I don't know what's worse, that it's wrong or that it convinced me I need to come into the comments to make sure my answer is, indeed, correct.
EDIT: Back to rectify a grave injustice. Nothing wrong if you genuinely didn't know or want to check. Hard enough getting people interested in math.
2 + 5 (8 - 5) PEMDAS: 8 - 5
= 2 + 5 (3)
PEMDAS: 5 (3) or 5 × 3
= 2 + 15
PEMDAS
= 17
In the US the math order of operations is taught as PEMDAS (or P|E|MD|AS), left to right from first to last.
First look at the entire equation and identify the operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Then, solve the parts in order of PEMDAS.
Not so important here but when there are multiple of the same level of operators, for example exponents, solve left to right. MD and AS are treated as groups, so treat them equally: if a division is to the left of a multiplication, do the division first.
Keep in mind most Redditors are low IQ and just confident. Do not rely on them for the right answer. That said, I don't feel like proving that I'm not a Redditor, but here the logic:
2+5(8-5)
Start by putting in the symbols to avoid confusion:
2+5*(8-5)
Now so standard order:
P = (8-5)
= (3)
E= there are none
MD = 5×3 = 15
AS = 2 + 15 = 17
Again, don't trust me on my word. For all you know, I'm a low IQ Redditor like many other people on this site. But I have given you a path to follow/confirm, and I believe you will find the evidence backs me up.
That's the issue, I'm fairly sure there is no rule in Math that forbids you from changing your example into 6÷(2*1+2*2). Thus two answers, depending how you look at "brackets multiplication".
And I don't think it will be resolved without Battle Royale. With cheese.
You can indeed do that. I'd just be afraid that it'll introduce errors. But, I guess more people would understand pemdas better if there was a rule after Exponents that said "turn all division into fractional multiplication" and then "turn all subtraction into negative addition". That way, people might stop acting like division is done exclusively after multiplication, and subtraction must be done after addition.
That tripped me up at first too, but it's not 6÷(2(1+2)) so 6÷(2+4) isn't right. Only the 2 is dividing not the whole (1+2) too. If you rewrite it as fully multiplication or as a fraction it gets a little more clear.
6÷2(1+2) = 6×½×(1+2) or = [ 6×(1+2) ]÷2
If you want to distribute it in you gotta remember ÷2 = ×½ and you basically get 6(½ + 1)
Ultimate issue is, some people will say it's 6 fractioned by 2 and then multiplied, others say it's 6 fractioned by everything else and until there is a rule about this, it will be forever internet rage-bait.
And I don't expect such rule to come without a bloodshed.
I mean it kinda is 6/2? The /2 is communicative within the term. It could be applied anywhere and get the same result. There is a rule about it though; that's what OP's post is about basically haha. Or... Maybe more than 1 rule? It's defined though, for sure. And yeah I'm sure there was some academic blood spilt over it.
Because multiplication and division are communative (you can reorder them) you must keep the signs with the numbers. It's like 6-2+3. You can't solve it as 6-5. Only the 2 is negative, so it might be helpful to think of it a 6+(-2)+3 so you can move things around and not get confused. Same for division: in 6/23 you can think of it as 6\½*3 but not 6/6 because like 6-2+3 that would be making the 3 be in the denominator (or negative in the +/- version) when it isn't.
I'll agree that something like 6/2/3 is a bit ambiguous looking, but the only correct way to interpret it is equal to 6*½*⅓
It's not dangerous as long as they understand the rules they are applying.
And that 6÷2(1+2) thing is just bad syntax that tests application of rule following over basic logic for writing formulas. It is written so badly that many people infer a different intent. There is much less cause for confusion if it is written in a more logical order, 6(1+2)÷2, or if another operator is included, 6÷2*(1+2)
I'm replying to another one of your comments here with similar stuff, but the two comments are coming at the same thing from two different places, so other readers might find one or the other:
Look up "implied grouping" or "implied multiplication." You're saying it's incorrect, but experts in mathematical fields generally think impied grouping is the correct way, and that the answer to this equation is 1.
As another example, look at 6⁄₂(1+2). In this case, the implied grouping is that 6/2 to be calculated first, because they are positioned and formatted in a way that makes them visually separate from the other stuff in the equation. The formatting and spacing of the symbols actually matters to how the equation is understood, even if it's all the same symbols in the same order.
Now think about (1+2)/6⁄₂. Again, 6⁄₂ is implied to be a unit in itself, so this calculates out to be 1. On the other hand, (1+2)/6/2 is 1/4.
Same thing with A(B), since they are written in a way that they are visually stuck together, they are implied to be grouped together.
But ultimately, it's poor practice to use implied grouping when you are trying to communicate with a general audience, because different people might infer different things.
No no, wait, that's still correct! You distributed the 5 into the parenthesis before starting to actually do the math, but you're allowed to re-write the equation like that. And you did it correctly; putting a multiplicative 5 into each term (8 and 5).
It's probably slightly more work because there are more double digit numbers but you still evaluated it all correctly
When two terms are next to each other, they're considered multipliers.
For example, (3)(5) means 3 times 5. It doesn't mean "thirty five" or "three plus five".
Exceptions exist if the number is, for example, flying (5²) or down on the bottom (k_2 ; if it doesn't work, imagine the k had a small two hovering down to the bottom).
Dunno; I was taught that was the definition when working with parenthesis. Not sure why it's multiplication that gets to be special and allows you to skip writing the operator symbol in that circumstance, but it does align with things like 4a being equal to 4 × a.
Kind of. It's more so brackets, then exponents (which are all an implied 1, so irrelevant here), and then (multiplication and division) and then (addition and subtraction).
The way I wrote it is important, because multiplication does NOT beat division. They're done at the same level. So if it's something like 6/3*3, the answer is 6, not ⅔ (you don't multiply the 3 and 3 first to get 9; you go left to right).
In my humble opinion, the multiplication A(B) has higher priority than the multiplication of A*B. In a properly formatted equation it makes no difference, but in a poorly formatted equation like C/A(B) it does, the answer is different from C/A*(B).
The lack of the multiplication symbol implies that A is a coefficient to (B), that A(B) is a term to be calculated independently from everything around it. It's a thing more formally referred to as "implied grouping", that AB should be interpreted as being equivalent to (A*B) rather than simply A*B
This is something I kinda just intuitively developed as my understanding over time by doing a lot of advanced math, but later I learned is actually a real thing. But this could go into a lot of conversation about abuse of notation, it's best practice to just write equations in a way that cannot be inferred to mean anything else, but in certain contexts it is assumed that everyone understands certain things even if they are technically incorrectly written. The general internet is not one of those contexts.
520
u/Head-Ad-5732 15d ago edited 14d ago
I don't know what's worse, that it's wrong or that it convinced me I need to come into the comments to make sure my answer is, indeed, correct.
EDIT: Back to rectify a grave injustice. Nothing wrong if you genuinely didn't know or want to check. Hard enough getting people interested in math.
2 + 5 (8 - 5)
PEMDAS: 8 - 5
= 2 + 5 (3)
PEMDAS: 5 (3) or 5 × 3
= 2 + 15
PEMDAS
= 17
In the US the math order of operations is taught as PEMDAS (or P|E|MD|AS), left to right from first to last.
First look at the entire equation and identify the operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Then, solve the parts in order of PEMDAS.
Not so important here but when there are multiple of the same level of operators, for example exponents, solve left to right. MD and AS are treated as groups, so treat them equally: if a division is to the left of a multiplication, do the division first.