The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Relating Decimal Answers to Remainders

Date: 02/15/2002 at 06:35:39
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 

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:

    5 ) 457

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 

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:

    5 ) 457.0
          2 0
          2 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 

- Doctor Peterson, The Math Forum   
Associated Topics:
Elementary Division
Elementary Fractions

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.