Changing Decimals to Whole Numbers when Dividing
Date: 12/10/2001 at 09:40:09 From: Joann Calabrese Subject: Dividing by decimals I am trying to think of ways to explain to my students why a decimal needs to be a whole number before one can divide.
Date: 12/10/2001 at 10:52:30 From: Doctor Ian Subject: Re: Dividing by decimals Hi Joann, You might start by considering why you think that's the case. Are you saying that I can't divide 3.6 by 2.4 without converting the 2.4 into a whole number? I'm pretty sure I can. Maybe you're having a hard time thinking of ways to explain it, because it isn't true. Could that be the case? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 12/10/2001 at 18:53:22 From: Joann Calabrese Subject: Re: Dividing by decimals Maybe. What about 2.003 divided by .02? Thanks.
Date: 12/10/2001 at 22:46:39 From: Doctor Ian Subject: Re: Dividing by decimals Hi Joann, Well, I'd look at that and think: 0.02 goes into that at least 100 times, right? And 2.003 - (100)(0.02) = 0.003 So the answer is 100 + something. Now, 1/10 of 0.02 is 0.002, and 2/10 of 0.02 is 0.004, and 0.003 is halfway between, so the something must be halfway between 1/10 and 2/10, which is 0.15. So 2.003 divided by 0.02 is 100 + 0.15. Of course, I wouldn't normally do it that way. I'd normally do it this way: 2003 ---- 2.003 1000 2003 100 2003 ----- = ---------- = ---- * --- = ------ = 200.3 / 2 = 100.15 0.02 2 1000 2 10 * 2 --- 100 Now, in a sense, I _have_ converted the decimals to integers, although I really converted them to fractions. I suppose the distinction is somewhat academic. However, the fraction trick shows why the trick of 'converting to integers by moving the decimal points' doesn't change the result of the division. Now that I think about it, I would probably just do this: Dividing by 2/100 is the same as multiplying by 100/2, or 50; so 2.003 divided by 0.02 = 50 * 2.003 = 50*2 + 50*0.003 = 100 + 0.150 But the important point is that there are lots of different ways to divide one number by another. We tend to teach one particular algorithm (long division), without worrying too much about whether the students understand what's going on; and that particular algorithm seems to work best when we manipulate the decimal point out of the divisor, but it's not _necessary_ to do that. It's just that lots of people find it _convenient_, because they find it hard to multiply anything except integers in their heads. A few examples should help your students see that it _is_ more convenient. But you'll never be able to convince them that it's _necessary_, because it isn't. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 12/11/2001 at 12:28:46 From: Joann Calabrese Subject: Re: dividing by decimals Thanks! I couldn't agree more about the more than one way idea! I like to be able to justify to them why someone decided one algorithm makes more sense or is easier to work with than another. Joann
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