Relating Decimal Answers to Remainders

Date: 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/