Division remainders - is there a way to know it before working the problem?

[klmama]

My ds sometimes just "knows" what the remainder is by looking at a problem, but I can't see how he does it. Just now it was one with a remainder of 4. When he worked it, he was right. He has no idea why he knows, and neither do I. Have we forgotten some rule that he's applying without realizing it?

[charlotteb]

These rules are useful for kids from the time they start division, on. They keep me from using a calculator and most of the time, I can even work it in my head faster than the calulator because of these rules. I use them most when reducing awkward fractions.


To Divide by ...Cheat Codes2A number is divisible by 2 if it ends in 0 or an even number. Example: 40 divided by 2 = 20
3974 divided by 2 = 1987
.
3A number is divisible by 3 if the sum of the digits is divisible by 3. Example: 321 add 3+2+1= 6 so 321 divided by 3 = 107
2460 add 2+4+6+0= 12 so 2460 divided by 3 = 820


4A number is divisible by 4 if the last 2 digits are both zeros or if they are divisible by 4. Example: 300 divided by 4 = 75
3548 divided by 4 = 887


5A number is divisible by 5 if it ends in 0 or 5. Example: 25 divided by 5 = 5
400 divided by 5 = 80


6A number is divisible by 6 if it is even and divisble by 3. Example: 246 is even and 2+4+6 = 12 so 246 divided by 6 = 41


9A number is divisible by 9 if the sum of the digits is divisible by 9. Example: 81 add 8 + 1= 9 so 81 divided by 9 = 9
972 add 9+7+2 = 18 so 972 divided by 9 = 18



10A number is divisible by 10 if it ends in 0. Example: 400 divided by 10 = 40

[kiana]

http://www.egge.net/~savory/maths1.htm

If you're interested, here are divisibility rules for all primes up to 50. Some of them, however, are almost as much work as doing the problem!

[Sweetpeach]

Thanks for the rules above.

[klmama]

Thanks for the divisibility rules. We've actually been working on them. I don't think you understood my question, though. I want to know how my ds can look at a problem and know the remainder only, not whether or not it is divisible by a certain number. Anyone?

[Ohio12]

mmmm rain man?

[emeraldjoy]

My daughter does this too. She has a much easier time knowing what the remainder will be than actually solving the problem. The remainder is the first thing she says.....and then it takes her awhile to get the rest of the answer (sometimes).
She has ways of figuring out the answers in her head that sometimes she does not even know about, it just happens. I am at the point where I will let her do it her way on some of them; and make her work it out on others. I think it is important for her to learn how to do the long part of division...but don't want to discourage her "natural" processing methods.

I think it may be just a different way to figure it out, outside of the standard ways, and they are not quite old enough or articulate enough to describe what is going on. I see it as a good thing so far.

emerald