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Q&A #4130

Teachers' Lounge Discussion: European long division

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From: loyd

To: Teacher2Teacher Public Discussion
Date: 2001071820:36:00
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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