Setting Up a Division Calculation Correctly
Date: 12/16/2005 at 22:57:34 From: Pat Subject: division help please I need math help, please. What exactly does "divided by" mean? I never know what number to divide by. I get the two numbers mixed up. Is there an easy way to remember what number goes where? So when they say divide this number by that number, what number goes in the calculator first? And what number goes on the outside or the inside if I am doing it on paper? What does the word "divide" mean? Maybe that will help with the problem? Thank you for your time in advance. Pat
Date: 12/16/2005 at 23:29:43 From: Doctor Peterson Subject: Re: division help please Hi, Pat. This is a very common problem! Let's pick a simple example to work with, that involves whole numbers. We know that 2*3=6 (I'm using "*" for the multiplication symbol.) So if we divide the product, 6, BY either of the factors (2 or 3) we get the other one: 6 / 2 = 3 6 / 3 = 2 (I'm using "/" as the division symbol; that's what it actually means in a fraction.) You can see that division is basically "undoing" a multiplication: starting with the result of the multiplication and one of the two numbers you started with, you can find the other. When we enter the problem into a calculator, we put the numbers in the same order we write on paper: 6 / 2, "this" "divided by" "that". "This" is called the dividend (the number being divided), and "that" is called the divisor (the number it is divided BY). When we do a division by hand, we put the divisor on the left, and the dividend under the bar: __3_ 2 ) 6 This is what confuses a lot of students, who read division problems the wrong way, as if this were 2 divided by 6. You might find it helpful to think of the bar as an operating table, and the patient lying on it is being "divided" by the surgeon, who stands next to it. (I suppose the organs being taken out are put on top.) The 6 is divided BY the 2. A division can be interpreted in several different ways. The most general way to talk about it is what I just did: division means finding what number you would have to multiply the divisor by (the 2) in order to get the dividend (the 6). In practical problems, we might divide 6 by 2 to find out how many piles I can make from 6 objects if I put 2 objects in each pile; or how many objects will be in each pile if I "divide" 6 objects into 2 piles. The basic idea here (and the origin of the word) is that we are "dividing" a group into parts. Incidentally, the word "quotient", which is used for the answer to a division, is essentially the Latin word for "how many?". Of course, once you stop talking only about whole numbers, some of these ideas disappear; we can't really talk about "dividing 2 objects into 3 piles", and it gets even worse if we want to divide a fraction by a fraction. But these images are the original ideas that motivate division; for deeper understanding of division, we move on from there to the idea of undoing a multiplication, which I started with. I hope that helps. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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