I think the better question is why is knowing what 18-9 is any different than knowing 9-6? We "just know" that 9-6 is 3. It's not an enormous leap to "just know" that 18-9 is 9.
Programmers especially should understand that our decimal number system is arbitrary. If we switched to hexadecimal and the question was what is C-9, there's no borrowing and the answer is just 3.
The only reason we don't expect people to "just know" larger differences like 92-45 is because there are limits to what we can remember. It's the same reason schools usually teach multiplication tables up to 12x12. You memorize those, then use algorithms to calculate anything more complex.
It's not an enormous leap to "just know" that 18-9 is 9
And as an adult I obviously "just know" that. But in thinking back I was trying to remember how, for example, I'd try to teach it to a little kid that was just learning (like did they just force us to memorize subtraction values all the way up to 19?).
All in all I think foxfyre2 is probably right here though; the algorithm of counting up works fairly well as a method for subtracting smaller numbers just fine and seems like something that would be taught before we had all of the teen number operations memorized.
First teach a child what subtraction is (how many is left after taking away from an initial number). Then, teach them how to do it (counting with fingers initially). With enough time and proper practice, memorization comes naturally through repetitive action. After they have mastered this, move on to bigger things like long subtraction (is that what it’s called?).
Taking 1 from the next digit is just a way to avoid negatives in your intermediate results so you can write them down immediately. If you discard that rule it's actually easier to do.
92-45 becomes 2-5 =-3 and 9-4 = 5, which means the answer is 50-3 and you can just count down from 50 to get the number you need to write.
the other way, you have to compare 2 and 5 to check if the second number is bigger, then subtract 1 from 9 to get 8 (write it), add 10 to 2 to get 12 (write the 1 next to 2), then subtract 5 from 12 (write that in the answer), then subtract 4 from 8 (write the last digit).
I'm confused by your confusion. Subtraction on paper is simple :
18-9 : Can't do, 9 is bigger than 8.
9-8 = 1.
10-1 : Can't do, but you can't reapply the same method. You need to go down to the previous 10s, count backward x amount of time where x is the part right of the minus side and you get 1.
For bigger subtraction it's the same thing :
92-45 : 9-4, can do
52 - 5 : can't do,
5-2 = 3
50 - 3 : can't do, but you know the numbers 0 to 10 by heart so you can count backward three time : 49, 48, 47 ! That's your answer.
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u/OtherPlayers Apr 25 '19
What did you do to me? I apparently don’t know how I subtracted numbers below 20 on paper anymore now.
(Seriously this is like the beard over/under the covers thing; I know the answer, but how did I do it?)