Maths: Long Division, or DMSCB - Does McDonalds Sell Cheese Burgers

I might be a programmer, but it was recently revealed to me that I couldn't remember how I was taught long division in school.

Finished laughing at me yet?

I searched around and found the technique, but didn't find enough examples that I understood the technique again straight away. Here is my attempt to clear that up for anyone else who forgets how to do long division (not that I am implying anything of course...).

The rule: Does McDonalds Sell Cheese Burgers.

A.K.A. DMSCB
A.K.A. Divide Multiply Subtract Check Bring down.

Example: 956 / 18.

Divide

   +-----
18 |  956

18 into 9? No.
18 into 95? 4 times.

       4
   +-----
18 |  956

Multiply

       4
   +-----
18 |  956

4 * 18 = 72

       4
   +-----
18 |  956
      72

Subtract

       4
   +-----
18 |  956
      72

95 - 72 = 23

       4
   +-----
18 |  956
    - 72
    -----
      23

Check that that the result of your subtraction is smaller than your divisor.

       4
   +-----
18 |  956
    - 72
    -----
      23

23 > 18 ... made a mistake! 

Start over again..

Divide

   +-----
18 |  956

18 into 9? No.
18 into 95? 5 times.

       5
   +-----
18 |  956

Multiply

       5
   +-----
18 |  956

5 * 18 = 90

       5
   +-----
18 |  956
      90

Subtract

       5
   +-----
18 |  956
      90

95 - 90 = 5

       5
   +-----
18 |  956
     -90
    -----
       5

Check that that the result of your subtraction is smaller than your divisor.

       5
   +-----
18 |  956
     -90
    -----
       5

5 < 18 ... whew! 

Bring down digits that haven't been divided yet.

       5
   +-----
18 |  956
     -90
    -----
       5

Bring the 6 from 956 down to the 5, to make 56.

       5
   +-----
18 |  956
     -90
    -----
       56

And repeat..

Divide Multiply Subtract Check Bring down.

       5
   +-----
18 |  956
     -90
    -----
       56

18 into 5? No.
18 into 56? 3 times.

       53
   +-----
18 |  956
     -90
    -----
       56

Multiply

       53
   +-----
18 |  956
     -90
    -----
       56

3 * 18 = 54

       53
   +-----
18 |  956
     -90
    -----
       56
       54

Subtract

       53
   +-----
18 |  956
     -90
    -----
       56
       54

56 = 54 = 2

       53
   +-----
18 |  956
     -90
    -----
       56
      -54
    -----
        2

Check

       53
   +-----
18 |  956
     -90
    -----
       56
      -54
    -----
        2

2 < 18

Bring down... nothing to bring down, so we have our answer.

       53 R 2
   +-----
18 |  956

956 / 18 = 53 R 2

Another example with much better presentation (but without the Cheese) is given by mathsisfun.com.

The first example of DMSCB that I found in my search helped a lot. It is on Shannan's Math Web Site on AngelFire, but I didn't find it sufficient because it didn't explain the Cheese. :)

On the same site I found an example of another technique, which I think is more useful for numbers larger than 4 digits. Check out this Partial-Quotients Example.

True story: I learned for myself what the Cheese was, when I made the very mistake I showed up top (18 goes into 95 only 4 times)! Yeah, you can laugh at me now. :)