Checking Division

Date: 08/18/98 at 23:16:00
From: Shannon
Subject: Checking 3-digit division

I know how to divide pretty well, but I always get the check wrong. Can 
you please help me?

Thank You,
Shannon

Date: 08/19/98 at 15:57:48
From: Doctor Peterson
Subject: Re: Checking 3-digit division

Hi, Shannon. I think the check you are referring to is not just for 
three-digit numbers, but for any division. Let me know if this is not 
the kind of check you are thinking of.

If I divide a number A by another number B, I get a quotient Q and a 
remainder R:

        Q rem R
      +---------
    B ) A

This is the same as saying that:

    A = B * Q + R

(where "*" means multiply).

since we are saying that there are R left over if you divide A into Q 
parts of size B. In pictures:

    +---------+   +---+---+-+
    |         |   |   |   | |
    |    A    | = | B | B |R|
    |         |   |   |   | |
    +---------+   +---+---+-+
                   \__Q__/

So to check your answer "Q rem R", you just have to multiply B by Q, 
add R, and see if you get back to A. It can be hard to remember what 
order you do this in. I would just think of the picture and what 
division means. Or you could remember to take the numbers in the order 
you find them in the division, clockwise starting at the left:

    +----------------+
    |  *  Q + R =    |
    |   +---------   |
    | B ) A          |
            <--------+

You can decide what method works best for you, depending on how you 
remember things best.

Now, if you get an F for doing the check wrong, do you mean that 
because you don't check correctly, you don't catch your mistakes, or 
that you "fix" a correct answer to make the check come out right, or 
that you get no credit unless the check is right? You might want to 
ask your teacher where the problem is, and see if there is something 
more wrong than the check.

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/