The question is this: Without calculating, is 15.99/3.99 greater than 4, less than 4, or equal to 4? Well, 16/4 is definitely equal to 4. 15.99/4 is less than 4, because I have less 1/4’s than I did before. 16/3.99 is more than 4, because more 3.99’s fit into 16 than 4’s do.

Because 15.99/4 < 16/4 And 15.99/4 < 15.99/3.99 So it doesn’t tell me how they compare to each other, only to 15.99/4. I need to know if one is biggerer than 15.99/4 than the other one is.

(And yes it’s not a typo. I meant biggerer.)

16/4 is more than 15.99/4 by 0.01/4. So a hundredth of a quarter. 15.99/3.99 is more than 15.99/4 by… some amount that’s not obvious to me at this time.

What would have happened if it was a different set of numbers? Like if I changed the top and bottom by 1? 16/4 vs 15/3 4 vs 5 Ok is this evidence for my situation?

What about 100/4 vs 99/3? 25 vs 33

10000/100 vs 9999/99? 100 vs 101

That one makes me believe it more. I’m suspecting 15.99/3.99 is more than 16/4.

I wonder what 4 lots of 3.99 is? It will be 4 lots of 0.01 off of 16, and that's 15.96. So slightly more than 4 lots of 3.99's fit into 15.99. So 15.99/3.99 is slightly more than 4.

Is that too much calculation? I don't know, but I'm ok with it. I still don't actually know what 15.99/3.99 is.

So I'll stop there. Thanks @howiehua.bsky.social

I was super proud of the 10000/100 vs 9999/99 example. I wonder what other solutions to (a-1)/(b-1)=a/b+1 ther are.

(a-1)/(b-1)=a/b+1 (a-1)=a(b-1)/b+(b-1) (a-1)b=a(b-1)+(b-1)b ab-b=ab-a+b^2-b 0=-a+b^2 a=b^2 Oh wow!