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Q&A #4130

Teachers' Lounge Discussion: European long division

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From: loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2001071819:36:00
Subject: Re: confused

On 18 Jul 01 13:18:46 -0400 (EDT), bong wrote:
>	Hi! I'm confused where the nos. 100x, 50x, -1x etc came from.
>Pls let me know.
>Thanks,
>bong
>

Bong, the 100 happens because you placed the 1 over the hundreds
digit.  For example, when we divide 910 by 7 we say, "How many 7's are
in 9 and write 1 above the 1.  But the truth is, we could have said,
"How many 7's are 900.  When we place a 1 above 9, we are really
putting 100 there.  It all comes about because of the place value of
the digits.  

See my post re division about 8 Jul 2001 (below also).  I show an
example of long division on a web site and also, in one of the
following posts, I try to show that the division algorithm is really
repeated subtraction. Multiples of the divisor are subtracted until
the remainder is a number less than the divisor.
Here is a repeat of my post of 8 Jul 2001

"The following relates to the previous post and shows that division is
just repeated subtraction.  A student should understand place value to
properly understand the procedure. To start the process, the student
asks, "How many 357's are in 768" or more precisely, "How many
357000's are in 768000?"  As one can see, adding the three zeros is
not necessary.  Also, to simplify the problem, the student just asks
the question, "How many 300's are in 768?" This is easier than using
357. The first guess would probably be two.  At times, the student may
have to use a little trial and error to determine the first guess.

Divide 768949 by 357 using repeated subtraction:  We subtract 357
repeatedly until the remainder is 328.  To save time we can do the
same thing by subtracting multiples of 357 repeatedly. 

              7 6 8 9 4 9       Dividend
              7 1 4 0 0 0       subtract 357 x 2000 =714000
            ----------------
                5 4 9 4 9       Remainder 1 or new dividend
                3 5 7 0 0       subtract 357 x 100 = 35700
            -----------------      
                1 9 2 4 9       Remainder 2 or new dividend
                1 7 8 5 0       subtract 357 x 50 = 17850
            ----------------
                  1 3 9 9       Remainder 3 or new dividend
                  1 0 7 1       Subtract 357 x 3  - 1071
             --------------
                    3 2 8       Remainder 4 is the final remainder
because it less than 357.  

The answer is 2000 + 100 + 50 + 3 + 328/357.

I still favor using the old fashioned algorithm, although it wouldn't
hurt to show that division is repeated subtraction as in above. 
Myself, I was taught the old fashioned way, but figured it out that it
was just subtraction later in life.  If you look closely, the old
fashioned method is almost the same as above.  Look at my previous
post to click on two web sites that show the old fashion method.



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