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Were you taught divisibility rules/tricks?


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I learned 2,3,4,5,6,9,11 in middle school.

 

I'm confused how people can do any math past pre-algebra without knowing them. How do you factor? Simplify? I'd be lost simplifying a fraction like 426/591 without knowing both numerator and denominator were divisible by 3. How would you approach it otherwise?

 

I was never taught anything in school except to guess.  :glare: And then by the time one might be doing that as part of another problem, such as after algebra, there were always calculators allowed.

 

This gets to why it's important to know primes as well. My kids are dreadful at memorization though. They don't just see a number like 67 and think prime, unfortunately.

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I remember learning divisibility rules for 2 through 10 in elementary school.  I graduated high school in 1999, and the elementary school I went to used A Beka.  I think the rule for 7 wasn't included in the text, but I remember our teacher showing it to us anyway, in a "this is cool but you don't have to memorize it" sort of way.  

 

It is possible that my husband and I race to find the prime factorization of mile markers when we're on road trips.  Or that we factor the mileage on the car's odometer, if we want more of a challenge.  ...I should probably just stop there.

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I learned them -- I believe when we were breaking a number down into its prime factors. But I also did Number Sense tests so possibly I learned them there.

 

(I did know there was supposed to be a trick for 11 but I never learned it that well.

 

BTW 121 is divisible by 11 with 1-2+1=0  so there must have been something about that as well in it)

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I was taught the rules by my mom. I was in the fourth or fifth grade at the time and don't remeber them being taught in school. I have come across them in Singapore and saxon (6/5 I believe). Not sure about MIF - I have the fourth grade book but don't recall seeing them in there.

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Note, these tricks only work if you're operating in base 10. Which I assume we all are.

 

It's interesting to realize that the 9 trick always works for the number that's one less than the base. So if you're working in octal, for some reason, anything divisible by 7 will add up to 7. Or if you're using a duodecimal system, then the trick works for 11. Of course, now that I've explained it it should be obvious why that is the case.

My head just exploded.  :lurk5: I am now going to bed.  I'll read the rest of the thread in the morning.

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I did not learn them in school in the seventies and eighties. When dividing, if it wasn't a fact that I had memorized, I would guess. As far as I remember, that is what I was taught when we learned long division.

 

On the other hand, DS10 just learned them this week in CLE level 400.

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I did not learn them in school in the seventies and eighties. When dividing, if it wasn't a fact that I had memorized, I would guess. As far as I remember, that is what I was taught when we learned long division.

 

On the other hand, DS10 just learned them this week in CLE level 400.

Which level book because I don't remember learning this and want to make sure we go over it in detail.

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I learned 2,5,9 and 10 in school in the early 90's in Canada. I learned the rule for 11 a few weeks ago on these boards. :)

 

I just taught my children 3 and 4 in the MEP curriculum. The MEP curriculum has the children work out a proof for the 4 rule. It's really simple. It's just that all whole 100 is divisible by 4 therefore you can just look at the last two digits in order to deduce whether it is divisible by 4. Example: 348 is divisible by 4 because 348=300+48 and 300 and 48 are both divisible by 4. MEP generally teaches children to find divisibility by this type of method. For example, if you want to check 7 for the number 117 you could think, 49+49=98, 98+19=117, 19 is not a multiple of 7 therefore 117 is not divisible by 7. I <3 MEP.

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If you and your kiddo like to think about divisibility rules, here's a fun one to try.  What's a quick way to test whether a number written in base 5 is even?

 

Digits add up to 2 or 4?

 

Edit: Just worked out the divisibility rules for 5 and 10 in base 16. That's nifty, though not surprising.

 

http://www.johndcook.com/blog/2010/10/31/hexadecimal/ (If you don't want to do it yourself!)

 

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If you and your kiddo like to think about divisibility rules, here's a fun one to try.  What's a quick way to test whether a number written in base 5 is even?

 

Digits add up to 2 or 4?

 

I think you're on the right track.  But what about 33 base 5?  It's even (since it's equal to 18 in ordinary base 10), but its digit sum isn't 2 or 4.

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I think you're on the right track.  But what about 33 base 5?  It's even (since it's equal to 18 in ordinary base 10), but its digit sum isn't 2 or 4.

 

3 + 3 = 11 (6 in base 10). 1 + 1 = 2. If the number you get when you originally add the digits isn't one digit, you keep adding until it is. You do the same thing in base 10 to find out if the number is divisible by 3, 6, or 9.

 

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Ah, I see.  Very nice.  When your first post said to add up the digits, you were referring to digital roots (repeated digit sums), not plain digit sums:

http://en.wikipedia.org/wiki/Digital_root versus http://en.wikipedia.org/wiki/Digit_sum.

 

Another way to express the evenness test in base 5 is to say that the (nonrepeated) digit sum is even.  (You can add the digits in base 10 if you like.)  Yet another way to express the test is to say that the number of odd digits is even.  

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Which level book because I don't remember learning this and want to make sure we go over it in detail.

 

It's the very first lesson in CLE light unit 405, called "common factors."

 

Not sure if you are familiar with how CLE works. As a spiral program, it introduces concepts and then practices them each day, but only with one or two problems (the rest of each lesson reviews other skills). So there is not an entire chapter of practice problems related to this; instead they are sprinkled throughout the subsequent lessons.

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