When I was a kid, I sucked at math. I mentioned it before but it was a while ago.
I thought I'd share some more "tips" for multiplication tables. I already shared the one about the 6 table in a previous post but there are others. I'll start with one that I mentioned to my husband recently, and which he wasn't aware of. I worked on turning it into a valid formula, and ended up with:
x2 = (x-y)*(x+y)+y2
But what I actually mostly used it as was "x2 = (x-1)*(x+1)+1".
So for instance, the other day when the talk was about figuring out what's 7*7, I thought "49" right away, because I know from my 6 table that 6*8 is 48, and 48+1=49. I could also have used the fact that 5*9=45 and 45+4 is 49.
I always thought of it as "a number times itself is equal to the numbers on either side of it multiplied, plus one". But when talking about it, I realise it also worked for (x-2)*(x+2)+4. And then I realised it kept working regardless of y.
At first I thought x needed to be greater than or equal to y, otherwise you'd get into negative amounts and it would stop working, right? Except I tried it with x=5 and y=6 and it still worked. I assume it would work the same if x and/or y are negative numbers, because the squaring makes it irrelevant.
Another trick was for the 3 table. Now, I guess most people just remember it and don't need tips. But multiples of 3, if you add up their digits together until you're left with a single digit, equal 3, 6 and 9 in order, over and over again. And the tens digit increases by one every set.
What I mean is the first set start with a 0 in the tens position. So it's 03, 06, 09. The second set starts with 0+1, which is 1, and still totals 3, 6, 9. In other words, it's 12, 15, 18, the ones digit being 3-1, 6-1 and 9-1. The next set starts with 2 followed by 3-2, 6-2, 9-2 and so on...
Once you go past 12, it gets a little bit more complicated. With this method, 3*13 = 40+(3-4). That's 40-1, which makes it 39. It's true, 3*13=39, but you start getting into subtraction instead of addition. It's a bit like odd numbers in the 6 table. It still works, but it requires a little bit more math, making it a bit less useful as a trick.
No you'll tell me, how do I know what's the tens digit for, say, 42? It's not help if I have to go through every single multiple of 3 until I reach 42.
But what you do is divide 42 by 3, round up and remove one. That would work fine, you get 14 exactly, not need to round up, you remove 1 and that gives you 13. Because you didn't need to round up, you know it's a "9" (the last number of each set. The other two would need rounding up, as they would end with either .3333 or .6666). So you do 130+(9-13) which is 130-4, which is 126. 42*3=126.
The main problem is that at this point, it's easier to just multiply 42 by 3 than going through the whole process. So it's not the most useful "trick" to know as it's actually more difficult to divide by 3 than multiply by 3, as far as I'm concerned at least.
So that "trick" is probably best used for multiplying 3 by a single digit. Which most people can do on their own to begin with, making the whole thing pretty superfluous. But I think it's still cool to know.
I promise all of this makes sense in my head. I can't figure out how to make it less confusing on the screen, sadly.
