SOLUTION: How would you explain to a fifth grader why the sum of 4 consecutive number is not divisible by 4? Examples would be great Thanks for the help.

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Question 560031: How would you explain to a fifth grader why the sum of 4 consecutive number is not divisible by 4? Examples would be great Thanks for the help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Start with any number. Call it +n+
Then write down the number +n+
and the following 3 numbers this way:
+n+
+n+%2B+1+
+n+%2B+2+
+n+%2B+3+
Now add these up. You get
+4n+%2B+6+
+4n+ is divisible by 4, then when
6 is divided by 4, you always
get a remainder of 2.
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Here's an example:
Suppose +n+=+17+
+17+
+17+%2B+1+
+17+%2B+2+
+17+%2B+3+
Adding these 4 consecutive numbers,
+4%2A17+%2B+6+
If I divide 4 +17 's by +4+, I get +17+
Now I divide the +6+ by +4+, and I get 1
with +2+ left over, so my answer is
+17+%2B+1+%2B+2%2F4+ and that equals
18 1/2, which is not a whole number of times
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Since 17 was any number, this works for all numbers