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The P in PEMDAS just means resolve what's inside the parentheses first. After that, it's just simple multiplication with adjacent terms, and multiplication and division happen together left to right.
6÷2(1+2)
6÷2(3)
3(3)
9
This is actually a generational thing. Millennials were taught “PEMDAS”:
But younger generations have been taught “BEDMAS” instead:
Notably, Division and Multiplication are swapped on PEMDAS and BEDMAS, to make this “both happen at the same time” more straightforward. But that only applies if the entire operation can happen at the same time.
For instance, let’s say
6/2(3)compared to6÷2(3). At first glance, they both appear to be the same operation. But in the former, the6dividend would be over the entire2(3)divisor. Which means you would need to simplify the divisor (by resolving the multiplication of2•3) before you divide. So the former would simplify to6/6=1, while the latter would divide first and become3(3)=9.Technically, if you wanted to be completely clear, you would write it using multiple parenthesis as needed. For instance, you would write it as either:
(6÷2)(3)=9or6÷(2(3))=1to avoid the ambiguity. Then it wouldn’t matter if you’re using PEMDAS or BEDMAS.Usually, no sign before the bracket means juxtaposition. Scientific calculators do account for it (not all, tho), while regular ones may not.
So 2(1+2) is really (2+4)
Compare 2/2x and 2/2×X where x is (1+2)
The first is 2/(2+4)=1/3, the second is (2/2)×(1+2)=3
Basically, either 1 or 9 can be considered correct. And yes, it's ambiguous.
Also, there's no real rule about solving left to right due to associative and commutative properties: 1×2×3 = 1×(2×3) = (1×2)×3 = 3×1×2 = 2×1×3 = 6
would you say the same thing if the division was written out like a line under 2(3) and under that 6
idk how this'll come out but something like this:
2(1+2)
-----------
6
edit : wow i did a formatting thing
edit2: i got it (ish)
In that case, I'd say the answer is 1. Top and bottom are each resolved to the fullest extent possible before dividing top by bottom. It's equivalent to (top)÷(bottom), but it's clearer and preferable if you can easily format that way in my opinion, just harder on a computer.
I think that’s why people are complaining about the division sign.
It’s been decades since I took a math class so I am definitely not the right person to explain things, but I am using technology to confirm my understanding of the various notations:
So yeah, if you put 6 over a denominator of 2(1+2), the answer is different (1) because the equation is different. But if you write it out literally, it would be 6 over 2 times (1+2).
What you wrote swapped the denominator to make it 2(1+2)÷6, which will always be 1.