Mathematical epiphanies

So, I'm mathematically challenged. Always have been. When I was a little kid, I got into so much trouble for not learning my multiplication tables. I just couldn't.
I don't have such a bad memory, but it's easier to remember things when they make some sense to you. And it seemed to be pure memory without any logic.

Well, I was reading notalwaysworking.com, more specifically this one.
And I was thinking to myself, 25 is such an easy one to remember. I still don't know my multiplication tables, you see. But there are a few I remember, such as 25, 36 and 48, and a few I know how to get to, such as the 9 table.

I was thinking, 25 is easy because 5*5 = 25. One one side you have two fives, on the other you have two-five. And then 5*(5*5) = 125. On one side you have one and two fives, and on the other you have one-two-five.

I thought about 6*6 = 36 and 6 * 8 = 48, and for the first time ever I noticed that they don't just end with the thing multiplied by 6. The digit is half that. I wondered why it only worked for these two, then realised it didn't. It's the same for every number.
But for odd number, such as 5, you get 2.5 as the tens, and 5 as the singles, and that adds up to 30, and so it's hidden. As for 12, it's pronounced differently so I never really noticed it. Not sure why I didn't notice 24 before, though.

Then I realised, multiplying by six does that because multiplying by 5 results in half the number put in the tens position. So, 5*5 is half of five with the period moved over once. So, 25. And then you add one more of it, because you're multiplying by six. And that's what you do for every number.

That also means that 1.25 is a quarter of 5, since 5*5*5 = 125. Which most people would already know, I guess. But I'm mathematically challenged.

Suddenly, some multiplications are making sense. Now if I'm asked what 6*7 is, instead of not having the first clue, I can know it's 35+7. Which, to be fair, is still hard for me to calculate, but after some thinking about it, I can reach 42.

I don't expect this blog entry to be of much interest to most people. But I was excited by this realisation, and I decided I needed it written down. Someday I can look back and remember what day it was that I realised how some numbers work.

It also makes me wonder why they teach it to children as a "learn it by heart just because" thing. If I had been told the trick back in primary school, I would have remembered the 6 table. They did teach me a trick for multiplying by 9, so it's not like they're beneath it. I wonder if they assumed it was obvious and didn't need a mention, or if they thought most kids would only be more confused by that kind of explanation.

This is going to be so helpful. I know people pretty much have constant access to a calculator nowadays, but there are times when using it takes too much time and causes you to be laughed at too much. Being able to make simple calculations in my head will be valuable. Thanks, epiphany. I like you.