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
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
d  *  b|xx        c * b = xx
e *  b| xx       d * b = xx
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
d   *  b|xx       d * b = xx
e  *  b| xx      e * b = xx
f *  b|  xx     f * b = xx
d   * a|xx        d * a = xx
e  * a| xx       e * a = xx
f * a|  xx      f * a = xx
ans:   |xxxxxx
```