7
Oct

Aside: The Traditional Subtraction Algorithm


Okay, let’s take a moment to compare
the strange method I do for subtraction to the standard algorithm
once typically taught in school. Now just recall, when I do something like
512 take away 347, I just go left to right. Why not. Five take away three is two,
one take away four is negative three, two take away seven is negative five. So what I’m really doing is
adding the opposite of 347 and after some annihilations
we get two, negative three, negative five. Two hundred, negative three-t, negative five. Grand. And then we did un-explosions
to fix this up for society. I believe we got the answer 165 from there. All right, what’s the standard algorithm? Let’s see if it’s actually doing the same thing. Now, it starts of course by going what feels
backwards to me, right to left. And you say, okay, two take away seven. You say, oh, I can’t do that,
I can’t do two take away seven. Now I want to write negative five,
and I can, you can too, but the standard algorithm says
no, no, no. What I want you to do
is take one of these dots here and make it one less,
now I have zero of them, and put here an extra ten dots there. Do you see what that was? It’s like taking one of these dots,
make an extra ten or one of these dots
and make an extra ten. That was just an un-explosion. Now here’s the sneaky thing,
they don’t write ten. They have you write a little one
right next to this two and make that ten and that two
become a twelve. Little shortcut for saving ink. So now we’ve got twelve
take away seven is five. Grand. Then you go to the next column. Zero take away four,
so you can’t do it. Well of course you can,
you can write negative four and be correct. However, in the standard algorithm
they say no, no. Take one of these dots,
make one less, and then what I’m going to do now
is un-explode, make an extra ten here, but you don’t write ten
you just put a little one next to it, just make that one zero actually
ten to begin with. Ten take away four is six,
four take away three is one. Beautiful. So the standard algorithm is actually doing
exactly the same thing as me, it just goes right to left
and does the un-explosions as you go along, uses way much less ink, maybe. Well maybe it uses more ink,
I don’t know. But, it goes right to left
and does un-explosions as you go along. I go left to right
and do the un-explosions at the end. Again, it’s a style thing. All correct math is good and correct. In fact, they all lead to the same answer
in the end, 165, 165. Brilliant. Whatever you like best
is up to you to do. You’re choice. All right, I love math,
I love its flexibility and I love its creativity here. Beautiful stuff.

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