jacobolus 18 hours ago

There are lots of good ways to break down this multiplication problem:

8 × 12 = 8 × (10 + 2) = 8 × 10 + 8 × 2 = 80 + 16 = 96

8 × 12 = (10 − 2) × 12 = 10 × 12 − 2 × 12 = 120 − 24 = 96

8 × 12 = (10 − 2) × (10 + 2) = 10 × 10 − 2 × 2 = 100 − 4 = 96

8 × 12 = (5 + 3) × 12 = 5 × 12 + 3 × 12 = 60 + 36 = 96

8 × 12 = 4 × 24 = 2 × 48 = 96

8 × 12 = 2³ × (2² × 3) = 2⁵ × 3 = 32 × 3 = 96

etc.

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eszed 2 days ago

:-)

12 is made up of a 10 and a 2.

What's 8 x 10? 80.

What's 8 x 2? 16.

Add 'em up? 96, baby!

They teach you to do math on paper from right to left (ones column -> tens column, etc), I find chunking works best if you approach from left to right. Like, multiply the hundreds, then the tens (and add the extra digit to the hundreds-total you already derived), then the ones place (ditto).

It's limited by your short-term memory. I can do a single-digit times anything up to maybe five digits. Two-digits by two digits, mostly. Three-digits times three digits I don't have the working memory for.

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  • neom 2 days ago

    Seems my math teachers in school...er..didn't. That makes sense, I know how to write math out on paper and solve it, but then my instinct has always been to reach for that method mentally, so I literally draw a pen and paper in my imagination, and look at it and do the math and it takes way too long so I just give up, this seems like I can just learn more rules and then apply them, as long as I have the rules.

    Thank you kindly for taking the time to teach me this! This thread has been one of the most useful things in a long ass time that's for sure. If I can ever be helpful to you, email is in the bio. :)

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    • eszed 2 days ago

      My pleasure! I'm no one's idea of a mathematician, but I enjoy employing arithmetic tricks and shortcuts like this one.

      A few years ago I had an in-depth conversation with a (then) sixth-grader of my acquaintance, and came away impressed with the "Common Core" way of teaching maths. His parents were frustrated with it, because it didn't match the paper-based methods of calculation they (and you and I) had been taught, but he'd learned a bunch of these sorts of tricks, and from them had derived a good (probably, if I'm honest, better than mine) intuition for arithmetic relationships.

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