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Comment by Taek | Hacker News Reader

I use the fib conversions quite regularly.

Both of your examples are actually easy Fibonacci numbers.

50kph - 5 is a fib number, and the previous number is 3. I can go 50->30 without any math at all.

And 80kph, well 8 is also a fib number. And the previous is 5. I can go 80->50 without any math at all.

120kph is close to 13, so I know 120kph is somewhere below 80mph. I always divide any remainder by 2, so I would quick math my way to 120->75. That's accepatably close to the real answer of 74.4

Same thing with 110kph. That's close to 13, so I'd quick math to 70 mph (130->80, remainder is 20, subtract half the remainder). That's acceptably close to the real answer of 68.2

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Instead of halving the remainder, you can do 3/5 - since it’s always going to be a multiple of five - so 120kph is going to be more like 74mph because it’s 10kph less than 130, and 10kph=25kph≈23mph=6mph

Also, this doesn’t only work with Fibonacci numbers, it works with any Lucas sequence, since they all tend to phi, so as well as 2-3-5-8-13 you can also use the higher numbers from 1-3-4-7-11 to fill in some gaps and help estimate.

And as a bonus, it means if you know A kph is equal to B mph, you also know that A mph is ~equal to A+B kph.

So given your result above of 120kph=74.4mph, I would estimate 120mph≈194kph. And it turns out it’s actually 193.1koh, so… not far off.

To mult by 1.6: double it four times then divide by 10. Eg. 55mph = 110, 220, 440, 880, 88.0 kph

To divde by 1.6, multiply by 10, then divide by 2 4x. Eg : 200 kph, 2000, 1000, 500, 250, 125 mph

I guess that I was taught basic mental arithmetic differently. Multiply by 8 and divide by 5, or (it's inverse) is two single instruction cycle opcodes (or whatever my brains equivalent is).

Regularly needing to translate between sane units and US (and occasional British) idiosyncrasies keeps these mental muscles worked enough that it's mostly subconscious now.

I didn't enjoy rote repetition of times tables and drills as a kid, but it's frustrating seeing my daughter being taught to understand multiplication, and learning "strategies", but struggling with mental arithmetic (I mean she tests above grade level, so I'm not worried, it's just a _get off my lawn_ reflex)

Arithmetic strategies are great but you still need a bunch of quick operations (like doubling and multiplying by 10) and fundamental lookup tables (like basic multiplication tables, squares, powers of two) to bootstrap them from.

I don’t think knowing all the times tables up to 12 is as helpful as having a good appreciation for how to break a multiplication into simpler parts, but you do need immediate recall on multiples of all the single digit numbers, up to at least times five or six.

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