Relating Decimal Answers to RemaindersDate: 02/15/2002 at 06:35:39 From: HAROON SALEEM Subject: Division and quotient How to find the quotient and the remainder? 457 divided by 5 = 91.4 - how did this answer come, and why is it decimal? Date: 02/15/2002 at 12:37:00 From: Doctor Peterson Subject: Re: Division and quotient Hi, Haroon. If you divide 457 by 5 on an ordinary calculator, it does not know about remainders, and gives you a decimal answer like this. Let's see how that is related to the remainder. First, we will divide to get a quotient and remainder: ___91_rem_2 5 ) 457 45 -- 07 5 -- 2 This tells us, for example, that if we had 457 apples to divide among 5 people, each would get 91 whole apples, and there would be 2 left over. But if we don't want anything left over, we have to cut up the 2 extra apples and give pieces to each person. How much will each get? We can cut each apple into 5 fifths, and give each person one fifth from each apple: 2/5 of an apple for each person. So 457 divided by 5 is 91 2/5: 91 whole apples, plus 2 fifths. The decimal part .4 in the answer you found means 4 tenths. And that fraction, 4/10, is the same as 2/5. We can get that answer directly by just continuing to divide, adding .0 to the 457: ___91.4_ 5 ) 457.0 45 -- 07 5 -- 2 0 2 0 --- 0 What we are doing here is dividing the remainder, 2, by 4, by treating it as 20 tenths; 20 divided by 5 is 4, so 20 tenths divided by 5 is 4 tenths. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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