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Casting out nines


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Since we're on the topic, here are some other cool divisibility rules.

 

If you add up the digits of a number and the sum is divisible by three, the number is divisible by 3.

If you add up the digits of a number and the sum is divisible by nine, the number is divisible by 9.

If you add and subtract the digits in an alternating manner, and the sum is divisible by 11, the number is divisible by 11.

 

An example of the last: Consider 143418. The alternating sum is 1-4+3-4+1-8 = 5-16 = -11, which is divisible by 11. Therefore 143418 is divisible by 11.

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A Beka teaches it also (3rd or 4th I think - we didn't use AB beyond that). We honestly tried it once and then skipped it all from there out. Ds got it and thought it was a waste. Dd was confused by it and we didn't think it was a hill we needed to die on so we ignored it.

 

I have never heard of anyone (outside of possibly accounting) that uses it or for that matter has even heard of it.  

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I have never heard of that. And it begs the question...why? What would be the point? Other than a random puzzle type activity. 

 

It is a way to check for arithmetical errors that is much, much quicker than redoing the calculation. With as much technological assistance as we have now, it is of little use, but if I were adding pages of numbers in an accounts book and did not have a calculator, it would be an extremely good idea to use this for a check.

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CLE Math teaches it in the fifth grade book for sure, maybe in the fourth, also . . .I can't remember when it started but they don't call it casting out nines, they call it digit sums.

 

My 10yods is doing it in his sixth grade R&S right now and I'll tell you, it is a great, quick way for him to check his multiplication and division problems and his careless errors have gone way down!  He also just thinks it's a cool thing :)

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It is a way to check for arithmetical errors that is much, much quicker than redoing the calculation. With as much technological assistance as we have now, it is of little use, but if I were adding pages of numbers in an accounts book and did not have a calculator, it would be an extremely good idea to use this for a check.

 

This, in bold text.

 

I usually don't allow my little man to use a calculator during our math studies, so utilizing the "check numbers" method comes in handy when working through multi-step problem solving—which includes addition, subtraction, multiplication, division, etc.—during geometric, algebraic, or word problems. It prevents much frustration and ultimately saves time.

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Thanks, all, for your info and some additional nifty tricks. I have never been truly math-smart, so I never would have said it was my favorite subject. However, tidbits like this are fascinating to me. Makes me appreciate how black and white and yet surprising math can be, especially in a subjective world.

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