Another person already replied using your equation, but I felt the need to reply with a simpler one as well that shows it:
9-1+3=?
Subtraction first:
8+3=11
Addition first:
9-4=5
Comment on A fake Facebook event disguised as a math problem has been one of its top posts for 6 months
vithigar@lemmy.ca 4 days agoThe same priority operations can be done in any order without affecting the result, that’s why they can be same priority and don’t need an explicit order.
6 × 4 ÷ 2 × 3 ÷ 9 evaluates the same regardless of order. Can you provide a counter example?
Robust_Mirror@aussie.zone 4 days ago
troistigrestristes@lemmy.eco.br 4 days ago
Oh my god now this is going to be Lemmy’s top thread for 6 months, isn’t it?
Btw, yeah I’m with you on this, you just need to know the priorities and you’re good, because the order doesn’t matter for operations with the same priority
HereIAm@lemmy.world 4 days ago
Except it does matter. I left some examples for another post with multiplication and division, I’ll give you some addition and subtraction to see order matter with those operations as well.
Let’s take:
1 + 2 - 3 + 4Addition first:
(1 + 2) - (3 + 4)
3 - 7 = -4Subtraction first:
1 + (2 - 3) + 4
1 + (-1) + 4 = 4Right to left:
1 + (2 - (3 + 4))
1 + (2 - 7)
1 + (-5) = -4Left to right:
((1 + 2) - 3) + 4 (3 - 3) + 4 = 4troistigrestristes@lemmy.eco.br 3 days ago
Oh, but of course the statement changes if you add parentheses. Basically, you’re changing the effective numbers that are being used, because the parentheses act as containers with a given value (you even showed the effective numbers in your examples).
Get this : + 1 - 1 + 1 - 1 + 1 - 1 + 1
You can change the result several times by choosing where you want to put the parentheses. However, the order of operations of same priority inside a container (parentheses) does not change the resulting value of the container.
In the example, there were no parentheses, so no ambiguity (there wouldn’t be any ambiguity with parentheses either, the correct way of calculating would just change), and I don’t think you can add “ambiguity” by adding parentheses — you’re just changing the effective expression to be evaluated.
By the way, this is the reason why I absolutely overuse parentheses in my engineering code. It can be redundant, but at least I am SURE that it is going to follow the order that I wanted.
HereIAm@lemmy.world 4 days ago
So let’s try out some different prioritization systems.
Left to right:
(((6 * 4) / 2) * 3) / 9
((24 / 2) * 3) / 9
(12 * 3) / 9
36 / 9 = 4
Right to left:
6 * (4 / (2 * (3 / 9)))
6 * (4 / (2 * 0.333…))
6 * (4 / 0.666…)
6 * 6 = 36
Multiplication first:
(6 * 4) / (2 * 3) / 9
24 / 6 / 9
Here the path divides again, we can do the left division or right division first.
Left first:
(24 / 6) / 9
4 / 9 = 0.444… Right side first:
24 / (6 / 9)
24 / 0.666… = 36
And finally division first:
6 * (4 / 2) * (3 / 9)
6 * 2 * 0.333…
12 * 0.333… = 4
It’s ambiguous which one of these is correct. Hence the best method we have for “correct” is left to right.
vithigar@lemmy.ca 4 days ago
I stand corrected
Melvin_Ferd@lemmy.world 4 days ago
Maybe I’m wrong but the way I explain it is until the ambiguity is removed by adding in extra information to make it more specific then all those answers are correct.
HereIAm@lemmy.world 4 days ago
100% with you. “Left to right” as far as I can tell only exists to make otherwise “unsolvable” problems a kind of official solution. I personally feel like it is a bodge, and I would rather the correct solution for such a problem to be undefined.
Robust_Mirror@aussie.zone 4 days ago
It’s so we don’t have to spam brackets everywhere
9+2-1+6-4+7-3+5=
Becomes
((((((9+2)-1)+6)-4)+7)-3)+5=
That’s just clutter for no good reason when we can just say if it doesn’t have parentheses it’s left to right. Having a default evaluation order makes sense and means we only need parentheses when we want to deviate from the norm.
barsoap@lemm.ee 4 days ago
The solution accepted anywhere but in the US school system is “Bloody use parenthesis, then”, as well as “Why is there more than one division in this formula why didn’t you re-arrange everything to be less confusing” up to “50 Hertz, in base units, are 50s^-1^”.
HereIAm@lemmy.world 4 days ago
I fully agree that if it comes down to “left to right” the problem really needs to be rewritten to be more clear. But I’ve just shown why that “rule” is a common part of these meme problems because it is so weird and quite esoteric.