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Comment by kloop | Hacker News Reader

> I think the song is very funny and charming, but I do think this is a rare case where Lehrer is just wrong, the "borrowing" style is a much better and clearer way to explain subtraction.

How much of that is that you're familiar with this method (the same way Tom was familiar with the old method)?

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It's a good question, I'm not sure. I do think it's clearer what's going on, and the steps are more obvious. Like, there's a joke in the song about what to do with the carry, if you add it to subtrahend digit or remove it from the minuend digit ("if you're over 35 and went to public school...") which to me indicates that it's rather arbitrary and "learn algorithm by rote". Like, the "borrowing" thing just much better describes what is actually happening, rather than having to memorize a subtraction table and then have arbitrary rules about how to proceed with the carry.

But who knows, I wasn't taught the other system, maybe it's equally obvious. I do think it's indicative that the "borrowing" system is nowadays much more common (that's how I learned it in Sweden in the 90s), which probably indicates that it does have some pedagogic value. I don't think for a second either way is "more efficient" than the other: once you get the hang of the borrowing system, you do it very fast.

The other system, as described in 19th-century textbooks, says this:

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[What if the digit in the subtrahend is bigger than the one in the minuend?]

Imagine adding 10 to both numbers. Obviously, the difference between them will not be changed.

But adding 10 to the digit in the subtrahend is the same as adding 1 to the digit immediately to its left.

So, add 10 to the [current] digit in the minuend, add 1 to the [next] digit in the subtrahend, and then perform the subtraction.

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