d   *   c|xx      d * c = xx
 e  *   c| xx     e * c = xx
  f *   c|  xx    f * c = xx
         |xxxx    interim answer, clear c
d   *  b|xx       d * b = xx
 e  *  b| xx      e * b = xx
  f *  b|  xx     f * b = xx
        |xxxxx    interim answer, clear b
d   * a|xx        d * a = xx
 e  * a| xx       e * a = xx
  f * a|  xx      f * a = xx
ans:   |xxxxxx

 

▪ Multiplication Examples
 

© September, 2007
Totton Heffelfinger   Toronto Ontario  Canada
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totton[at]idirect[dot]com