this post was submitted on 03 Mar 2024
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[–] Leviathan 15 points 9 months ago (5 children)

Maybe someone better at math can answer this, but is 0.25/0.5 functionally the same as 0.5/1, or simply 0.5?

[–] [email protected] 17 points 9 months ago (1 children)

You can call it whatever you want, as long as it equals 1/2 it's the same number.

So yes, multiplying by 2/2 to make it more intuitively obvious is perfectly valid and a good way to think about it. Most arithmetic tricks are ultimately multiplying by 1 or adding 0 just to make the problem easier to handle.

[–] Leviathan 2 points 9 months ago

Oh yeah, I just meant that they said I multiplied by 2, which in my head is 2/1 but I was multiplying by 1. Just trying to be clear.

[–] spicytuna62 4 points 9 months ago* (last edited 9 months ago)

I think it's easier to picture it in terms of fractions. When you divide by a fraction, you reciprocate the divisor. That is, you flip its numerator and denominator, then multiply them. In this case, we're taking 1/4 and dividing it by 1/2. You take the reciprocal of 1/2, which is 2/1. Then multiply the numerators and denominators. You end up with (1/4)*(2/1)=2/4=1/2=0.5

[–] [email protected] 1 points 9 months ago

Huh, that's a cool way to think of it. I've done a decent amount of higher level maths but stuff like this always cooks my brain if I let it. I thought of the numbers as the fractions 1/4 and 1/2, which then reminds me that 1/2 * 1/2 = 1/4, but I think your way feels more elegant

[–] [email protected] 1 points 9 months ago (1 children)

0.25 is half of 0.5. Alternatively: A quarter is half of half. If you multiplied 0.25/0.5 by 2, then it would be 0.5/1, which is just 0.5.

[–] Leviathan 5 points 9 months ago* (last edited 9 months ago) (1 children)

Didn't I multiple it by 2/2 which is the same as 1? Like isn't 2/8 the same as 1/4?

[–] Aleric 2 points 9 months ago

You've got it. The trick to working with fractions is multiplying them by fractional equivalents to one (2/2, 7/7, 13/13, etc) to change them into numbers that our monkey brains can handle more easily.