Estimating and Rounding
Date: 03/04/2002 at 15:49:48 From: Amy Subject: Division - one answer problems I am doing my math homework and we have to divide a two-digit number into another number and get a one-digit quotient. For example, 192 divided by 86 = . Can you please help me?
Date: 03/04/2002 at 22:56:59 From: Doctor Peterson Subject: Re: Division - one answer problems Hi, Amy. You can find some discussions of the tricks you need in our archives: Division by Estimation http://mathforum.org/dr.math/problems/humphrey11.4.96.html Long division, Egyptian Division, Guessing http://mathforum.org/dr.math/problems/kiran.06.13.01.html Compatible Number Estimating http://mathforum.org/dr.math/problems/matt.01.31.02.html There are a couple of important things to remember: you have to estimate (because you don't have a multiplication table that goes up to the 86's), and when you estimate you expect not to be exact. Therefore, you will be learning not only to make the best guess you can, but to correct the guess WHEN (not if) it turns out to be wrong. That's just part of the process, and doesn't mean you've made a mistake. So let's look at your example. The first thing I usually do is to round both numbers, generally so that there is one non-zero digit left in the divisor and two in the dividend (though that's not always true - you'll get used to how to make this decision with a little practice). In this case, 86 rounds up to 90, and 192 rounds down to 190. It won't matter here, but I like to round both numbers in the same direction, because that's more likely to give a good estimate. So I'd round both numbers up here (giving preference to the divisor), making it ______ 90 ) 200 Now, we can divide both numbers by 10 and it won't change the quotient; so ignore the zeroes on the end: _____ 9 ) 20 Now we've got something we can do: the answer is 2, since 9 * 2 = 18. That's our estimate; but is it the right answer for the real problem we're doing? All we can do is check it by multiplying. We're hoping that ____2_ 86 ) 192 To check that (and also to find the remainder), we multiply the divisor by the quotient: 2 * 86 = 172. This is good: it's less than 192, but not so much less that we could fit another whole 86 into it. That is, we can subtract to get a remainder, and the remainder is less than the divisor: ____2_ 86 } 192 172 --- 20 So the remainder is 20. At leat one of the links I gave you goes into how to correct an estimate if the check doesn't work out; briefly, you subtract one from the quotient if it's too big (so that the product was too big to subtract at all), and you add one if the quotient is too small (so that the remainder is too big). Let me know if you need more help. You might want to send a sample problem worked out, so I can see where you might be going wrong or getting stuck. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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