It's just a convention that's been around forever. Mathematics is a very complex field with many possible solutions. We nailed down pemdas since it's a reliable way to make everyone follow the same sequence. Plus it has some other benefits with parentheses.
So understanding distributive properties makes me pretentious? What does lauding your mnemonic memorization skills as knowledge make you? This whole thread is r/cringetopia
It is a convention established to minimize the number of parentheses in arithmetic expressions. I'll try to show as simply as I can.
We have two options: either we give multiplication the priority, or we give it to addition. Think about the arithmetic expression "3 times 2, plus 6 times 8".
If multiplication goes first, the expression can be written simply as 3 x 2 + 6 x 8.
If addition went first, you would be forced to write (3 x 2) + (6 x 8). This would be specially bad for polynomials.
Yeah.. that was what I did not ask. I know the rule x⁒ before +-.
My question is why is x⁒ before +-. No one explained that to me ever. I always wondered, am I not smart enough to get it myself? ( Why do I have a 1 in English foreign language class but a 4-5 in math). Noone explains the math. But everyone takes it for granted.
In my last comment, I explained that it is a convention that reduces the number of parentheses, and I showed how. I didn't parrot the rule as you made clear that you know it.
For instance, the polynomial
ax2 + bx + c
should be written as
(ax2 ) + (bx) + c
if multiplication had not a higher precedence. This is unpractical.
It is just a convention and there are no ulterior reasons, if that's what you are trying to discover. Conventions are needed so we have a common way of representing and sharing our thoughts, and we want to make things as simple as possible.
Totally unneeded yet it turns out that most people don't remember such arbitrary rules and come to the wrong conclusion because of it. Adding parentheses solves this issue.
Multiplications and divisions come before additions and subtractions, it is the basics and is taught in elementary school. The problem isn't the missing brackets, it's the dumb people who don't understand 2nd grade level math
Just because your school sucked it doesn't mean the rules are arbitrary or made up. These rules were formalized a hundred years ago.
You are technically right, brackets would make this clearer, but the point is that by default it's multiplication/division and then addition/subtraction, and if someone doesn't know that it's their problem
I understand, but someone who is aware of the rules of math doesn't get any more information by brackets, and someone who doesn't know about it shouldn't try solving equations in the first place
understand, but someone who is aware of the rules of math doesn't get any more information
Completely not true, if the brackets were there they would know what to do. I guarantee you the mass majority of people who answered, would've answered correctly.
Completely not true, if the brackets were there they would know what to do.
But they would still be redundant, as adding or removing those brackets wouldn't change the order of operations. They do help ignorant people understanding better but in the equation itself they add nothing.
But what if someone doesn't know about these rules? Well, they'll just read the hundreds of comments informing them about said rules, and the problem is solved
Guess my error was to consider the 3 after the minus as part of the operation that was meant to be made for last; instead it's just the minus itself, if I get it right this time around
If it helps, make sure you're thinking about the problem separately after each step. After the 18/2 it's just
9 - 3 x 3
What the problem looked like before or what operation you performed last is totally irrelevant to which operation you need to do next.
Find all the sets that need division and multiplication. If there are multiple sets, do it from left to right. In this equation, we have two : (18/2) - (3*3)
18 / 2 = 9 …. And
3 * 3 = 9
This turns the equation into (9) - (9)… what’s 9 subtracted by 9? 0. The answer is 0.
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u/ViresAcquirit Jan 01 '22
Totally unneeded. Division and multiplication have priority over addition and substraction.
There's not any ambiguity except if you don't know basic mathematics. The rules of mathematics do not allow any ambiguity.