I am an upgrading instructor at a drop-in program in Regina.  One of my students is taking General Math 30 through correspondence, and we have run into some confusing instructions. The section is about divisibility rules, and we did just fine up until the rule for Divisibility by 11. The statement is as follows:

If the difference between the sum of the odd-numbered digits and the sum of the even-numbered digits, counted from right to left, is divisible by 11, then the number is divisible by 11.

Example: 528

(sum of odd-numbered digits) 8 + 5 = 13
(sum of even-numbered digits) 2
13 - 2 = 11
11 divided by 11 = 1 therefore, 528 is divisible by 11.

There then follows a series of numbers which, although we tried to use the rule, simply don't work.  Using the rule (as we interpret it) indicates the number should not be divisible by 11, but when actually solved, the rule didn't necessarily make sense.    (Does this make any sense?) Other numbers used:  9361, 2805, 6182, 7893, 11,097 Maybe I'm missing something, but I thought 8 was an even number....... I have never heard of this rule before.  Is there a simple way to explain it to me and my student???

Please save my sanity!!!!!!

Pat Duggleby   pat.duggleby@cableregina.com

Hi Pat
I think that your difficulty comes from the way you are reading the divisibility rule. You are not looking for the odd or even digits but rather the digits in the odd or even positions counting from the right. So with 528, 8 is in the first position, 2 is in the second position and 5 is in the third position. Hence the digits is odd numbered positions are 8 and 5 and the only digit in an even position is 2.

Now try 9361. 1 and 3 are in odd positions and 6 and 9 are in even positions. 1+3=4 and 9+6=15. Subtracting the smaller from the larger gives 15-4=11 and hence 9361 is divisible by 11.

Cheers,
Penny