I put "division algorithm" but what I actually mean is the algorithm for dividing large numbers (I couldn't find the English name for it). Let's say we want to divide $3283$ by $38$ without a help of machines. We would check the whole part of $\frac{328}{38}$, then subtract it from $328$, then repeat it until we "arrive" at $0$. But how do we prove that this algorithm is correct? My main issue is in the underlined place from the picture below:
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Jyrki Lahtonen
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Archil Zhvania
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Closely related: who invented division and why we do division in those steps told? – MJD Feb 22 '21 at 23:02
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I'm sorry for informal explanation, but I found it hard to put in formal words. My main issue is, why aren't we adding zero in the last step shown in the picture. – Archil Zhvania Feb 22 '21 at 23:19
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328=328.000000... – Steven Alexis Gregory Feb 23 '21 at 00:20
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"why aren't we adding zero in the last step shown in the picture" because first we need to take 35 from 40 and get 5, then extend it to 50 then see 7 goes in 7 times, so we take away 49 etc etc – ancient mathematician Feb 23 '21 at 20:13
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1I would call it "Long Division". – ancient mathematician Feb 23 '21 at 20:14