this post was submitted on 18 Oct 2024
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I would have done 10+6, but that's effectively the same thing as the OP.
Aside from literally counting, what other way is there to arrive at 16? You either memorize it, batch the numbers into something else you have memorized, or you count.
Am I missing some obvious 'natural' way?
For my kids, apparently some kind of number line nonsense, which is counting with extra steps.
I just memorize it. When the numbers get big, I do it like you did. For example, my kid and I were converting miles to feet (bad idea) in the car, and I needed to calculate 2/3 mile to feet. So I took 1760 yards -> 1800 yards, divided by three (600), doubled it (1200), and multiplied by 3 to get feet (3600). Then I handled the 40, but did yards -> feet -> 2/3 (40 yards -> 120 ft -> 80 ft). So the final answer is 3520 ft (3600 - 80). I know the factors of 18, and I know what 2/3 of 12 is, so I was able to do it quickly in my head, despite the imperial system's best efforts.
So yeah, cleaning up the numbers to make the calculation easier is absolutely the way to go.
A mile is 1760 yards, and there are three feet in a yard. Therefore, 1760 feet is 1/3 of a mile, and 2/3s of a mile is 3520 feet.
The imperial system is actually excellent for division and multiplication. All units are very composite, so you usually don't need to worry about decimals.
Yup. The reason I went with yards was because I knew 1760 was closer to a nice multiple of 3 than 5280 (neither 5200 or 5300 is a multiple of 3; I'd have to go to 5100 or 5400).
But yeah, imperial works pretty well for multiplication and division, it's just not intuitive for figuring out the next denomination. Why is a mile 1760 yards instead of 1000 or 1200? Why is it 5280 feet instead of 6000? Why is a cup 8 oz instead of 6 (nicer factors) or 10? Why is a pound 16 oz instead of 8 oz like a cup would be (or are pints the "proper" larger unit for an oz)?
The system makes no sense as a tiered system, but it does make calculations a bit cleaner since there's usually a whole number or reasonable fraction for common divisions. Base 10 sucks for that, but at least it's intuitive.
Metric would be perfect if 10 wasn't such a dog shit number to base our counting off of. Sure it works for dividing things in half, but how often do you need to break something down into fifths? Halves, thirds, and quarters are 90% of typical division people do, with tenths being most of the rest since 10 is that only number that our base system actually works with.
It is not as if any other system of measurement used base 12 which would be the sensible choice by that standard (or base 60 but that might be a bit unwieldy in terms of number of digits required).