If it's 2(1 + 2) that's considered one "term" and heavily implies that you should FOIL first before anything else. It isn't the same as 2 * (2 + 1). Of course you wouldn't likely get an equation like that without knowing "what" you're doing, which would answer any ambiguity.
2(1 + 2) does imply multiplication: 2 * (1 + 2). The reason it counts as one term, as I noted below, is because it is inside a two-dimensional fraction which has implicit parathenses in the numerator, denominator, and the fraction itself. The first equation is actually ((6) / (2(1 + 2))). When a fraction is written in two dimensions instead of a single string, the division between the numerator and the denominator is supposed to be done last.
The first equation is not 6 / 2(1 + 2). If it was, this means you get (6 / 2) * (1 + 2) as in the second equation, which means (1 + 2) is moved up to the numerator ((6(1+2)) / 2 = (6 / 2) * (1 + 2)), which means the two problems are not equal to each other. I believe this is the point of the "joke".
If I wrote 6 ÷ 2x, x=3 you wouldn't try to divide by just the 2. The 2 is "part of" the term (2x) which is how the majority of cases where you would actually see something like 2(some number) would work. PEMDAS BODMAS or whatever other mnemonic be damned
(I'm not arguing this passionately in any way I just like arguing <3)
x is still multiplied last. There's not a rule for implied multiplication shorthand preceding operations to the left. You still need to wrap 2x in parentheses if you want the operation to occur first.
https://www.wolframalpha.com/input?i=6%2F%282x%29
This isn't like a polynomial like ax^2 + bx + c as division is done between 6 and 2 before multiplication with x. Typically you wouldn't see such an equation (which is intended to trick you) as normally addition or subtraction would occur like in a polynomial or another variable equation (such as a linear graph), which would be done after the exponents, multiplication, and division with the variables are calculated. In the instance you wrote, it should be written as (6/2)x, or 3x, to avoid obscuring the equation. Though you intended for 6/(2x), or 3/x.
And no worries, comrade, I'm just meaning to help since I am good at math and like helping people (I don't mean this in an egotistical way). I'm not taking offense, and I am not meaning to offend anyone.
If it's 2(1 + 2) that's considered one "term" and heavily implies that you should FOIL first before anything else. It isn't the same as 2 * (2 + 1). Of course you wouldn't likely get an equation like that without knowing "what" you're doing, which would answer any ambiguity.
2(1 + 2) does imply multiplication: 2 * (1 + 2). The reason it counts as one term, as I noted below, is because it is inside a two-dimensional fraction which has implicit parathenses in the numerator, denominator, and the fraction itself. The first equation is actually ((6) / (2(1 + 2))). When a fraction is written in two dimensions instead of a single string, the division between the numerator and the denominator is supposed to be done last.
The first equation is not 6 / 2(1 + 2). If it was, this means you get (6 / 2) * (1 + 2) as in the second equation, which means (1 + 2) is moved up to the numerator ((6(1+2)) / 2 = (6 / 2) * (1 + 2)), which means the two problems are not equal to each other. I believe this is the point of the "joke".
If I wrote
6 ÷ 2x, x=3you wouldn't try to divide by just the 2. The 2 is "part of" the term (2x) which is how the majority of cases where you would actually see something like 2(some number) would work. PEMDAS BODMAS or whatever other mnemonic be damned(I'm not arguing this passionately in any way I just like arguing <3)
2x still means 2 * x.
https://www.wolframalpha.com/input?i=6%2F2x
x is still multiplied last. There's not a rule for implied multiplication shorthand preceding operations to the left. You still need to wrap 2x in parentheses if you want the operation to occur first.
https://www.wolframalpha.com/input?i=6%2F%282x%29
This isn't like a polynomial like ax^2 + bx + c as division is done between 6 and 2 before multiplication with x. Typically you wouldn't see such an equation (which is intended to trick you) as normally addition or subtraction would occur like in a polynomial or another variable equation (such as a linear graph), which would be done after the exponents, multiplication, and division with the variables are calculated. In the instance you wrote, it should be written as (6/2)x, or 3x, to avoid obscuring the equation. Though you intended for 6/(2x), or 3/x.
And no worries, comrade, I'm just meaning to help since I am good at math and like helping people (I don't mean this in an egotistical way). I'm not taking offense, and I am not meaning to offend anyone.