Multiplying by NineDate: 01/10/97 at 03:28:45 From: Jeffrey Gleaves Subject: Number nine Hi, Why is it that when you multiply nine times any number between one and ten, the sum of the two digits added together equals 9? 9*1=9 9*2=18 1+8=9 9*3=27 2+7=9 9*4=36 3+6=9 Please forgive my stupidity and thank you for your time. Date: 01/10/97 at 14:54:24 From: Doctor Rob Subject: Re: Number nine No stupidity displayed here! Basically, it is because 9 = 10 - 1, and 10 is the base of our system of numerals. 9*a = 10*a - a = 10*(a - 1) + (10 - a) (by borrowing 1 from the 10's) If 0 < a < 10, then the digits of 9*a are: a-1 is the 10's digit, and 10-a is the 1's digit. (a-1) + (10-a) = 9. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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