Deciding How to Express the Answer to a Division Problem
Date: 07/22/2006 at 06:52:09 From: Donald Subject: How do I know when to express a remainder? There are 3 possible answers when I divide 3 by 2: 3 divide by 2 = 1 and 1 left over 3 divide by 2 = 1 and 1/2 3 divide by 2 = 1.5 How do I know which form I should use?
Date: 07/22/2006 at 11:53:16 From: Doctor Rick Subject: Re: How do I know when to express a remainder? Hi, Donald. That's a good question! If you are dividing 3 by 2 because you were given a problem that said, "divide 3 by 2", then you may have been also instructed whether to write the result as quotient and remainder, mixed number, or decimal. If not, it's probably best to give the result as a mixed number. I say that because, on the one hand, in the future you will be needing a quotient and remainder less often than you'll need a fraction or decimal. On the other hand, decimals have the problem that, if you want an *exact* answer, it can take a lot of work to get to the point where the decimal either terminates or repeats. Have you learned about that? For instance, if I divided 281 by 34, the exact answer in decimal form (with a repeating decimal) is ________________ 8.26470588235294117 That's a mess, and a lot of work, compared to the mixed-number answer, which is 8 9/34. If you are dividing 3 by 2 because you're solving a word problem and you decided that dividing by 2 would help you find the answer, then you have to decide for yourself which form is best. For most problems, an answer with a quotient and remainder will not make sense. For example, suppose you have this problem: "The 24 children in a class sold a total of 421 candy bars for a fund-raiser. What is the average number of candy bars each child sold?" You find the answer by dividing the total, 421, by the number of children, 24. If you wrote the answer as "17, remainder 13", someone who didn't know what you did to get that number (that you divided by 24) wouldn't know what that meant. When you say instead, "17 13/24", your answer includes the information about the divisor. Without it, the answer is incomplete. (An answer of 17.54 is also complete; it is less accurate, but probably more useful. More on that in a moment.) There are some special types of problems where the remainder is important. For instance: "Nine boys have 75 carrot sticks to share. If they share them equally, how many will be left over?" That's a remainder problem. If you divide 75 by 9 to get 8 1/3, you won't see the answer. If you get 8.33333..., that won't help either. But "8, remainder 3" tells you right off that each boy gets 8 carrot sticks and 3 are left over. If the problem calls for an exact answer, then it's best to get a mixed number as a result of the division, because as I said, an exact decimal can be a real pain to calculate and to work with. It's easier to be exact with fractions. If it's a "real-world" type problem involving measurements of things, then you don't need an exact answer. A girl's height, for example, isn't going to be *exactly* 134 12/41 centimeters. Usually a decimal answer will be best (especially if you're working in the metric system). You can decide to round 134.292682926829268292682 to 134.3 centimeters, accurate to the nearest millimeter--that's probably good enough. (And you can stop calculating when you reach 134.2 with a remainder; comparing the remainder to the divisor is enough to decide whether to round up or down.) Even with problems in which you don't need an exact answer, if the division comes in the middle of a problem, it may be a good idea to keep the result in mixed-number form. That way you don't have to round the intermediate result; you can save rounding until the very end, when you have a better idea of how accurate the answer has to be. I hope that helps a bit! I'm sure I haven't covered all the possibilities. If you have a specific instance in which you aren't sure what kind of answer to give, show me the problem and we can discuss it. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 07/23/2006 at 03:42:22 From: Donald Subject: Thank you (How do I know when to express a remainder?) Thanks heaps for answering my question. It was very much appreciated. You are the best!
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.