Math folks: Isn’t a BASE basically a DENOMINATOR? What does a BASE and a DENOMINATOR have in common? It’s CLOCK MATH. 0/2, 1/2, 2/2, 3/2, 4/2, 5/2, 6/2, 7/2, 8/2 = 0/1, 1/2, 1/1, 1/1 1/2, 2/1, 2/1 1/2, 3/1, 3/1 1/2, 4/1 = 0, 1, 10, 11, 100, 101, 110, 111, 1000 = 0000,0001,0010,0011,0100,0101,0110,0111,1000 = 0/16,2/16,4/16,6/16,8/16,10/16,12/16,14/16,16/16 The RATIOS should be the same! 0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1 Because watch when you multiply that by 4: 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4 Back to the start. So HOW you represent RATIO doesn’t matter so long as it’s consistent. 0.0%, 12.5%, 25.0%,37.5%, 50.0%,62.5%, 75.0%,87.5%, 100.0% is just BASE 100 0%, 50%, 100%,150%, 200%,250%,300%,350%, 400% is just BASE 400. So if you end up with a REMAINDER or a MOD (modulo) that isn’t 0, you can bump up the denominator (or BASE) and do it again until MOD=0. If you’ve done that, you can do everything in fractions because the RIGHT denominator IS the BASE that will give you the correct RATIO.

Math folks: Isn’t a BASE basically a DENOMINATOR?
What does a BASE and a DENOMINATOR have in common?
It’s CLOCK MATH.

0/2, 1/2, 2/2, 3/2, 4/2, 5/2, 6/2, 7/2, 8/2 =
0/1, 1/2, 1/1, 1/1 1/2, 2/1, 2/1 1/2, 3/1, 3/1 1/2, 4/1 =
0, 1, 10, 11, 100, 101, 110, 111, 1000 =
0000,0001,0010,0011,0100,0101,0110,0111,1000 =
0/16,2/16,4/16,6/16,8/16,10/16,12/16,14/16,16/16

The RATIOS should be the same!

0,0.125,0.25,0.375,0.5,0.625,0.75,0.875,1

Because watch when you multiply that by 4:

0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4

Back to the start.

So HOW you represent RATIO doesn’t matter so long as it’s consistent.

0.0%, 12.5%, 25.0%,37.5%, 50.0%,62.5%, 75.0%,87.5%, 100.0%
is just BASE 100

0%, 50%, 100%,150%, 200%,250%,300%,350%, 400%
is just BASE 400.

So if you end up with a REMAINDER or a MOD (modulo) that isn’t 0, you can bump up the denominator  (or BASE) and do it again until MOD=0.

If you’ve done that, you can do everything in fractions because the RIGHT denominator IS the BASE that will give you the correct RATIO.

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The world I’m looking for is akin to what I just found out is called the “GCD Domain” which is linked to:
https://en.wikipedia.org/wiki/Unique_factorization_domain
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 Yes, the author’s pedagogical abilities is top notch. I was able to follow along. I didn’t have to do the math to understand what was happening and why. That’s a good instructor.
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 I agree that integers are a human workaround but even within them, these’s much to be done that could be better.

Thinking in terms of ratios in parts of wholes and also over parts vs parts rather than fixing everything to a BASE-10 grid is a healthy mental exercise and allows one to visualize functionality of real world interactions with a greater accuracy, if at a loss of some precision.

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