Just4Fun 3: Mathematics 1

Just4Fun 3

Arithmetic Puzzle

A tribe of (Native American) Indians use finger reckoning to multiply numbers between 5 and 10.  They extend the number of fingers equal to the excess of  one number over 5 and do the same with the other number on the other hand.  The sum of the extended fingers gives the first figure of the product, and the product of  the unextended fingers gives the second figure. 


For example, if we wish to multiply 8 times 6 we extend 3 fingers on one hand and one on the other.  These are the excesses over 5 of 8 and 6.  Then 3 + 1 = 4 is the sum of the extended fingers, and 2 x 4 = 8 is the product of the unextended fingers.  We get 4 and 8, or 48, the product of 8 times 6.


Can you explain why this Indian finger method is correct?

Problem source:

"General College Mathematics", W. L. Ayres, Cleota G. Fry, H. F. S. Jonah, McGraw Hill Book Company, 1952  p. 196