Finger Multiplication for the 9s, Explained
Date: 04/22/2002 at 10:29:39 From: Sarah Richards Subject: 9 Times Table Finger Trick I long ago learned the nine times table 'finger trick' that you feature in the Dr. Math archives, but am puzzled as to exactly WHY it works. Thanks a lot. Sarah
Date: 04/22/2002 at 12:17:46 From: Doctor Peterson Subject: Re: 9 Times Table Finger Trick Hi, Sarah. You are referring to this page, I believe: Finger Multiplication for the 9s http://mathforum.org/library/drmath/view/59085.html Suppose you multiply a single digit number N by 9. This is the same as multiplying it by 10-1: 9N = (10-1)N = 10N - N This looks almost like the expanded form for a two-digit number, where "AB" means 10A + B. Unfortunately, we have a negative "second digit," -N. So we borrow one from the tens: = 10(N-1) + (10-N) Since N-1 and 10-N are both single digits, this tells us that 9N has tens digit N-1 (the number of fingers to the left of the Nth finger), and ones digit 10-N (the number of fingers the to right of the Nth finger). Note also that the sum of the digits is N-1 + 10-N = 9, so that it uses up all your fingers except the one you bent down. Does that help? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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