Remainders

Date: 01/30/2001 at 11:09:09
From: Bianca Peier
Subject: Math

What do you do with the remainder in division?

Date: 01/30/2001 at 12:20:31
From: Doctor Peterson
Subject: Re: Math

Hi, Bianca.

What you do with the remainder depends on what you want to do with the 
result, and the meaning of the problem. You may have to tell me more 
about your question, such as what kind of division you are doing.

Sometimes the remainder means just what it says, and should be part of 
the answer. If I have thirteen apples to divide among five people, and 
I want to give each one of the people only whole apples so they can 
take them home, then I divide

      ___2_rem_3
    5 ) 13
        10
        --
         3

and say that each person gets two apples, and I have three apples left 
over - the remainder. The same thing would happen if I wanted to cut a 
13-inch board into 5-inch pieces: I would get two pieces, with a 
3-inch piece left over that I couldn't use (for this project, at 
least).

If it doesn't matter what's left over (or you aren't asked), you might 
just ignore it.

Other times, I don't mind having pieces. When we eat at home, I might 
be cutting up those apples to share, and each person will get not only 
the two whole apples, but his share of the three others - which would 
be 3/5 of an apple, since we can cut each apple into five pieces and 
give each person three of them. So in this case, the answer is 2 3/5 
apples: we use the remainder as the numerator of the fraction, and the 
divisor as the denominator.

When you want a whole number answer, you may have to look at the 
remainder just to decide whether to "round up" the answer. For 
example, if I have 135 students to take on a trip, and each bus can 
hold 60 students, how many buses will I need? I divide 135 by 60 and 
find

       ____2_rem_15
    60 ) 135
         120
         ---
          15

That means if I used two buses, I would have fifteen students left 
over who couldn't go! So I add one to the number of buses, and take 
three buses. If the remainder had been zero, I wouldn't have to do 
this.

If you can't decide how to use the remainder in some particular kind 
of problem, write back and tell me about it.

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