Well in the beginning I promised you multiplication tables using the fingers of your hands and without the use of calculator up to 20x20. I did not forget. In fact if you master the technique you never need a calculator for any multiplication and you never need to commit tables to memory.
But first remember few important things. Since we are using only the fingers of our hands which are finite and as the numbers grow we have to assign some values to the fingers depending upon the growth. That is all the care you have to take and remember.
Let us represent the fingers of the left hand as LL, LR, LM, LI and LT which respectively mean Little, Ring, Middle, Index and Thumb of the Left Hand. Similarly, RL, RR, RM, RI and RT represent respectively Little, Ring, Middle, Index and Thumb of the Right Hand.
In the first cycle we assign values 6 to 10 to LL, LR, LM, LI, LT and RL, RR, RM, RI, and RT.
Our tables start from 6x6 and we assume you know the values up to this point.
The procedure and the values
Suppose you need to find the values from 6x6 to 10x10 in this cycle you can give it in a trice if you practice well.
Join the fingers represenbting the multiplicands. That means
1) if you need 6x8 join LL and RM,
2) if you need 7x9 join LR and RI,
3) if you need 8x9 join LM and RI and so on.
All the fingers joined and lying below represent 10s.
In the first example given of 6x8, LL, RL, RR, and RM represents 10s
In the second case, LL, LR, RL, RR, RM and RI represent 10s
In the third case, LL, LR, LM, RL, RR, RM. and RI represent 10s
There may be free fingers on one or both hands. They represent units if they are there, otherwise zero.
In case 1, LR to LT are free (4 fingers on the left hand), and RI and RT (2 fingers on the right hand) are free.
In case 2, 3 on the left and 1 on the right is free.
In case 3, Multiply the number of free fingers on the left with the number of free fingers on the right.
Add the tens and the value of step 2 to get the final value.
In case 1, we have 4 tens and 4x2=8, therefore 6x8=48
In case 2, we have 6 tens and 3x1=3, therefore, 7x9=63
In case 3, we have 7 tens and 2x1=2, therefore, 8x9=72.
Please go through from 6x6 to 10x10, we get every value with ease. It seems sometimes, if god has given us 10 fingers to two hands to use decimal system. Isn’t it?
Next time we shall move further. Practice and master it. It is so easy.