Originally Posted by jhawkkw
Well, I teach math at the college level so I guess that contradicts XplosiV's idea that mathematicians would vote 1. These math question threads that pop up continue to convey the idea that mathematics is something you can opinionate, and is not absolute fact. If I add 3 apples to 5 apples, you get 8. Not 2, not 10, but 8. The laws of mathematics are absolute and breaking them results in contradictions. An example is one of the many division by zero fallacies. I'll show this one as an example:
let a=b,
by multiplying both sides by a, you would get a^2 = ab.
subtract b^2 from both sides yields a^2b^2 = ab  b^2.
factoring using the difference of squares on the left side, and the common factor of b on the right side yields (a+b)(ab)=b(ab).
dividing (ab) on both sides yields a+b = b.
since a=b, making the substitution yields b+b or 2b = b.
finally, dividing both sides by b yields a final result of 2=1, which is clearly not correct. This is because of the division of (ab) because that is equal to zero. Division by 0 isn't allowed under standard mathematical arithmetic, which causes the contradiction of 2=1.
6÷2x(2+1) is identical to 6÷2(2+1) under the standard rules of arithmetic. One of the topics one would encounter in the 4th year of a bachelor's in mathematics called modern/abstract alegrba, is a course where you investigate operations at it's absolute core. Addition and multiplication form an abelian ring, otherwise known as a field, on the set of real numbers. Subtraction and division is nothing more than addition and multiplication respectively by use of it's corresponding inverse. For example, 35 = 3 + 5; as well as 6 ÷2 = 6 * (1/2) (<one half). Using this idea, you can change the original problem: 6÷2(1+2) to 6*(1/2)*(1+2). Using PEMDAS normally, you would get 6*(1/2)*3. Performing the multiplication, 6*(1/2) gives you 3, and then 3*3 gives you 9.
