In the last post we looked at the problem of 926/18, and we simplified it to 463/9, so we could make it a short division problem.
What if the problem had been 927/18?
Both numbers are not even this time, so it is not readily apparent if they have common factors.
If you know how to factor (if you don’t, you can get a lesson at The Pretty Good Guide to Prime Factorization at MathMojo.com.) then you factor both of these numbers by 9.
Here’s a hint: If a number can be crunched to 9 or 0, then nine is a factor of that number. If you want to know more about crunching, I refer you to “The See-Say-Write Method of Speed Addition“.
There are also many hints you can find about how to determine if numbers are divisible by other numbers. MathMojo will eventually cover this in depth, but I’m sure you can find info if you google “divisibility rules.”
Ok, so let’s factor 927/18.
Using short division by 9, we get 103/2. How easy is the problem now? Just cut 103 in half in your mind and get 51 remainder 1. But remember, like in the last post,
If you factor a division problem before you solve it, you must multiply the remainder by that factor after you are done.
- So the answer to 927/18 is 51 remainder 9, (not 1).
Go ahead and check it. Remember how? If not, check out this post.
Check out the third and final post on this subject about Long Division Shortcuts.
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My son is finding division using decimals tricky? When he starts the division problem, he starts by finding the first number through comom factorization with the divisor, but does not know exactly where to place the first number above the dividen. Do you have time to explain this problem because he does not understand it the way I know how to explain it!
1) $3485.34 / 17
Hi, Lou,
Funny you should ask…
There’s an excellent, excellent (did I mention that it’s excellent?) article in a “American Educator” magazine, vol 33, No 3, Fall 2009, about exactly that. Unfortunately, you have to be a member of the American Federation of Teachers to get it. So if you’re not a teacher, cajole one into lending you that issue. It’s the cover-story. It makes so much sense that you’ll wonder why it’s seldom explained like that in schools (although the author will tell you why.)
I don’t have a good post of my own on the subject, and if I “wing it” now, It will be inadequate. It really would be worth your while to get a hold of that issue. Maybe you can find it in a library.
Anyone else reading this should check it out, too, especially if you are a grade-school teacher. Once you’ve read the article, you’ll be able to help children learn in ways you never considered before.
One caveat, though – in part of the article, the author, Hung Hsi Wu, defines multiplication as “repeated addition.” It is no such thing, although using repeated addition can mimic multiplication (see http://www.maa.org/devlin/devlin_06_08.html – you’ll either love it or you’ll hate it, but he’s got a point). Other than that oversight, I found the article very well written, and explains how I see it better than I could explaoin it.
I hope to try to write an illustrated version of my thoughts, or make a video, in the future, but it’s not in the immediate plan.
Please, though, do yourself and your son a favor and check out that article.
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