Ways to Add and Divide More Easily
Date: 11/17/2008 at 22:08:12 From: Sofia Subject: Word Problem Hi! Here is my question...Tianna has 2398 candies. Marina has 5752. They both have 37 friends in total. They want to split their candy in to 37 piles so each friend can get some candy. Can you tell me the quickest and easiest way to figure this out? I know that I have to add 2398 plus 5752. Then I have to find out how many times 37 goes into that number. But it takes me a really long time! I really dislike that! I want a good example so I know how to do division.
Date: 11/18/2008 at 08:07:14 From: Doctor Ian Subject: Re: Word Problem Hi Sofia, That sounds about right. One thing to consider is that this is the sort of problem you'd normally do with a calculator. You're probably being asked to do it without one, but that's just to prove that you CAN. Once everyone knows you CAN do it, you won't have to anymore. Weird, but that's how it is. A second thing to realize is that this is kind of a silly problem, since they're going to have to count the candies out into 37 piles anyway, so it's kind of like dealing cards from a deck. They can just do it, and each friend gets what he gets. Knowing how many candies will be in each pile doesn't change anything. It's a pointless calculation. Okay? Anyway, you want to add 2398 and 5752, and then divide by 37. That addition looks kind of ugly, 2398 + 5752 ------ but you can make it nicer by taking some away from one number and adding it to the other. For example, I can take 2 from the bottom number and add it to the top number to get 2400 + 5750 ------ Do you see why the sum doesn't change? I could do the same sort of thing again, taking 600 from the bottom number and adding it to the top number to get 3000 + 5150 ------ And now the addition is so easy I can do it in my head: 3000 + 5150 ------ 8150 So far, so good? Now, I want to divide this by 37. The first thing I'd do is estimate the answer, so I'll be able to check my actual answer later. What do I mean by that? Well, 8150 is close to 8000, and 37 is close to 40, and 8000 divided by 40 will be about 200. So my answer had better be close to 200, or I'll know I have a problem. What about the actual division? Probably you've learned how to do long division, or you wouldn't be given this kind of problem. So you can go ahead and do that, ? _____ 37 ) 8150 I probably wouldn't. I'd use multiplication instead: 37 * 200 = 7400 <- This gets me close. 37 * 20 = 740 <- This gets me closer. --- ---- 220 8140 and that's as close as I'm going to get. So '220 remainder something' is going to be my answer. Do you see what I did there? I just kept adding multiples of 37, until all my multiples add up to something close to my target number. To see why that works, it's important to always keep in mind that c __ a ) b means the same thing as a * c = b That is, division and multiplication are just two ways of expressing the same information. Whenever you have a multiplication, you can change it to a division if that will make your life easier; or you can change a division to a multiplication. It's all the same. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 11/18/2008 at 21:24:10 From: Sofia Subject: Thank you (Word Problem) Thank you so much Doctor Ian! That helps me a ton! I think this site really rocks!
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