Looking for an explanation!!

Rick Snyder

Silver
Nov 19, 2003
2,321
2
0
Going over my son?s arithmetic homework I came across a curious item concerning long division (division larga).

In the US we place the divisor (divisor) first followed by a parentheses (par?ntesis) and the vinculum (v?nculo) is placed over the dividend (dividendo). We then do the proverbial divide, multiply, subtract, bring down and repeat if necessary and the quotient (cociente) is place over the vinculum.

Here in the DR they are taught to place the dividend first followed by the parentheses and then the divisor. The vinculum is then placed under the divisor. The typical long division operation is then performed on the left and the quotient is placed below the divisor and vinculum.

The problem with this, as I see it, is that after the student has performed the multiplication, subtraction and carry down operations the excess of numerals are jumbled together with the quotient and therefore making it difficult to distinguish the quotient from the calculations.

The US way with the divisor first has a tendency to show the divisor ?going into? the dividend that is in the box formed by the parentheses and vinculum ie., 3 into 9. With the calculations below the dividend and the lone quotient placed above the vinculum it is very easy to distinguish the answer to the problem at quick glance.

I spent three hours researching this on my computer and all examples in both English and Spanish that I could find show the vinculum above the dividend and not below.

For those of you that have attended school in other countries I ask you. Is this way of doing long division, as I have explained it is done here in the DR, the way you were taught? What is your output on this?

Rick
 

qgrande

Bronze
Jul 27, 2005
805
4
0
In The Netherlands we're taught - or at least it used to be that way about 20 years ago - more or less the US-style, although it looks different because we put the quotient on the right, not above the dividend (I've send you a pm with an example). That way numbers don't get mixed up either. I do find it amazing to find out that the US style is different from what we learn and I never knew! I read the products of divisions of large numbers, many of them in articles from the US, on a daily basis but have never ever seen a long division in US-style. I suppose in the age of computers the only time you use it is when you learn it at school, after that you just push a button on your keyboard.
 

Rick Snyder

Silver
Nov 19, 2003
2,321
2
0
qgrande I want to thank you for your PM and because of it I hit the computer this morning for further research.

I did some more research on the subject this morning and came across this link which explains the question that I asked in the OP. It is very informative and if anyone out there was interested in the question I posed you might find this link interesting;
http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/acpaper.html

Their homepage;
http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/Alg.html

This link gives you the way that long division is taught in the US (Marshall Islands), Portuguese, Spanish and Arabic as examples;
http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/vocabwall.htm

This link shows how division is taught in Portugal, the Netherlands, Norway, Denmark, Catalan, Spain, Italy and Germany;
http://www.csus.edu/indiv/o/oreyd/ACP.htm_files/longdiv.eu.2003.htm

Rick