In the second numbering, or numbers above 10, renumber your fingers; thumbs, 11; first fingers, 12, etc.  Let us multiply 12 by 12.

Put together the tips of the fingers labeled 12.  At a glance you see four tens or 40.  At this point we leave the method explained in Case 1 and ignore the units (lower fingers) altogether.  We go back to the upper fingers again

[Illustration:  “12 Times 12”]

and multiply the number of upper fingers used on the one hand by the number of upper fingers used on the other hand, viz., 2 times 2 equals 4.  Adding 4 to 40 gives us 44.  We now add 100 (because anything over 10 times 10 would make over 100) and we have 144, the product of 12 times 12.

The addition of 100 is arbitrary, but being simple it saves time and trouble.  Still, if we wish, we might regard the four upper fingers in the above example as four twenties, or 80, and the six lower fingers as six tens, or 60; then returning to the upper fingers and multiplying the two on the right hand by the two on the left we would have 4; hence 80 plus 60 plus 4 equals 144; therefore the rule of adding the lump sum is much the quicker and easier method.

Above 10 times 10 the lump sum to add is 100; above 15 times 15 it is 200; above 20 times 20, 400; 25 times 25, 600, etc., etc., as high as you want to go.

In the third numbering to multiply above 15 renumber your fingers, beginning the thumbs with 16, first finger 17, and so on.  Oppose the proper finger tips as before, the upper fingers representing a value of 20.  Proceed as in the first numbering and add 200.  Take For example 18 times 18.

At a glance we see six twenties plus 2 units on left hand times 2 units on right hand plus 200 equals 324.

In the fourth numbering the fingers are marked, thumbs, 21, first fingers 22, etc., the value of the upper fingers being 20.  Proceed as in the second lumbering, adding 400 instead of 100.

[Illustration:  “18 Times 18”]

Above 25 times 25 the upper fingers represent a value of 30 each and after proceeding as in the third numbering you add 600 instead of 200.

This system can be carried as high as you want to go, but you must remember that for figures ending in 1, 2, 3, 4 and 5 proceed as in the second numbering.  For figures ending in 6, 7, 8, 9 and 10 the third numbering applies.

Determine the value of the upper fingers whether they represent tens, twenties, thirties, forties, or what.  For example, any two figures between 45 and 55, the value of the upper fingers would be 50, which is the half-way point between the two fives.  In 82 times 84 the value of the upper fingers would be 80 (the half-way point between the two fives, 75 and 85, being 80).  And the lump sum to add.

Just three things to remember: 

Which numbering is to follow, whether the one described in second or third numbering; the value which the upper fingers have; and, lastly, the lump sum to add, and you will be able to multiply faster and more accurately than you ever dreamed of before.