Comment on A fake Facebook event disguised as a math problem has been one of its top posts for 6 months
HereIAm@lemmy.world 1 month agoThe issue normally with these “trick” questions is the ambiguous nature of that division sign (not so much a problem here) or people not knowing to just go left to right when all operators are of the same priority. A common mistake is to think division is prioritised above multiplication, when it actually has the same priority. Someone should have included some parenthesis in PEDMAS aka. PE(DM)(AS) 😄
The issue normally with these “trick” questions
There’s no “trick” - it’s a straight-out test of Maths knowledge.
the ambiguous nature of that division sign
Nothing ambiguous about it. The Term of the left divided by the Term on the right.
A common mistake is to think division is prioritised above multiplication
It’s not a mistake. You can do them in any order you want.
when it actually has the same priority
Which means you can do them in any order
“A common mistake is to think division is prioritised above multiplication”
That is what I said. I said it’s a mistake to think one of them has a precedence over the other. You’re arguing the same point I’m making?
I said it’s a mistake to think one of them has a precedence over the other
And I said it’s not a mistake. You still get the right answer.
You’re arguing the same point I’m making?
No, I’m telling you that prioritising either isn’t a mistake. Mistakes give wrong answers. Prioritising either doesn’t give wrong answers.
Another common issue is thinking “parentheses go first” and then beginning by solving the operation beside them (mostly multiplication). The point being that what’s inside the parentheses goes first, not what’s beside them.
Another common issue is thinking “parentheses go first”
There’s no “think” - it’s an absolute rule.
then beginning by solving the operation beside them
a(b) isn’t an operation - it’s a Product. a(b)=(axb) per The Distributive Law.
(mostly multiplication)
NOT Multiplication, a Product/Term.
The point being that what’s inside the parentheses goes first, not what’s beside them
Nope, it’s the WHOLE Bracketed Term. a/bxc=ac/b, but a/b©=a/(bxc). Inside is only a “rule” in Elementary School, when there isn’t ANYTHING next to them (students aren’t taught this until High School, in Algebra), and it’s not even really a rule then, it’s just that there isn’t anything ELSE involved in the Brackets step than what is inside (since they’re never given anything on the outside).
vithigar@lemmy.ca 1 month ago
The 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?
HereIAm@lemmy.world 1 month 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 1 month ago
I stand corrected
SmartmanApps@programming.dev 3 weeks ago
No, you weren’t. Most of their answers were wrong. You were right. See my reply. 4 is the only correct answer, and if you don’t get 4 then you did something wrong, as they did repeatedly (kept adding brackets and thus changing the Associativity).
Melvin_Ferd@lemmy.world 1 month 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.
SmartmanApps@programming.dev 3 weeks ago
There isn’t any ambiguity.
No, only 1 answer is correct, and all the others are wrong.
Maths isn’t English and doesn’t have multiple meanings. It has rules. Obey the rules and you always get the right answer.
It isn’t incomplete.
HereIAm@lemmy.world 1 month 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.
SmartmanApps@programming.dev 3 weeks ago
Nope! 6 × 4 ÷ 2 × 3 ÷ 9 =4 right to left is 6 ÷ 9 x 3 ÷ 2 × 4 =4. You disobeyed the rule of Left Associativity, and your answer is wrong
Also nope. Multiplication first is 6 x 4 x 3 ÷ 2 ÷ 9 =4
Still nope. 6 × 4 x 3 ÷ 2 ÷ 9 =4
Still nope. 6 × 4 x 3 ÷ 9 ÷ 2 =4
And finally still nope. 6 ÷ 9 ÷ 2 x 4 x 3 =4
Hint: note that I never once added any brackets. You did, hence your multiple wrong answers.
No it isn’t. Only 4 is correct, as I have just shown repeatedly.
It’s because students don’t make mistakes with signs if you don’t change the order. I just showed you can still get the correct answer with different orders, but you have to make sure you obey Left Associativity at every step.
barsoap@lemm.ee 1 month 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^”.
SmartmanApps@programming.dev 3 weeks ago
No, the solution is learn the rules of Maths. You can find them in Maths textbooks.
Yes we do, and it’s what we teach students to do.
HereIAm@lemmy.world 1 month 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.
Robust_Mirror@aussie.zone 1 month ago
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
SmartmanApps@programming.dev 3 weeks ago
Nope. Addition first is 9+3-1=12-1=11. You did 9-(1+3), incorrectly adding brackets and changing the answer (thus a wrong answer)
troistigrestristes@lemmy.eco.br 1 month 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 1 month 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 + 4
Addition first:
(1 + 2) - (3 + 4)
3 - 7 = -4
Subtraction first:
1 + (2 - 3) + 4
1 + (-1) + 4 = 4
Right to left:
1 + (2 - (3 + 4))
1 + (2 - 7)
1 + (-5) = -4
Left to right:
((1 + 2) - 3) + 4 (3 - 3) + 4 = 4
SmartmanApps@programming.dev 3 weeks ago
No it doesn’t. You disobeying the rules and getting lots of wrong answers in your examples doesn’t change that.
Which you did wrong.
And I’ll show you it doesn’t matter when you do it correctly
Nope. Right answer for wrong reason - you only co-incidentally got the answer right. -3+1+2+4=-3+7=4
Nope. 4-3+2+1=1+2+1=3+1=4
Or you could just do it correctly in the first place, always obeying Left Associativity and never adding Brackets
There aren’t ANY ambiguous cases. In every case it’s equal to 4. If you didn’t get 4, then you made a mistake and got a wrong answer.
troistigrestristes@lemmy.eco.br 1 month 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.