Wednesday, June 13, 2007

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. :)

1 comment:

Blank said...

I programmed a little thing that generates long division worksheets.

I used Logo and Lout.