Huh, thanks for the insight. I’ve never been able to get my head around weird division like this, and that sounds like a great rule of thumb for thinking about it.
Dividing by a fraction is the same as flipping one it on its head and multiplying it.
0.25/0.5 is (1/4)/(1/2)
To multiply it we’d flip one, either works but for this example I decided to flip the second one: (1/4) * (2/1)
The top half of the fractions (numerators) multiply together, then the bottoms (denominators) multiply together. (1*2)/(4*1) = 2/4 which reduces to 1/2
I suspect people might be getting confused by this because of colloquialisms like “divided in half”, “divided in the middle”, “divided by two”
things is, math doesn’t care about idioms
another area in mathematics that I’ve seen ppl (myself included lmao) suffer from this is propositional logic. like with the non exclusive nature of the OR operator
Why is it not 0.125?
For that to be true it would have to say 0.25 / 2.
X/0.5 = X*2
Division by less than 1 is essentially multiplying with extra steps
Huh, thanks for the insight. I’ve never been able to get my head around weird division like this, and that sounds like a great rule of thumb for thinking about it.
Dividing by a fraction is the same as flipping one it on its head and multiplying it.
0.25/0.5 is (1/4)/(1/2)
To multiply it we’d flip one, either works but for this example I decided to flip the second one: (1/4) * (2/1)
The top half of the fractions (numerators) multiply together, then the bottoms (denominators) multiply together. (1*2)/(4*1) = 2/4 which reduces to 1/2
same as
x * .5 = .25if that somehow helps yaI suspect people might be getting confused by this because of colloquialisms like “divided in half”, “divided in the middle”, “divided by two”
things is, math doesn’t care about idioms
another area in mathematics that I’ve seen ppl (myself included lmao) suffer from this is propositional logic. like with the non exclusive nature of the OR operator
but this is all just a wild guess
I definitely struggle with any math that I can’t visualize in a physical way.
Sometimes it clicks if you graph it out with the confusing values on axes.