The Math Forum

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

Small Base, Long Division

Date: 10/06/2015 at 10:58:44
From: obinna
Subject: with respect to division of numbers with bases other than te

How can I divide 12343 by 24 in base five?

I haven't tried it, it's just too confusing.



Date: 10/06/2015 at 21:31:06
From: Doctor Peterson
Subject: Re: with respect to division of numbers with bases other than te

Hi, Obinna.

Here is an example of division in base five using different numbers, so 
you can practice with your own:

  Divide 2431 by 32 in base five.

First, I'll do something my son did when he was learning to divide, and 
which is very helpful in other bases: make a list of multiples of the 
divisor, to make it easy to find the appropriate quotient. This requires 
only repeatedly adding the divisor, all work being in base five.

    32   32*1
   + 32
   ----
    114   32*2
   + 32
   ----
    201   32*3
   + 32
   ----
    233   32*4
   + 32
   ----
    320   32*10
 
(I didn't need that last addition, but did it as a check: the answer is 
clearly right, so I probably did all the additions in between correctly.)

The resulting multiplication table is

        1    2    3    4
      +-----------------
   32 |32  114  201  233

Now I can start the division:

         4
     -------
  32 ) 2431    <-- The biggest multiple less than 243 is
       233     <-- 233, which is 4*32, so the quotient is 4.
       ---
        10     <-- Subtract 233 from 243, leaving 10

Now I "bring down" the next digit, 1, and repeat the process:

         41
     -------
  32 ) 2431
       233
       ---
        101    <-- The biggest multiple less than 101 is
         32    <-- 32, which is 1*32, so the quotient is 1.
        ---
         14    <-- Subtract 32 from 101, leaving 14

The quotient is 41 base five, and the remainder is 14 base five.

To check the answer, we can convert to base ten.

Our answer is a claim that

   32 * 41 + 14 = 2431 (base five)

Converting to base ten, this is

    17 * 21 + 9 = 366 (base ten)

This is correct!

We could also check by multiplying in base five, if you prefer:

     32
   * 41
   ----
     32
   233
   ----
   2412
   + 14
   ----
   2431

Again, the check passes.

Now try your problem; if you have trouble, show me your work and I can 
help you check the steps.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Division
Middle School Number Sense/About Numbers

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.
http://mathforum.org/dr.math/