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>i can also say you can fit half a RQ into a PR which means that a 1RQ:0.5PR ,

You meant 0.5RQ:1PR in that case.

Ratios don't inherently know about equality.  If there is a 3:1 ratio of boys to girls, that's fine.

But if I say that Jacob has twice as much money as Noah, then J=2N or J:N = 2:1.
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PR/RQ=1/2 = 1:2

You are mixing up ÷ with =
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I really mostly think algebraicly, for better or for worse :)

For every 1 dog there are 2 cats results in the ratio 1:2 for dogs to cats: D/C=D:C=1:2=1/2

The equivalent equation is 2D=1C, so now the 2 is with the dogs and the 1 is with the cats. This is what confused you. But 2 times the smaller quantity equals 1 times the larger quantity, which makes sense!





In general: If X/Y=a/b, then bX=aY

(Not aX=By)

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