So order of operations is hard?
Not for students it isn’t. Adults who’ve forgotten the rules on the other hand…
Comment on A fake Facebook event disguised as a math problem has been one of its top posts for 6 months
billwashere@lemmy.world 1 month ago
So order of operations is hard?
SmartmanApps@programming.dev 3 weeks ago
Zenith@lemm.ee 1 month ago
Yeah and I’m tired of pretending it’s not!
Gsus4@mander.xyz 1 month ago
Next we’re going to have an epic debate on whether work done by the system is positive or negative and we’re all going to feel really smart and passionate about it. Like one of those Science vs Religion debate clubs.
HereIAm@lemmy.world 1 month ago
The 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) 😄
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
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
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^”.
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
There’s no “trick” - it’s a straight-out test of Maths knowledge.
Nothing ambiguous about it. The Term of the left divided by the Term on the right.
It’s not a mistake. You can do them in any order you want.
Which means you can do them in any order
HereIAm@lemmy.world 3 weeks ago
“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?
SmartmanApps@programming.dev 3 weeks ago
And I said it’s not a mistake. You still get the right answer.
No, I’m telling you that prioritising either isn’t a mistake. Mistakes give wrong answers. Prioritising either doesn’t give wrong answers.
AnotherPenguin@programming.dev 1 month ago
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.
SmartmanApps@programming.dev 3 weeks ago
There’s no “think” - it’s an absolute rule.
a(b) isn’t an operation - it’s a Product. a(b)=(axb) per The Distributive Law.
NOT Multiplication, a Product/Term.
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).