Lots math problems been popping up on my Facebook feed lately. Some people doing it them from left to right, others arguing "parenthesis and multiplication first!" Well why? Why does that "have to" be done first?
shareHave you never taken a math class? "Parentheses first" is the proper way to solve a math problem. It's called the "order of operation."
https://blog.prepscholar.com/pemdas-meaning-rule
"It's called the "order of operation."
You don't say?
Where's BullSchmidt when you need him
shareQuite frankly, it matters because that's just the way the mathematics was developed. It's similar to, why did you use a period to end your sentences, or why did you use quotation marks to reference concepts that you were quoting?
It's for clarity and consistency within the rules of grammar.
With PEMDAS, this is just the shared understanding of how to simplify an expression. If people could freely do the operations in whatever order they wanted, then people would just get different responses. I'm not suggesting that like math is arbitrary either. The way we've selected our words and articulated our expressions are arbitrary, but they're linked to true statements such as 1+1=2.
Btw, side note, the reason why ppl are even arguing about it on social media is because a lot of ppl never understood or are misremembering pemdas, which itself is just a simplified heuristic to help young students remember (ironically). People are saying that because "m" is before "d", you do multiplication before division, which isn't true at all.
"With PEMDAS, this is just the shared understanding of how to simplify an expression. If people could freely do the operations in whatever order they wanted, then people would just get different responses"
Simplify, LOL? In what way is that more simple than going left to right like you would with any other basic math problem
Why would anyone do it in "whatever order they wanted" when you generally do math problems from left to right? What makes someone decided to randomly do a math problem in any order they wanted than what we were taught?
1+1=2
1+1+1=3
2x4=8
If problem says 1+2x3 why the hell wouldn't someone not follow the same logic? The order of operations throws that completely out the window. You don't go left to right and get 9, you do the multiplication first and get 7. WHY?
"simplifying an expression" is just the name for the action being performed here, which is to reduce the number of terms in an expression by putting like variables together. In this case, there are no variables, so simplifying the expression reduces it to a single term.
Why would anyone do it in "whatever order they wanted" when you generally do math problems from left to right?
What makes someone decided to randomly do a math problem in any order they wanted than what we were taught?
The order of operations throws that completely out the window. You don't go left to right and get 9, you do the multiplication first and get 7.
-character limit
Consider a line, how would you write the formula for it? Typically it'll be something like y = ax + b, with a and b being constants. The expression here is describing the angle and position of a line, with a representing the slope of the line, and b being where the line crosses the y axis. Given the way we describe that, there needs to be consistency on how to describe it.
If ax + b meant something different from b + ax, it would be incoherent.
Because according to these goofballs, you should do A * x + b in the former. And (b + a) * x in the latter, which are two entirely different lines. But they're not. Which is why we use parenthesis if want to add b + a before multiplying x.
This still applies even when you don't have have variables. Just replace a with 2, x with 3, and b with 1.
7 = 2(3)+1 = 1 + 2(3) =/= (1+2)3 = 9
the matter of why does order operations
shareI saw a YouTube video on this which was interesting. The argument was that until fairly recently it was not critical. But since computers sprung up you have to be very specific about the rules to get consistent results.
shareIt's definitely something that was changed or made up somewhere along the line. All the older people responding to a problem like 1+2x3 are saying 9; because they were never taught the order of operations. People who were, including me, are answering 7; and I don't understand why. Why not go left to right like I would with 1+2 or 2x2?
Doing some research, you don't get a logical answer. It's kind of laughable.
https://edu.gcfglobal.org/en/algebra-topics/order-of-operations/1/
"The order of operations is important because it guarantees that people can all read and solve a problem in the same way."
I never really thought about it before - I just follow the rules to get a consistent result.
But the example you gave, 1+2*3, can be thought of one plus three twos, because that's what multiplication actually does. So it becomes 1+2+2+2=7.
I think precedence was set as maths evolved - it just didn't affect most people until they started teaching it in schools so we understand how computers work. A few hundred years ago, before someone invented multiplication, just going left to right would have been fine.
All the older people responding to a problem like 1+2x3 are saying 9; because they were never taught the order of operations.
Consistency was always important. Doing the operations in a different order can result in different answers, which isn't what you want in any STEM field, even before computers came along. Even before computers came along, you'd need the people designing a bridge to be solving math formulas the same way when they were figuring how much weight the bridge can support.
Why in God's name would anyone decide to randomly do a problem/equation "out of order"? We are taught left to right.
1+1=2
2x2=4
4x4x4=64
But throw in some parenthesis or addition and multiplication *gasps* and it has to be done in a DIFFERENT order.
1+2x3= 7 because of the "oRdEr OF oPeRaTiONs"
Let's throw the order of operations out the window for a second. If that doesn't exist, people simply do it from left to right like every other basic math problem (and you get 9 as an answer). What is this out of order shit? No one is going to do it any other way than left to right.
I'm wondering when maths became necessary to build. For the longest time it would have been a process of trial and error and if you got it wrong it, whatever it was, fell down.
And when it did become necessary the people doing the maths would have been specialists. Meanwhile the ordinary person would have got along quite happily with just adding and subtracting and working left to right.
Looks like I was taught wrong.
I was taught that you do parenthesis first but always perform all of these tasks in this order: add, subtract, multiply, divide.
If this thread is to be trusted then that is wrong.
No, parenthesis are first. I am asking why.
shareYou were taught wrong, I'm afraid :(
-simplify by removing parentheses
-resolve exponents
-multiplication and division from left-to-right
-addition and subtraction
i probably switched it around in my head over the decades of disuse.
shareFair enough, that's usually what I just assume in most cases. Like, it's just the Mandela effect. People forgetting fundamentals that they never fully understood or just forgot from not using (cause really, when does this come up in our day to usage unless you work with numbers in your job)
But I was thinking earlier how I've seen teachers today literally teach basic mathematics incorrectly...so I can't discount that either lol
when i was doing pretty advanced maths ,for engineering the pedmas bullshit never came into it because things were written and expressed properly .
The "order of operations" was obvious
This --> ÷ was never used for one thing, and brackets were used a lot.
those "puzzles" on facebook are the math equivalent of a badly worded phrase with multiple double negatives that you have to deconstruct to work out if its a yes or a no.
those "puzzles" on facebook are the math equivalent of a badly worded phrase with multiple double negatives that you have to deconstruct to work out if its a yes or a no.
the pedmas bullshit never came into it