Problems with Zero; Writing Remainders

Date: 11/07/2001 at 10:16:10
From: lacy
Subject: Problem with zero

When I do long division I have trouble with some of my answers, where 
the answer is correct except for one thing in the middle that 
sometimes contains a zero.

For example, when I did this one:

   38/1294058

I got the answer 3465 r23/28
but when I checked the answer it read 34065 r23/38

Where am I going wrong?

Date: 11/07/2001 at 12:18:43
From: Doctor Peterson
Subject: Re: Problem with zero

Hi, Lacy.

You probably just forgot to write a zero in the quotient when you had 
to "bring down" an extra digit from the dividend because the remainder 
was bigger than the divisor. I'll do the problem in a way that avoids 
that:

       ____34054_r_6
    38 ) 1294058
         114
         ---
          154
          152
          ---
            20
             0   <-- the problem is here
            --
            205
            190
            ---
             158
             152
             ---
               6

(I don't know where one of us copied wrong, but I'll go with this 
problem anyway!)

When I found that 20 was too small to divide by 38, I had to bring 
down another digit, the 5. When I did that, I was really saying that 
20 divided by 38 is 0, so I had to put a zero in the quotient. To make 
sure I did that, I actually subtracted 0 from 20 as usual, rather than 
saving space by just putting 5 next to the 20 like this:

       ____34054_r_6
    38 ) 1294058
         114
         ---
          154
          152
          ---
            205  <-- two digits brought down need two digits in 
            190       quotient
            ---
             158
             152
             ---
               6

You can do it either way, but this helps if you have this problem. 
Another thing that helps is to make sure you line everything up, so 
that the digit you get after bringing down the 5 goes over the 5. If 
something doesn't line up at the end, you know you left something out.

Finally, you should always check your answer, which you can do by 
multiplying 34054 by 38, and then adding the remainder, 6. You should 
get 1294058.

Incidentally, if the book wrote the answer in the form 34065 r23/38 
they're not quite right; when you use the remainder to form a 
fraction, the result is a mixed number and you shouldn't include r ; 
just write 34065 23/38. You use  r  when you leave the remainder as a 
remainder: 34065 r23.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/