I was recently shown the equation $6 \div 2(1 + 2) = ?$, and it was disputed whether this equation equals $1$ or $9$.
To solve for $1$:
$$ 6 \div 2(1 + 2) \\ 6 \div 2(3) \\ 6 \div 6 \\ 1 $$
To solve for $9$:
$$ 6 \div 2(1 + 2) \\ 6 \div 2 \cdot 3 \\ 3 \cdot 3 \\ 9 $$
While it is more intuitive for the parentheses multiplication to come first, leading to $1$, PEMDAS dictates that the answer is $9$ due to left-to-right operation of multiplication and division.
What is the correct way to solve the problem? Why? What leads to this dispute? How could this ambiguity be prevented in the future?
Although Peter's left-to-right comment is correct, there's a temptation to make division the "top" operation because of all the times in physics and chemistry and engineering we see formulas like $$ z = \dfrac{2\pi f}{m g}$$ (which isn't real but sure looks like something you'd see in science class, doesn't it?). When you write this on a single line you might write $z = 2\pi f / m g$, even though you should write $z = 2\pi f /( m g)$ to be technically correct. If you actually intended the technically correct interpretation of $z = 2\pi f / m g$, which is $$ z = \dfrac{2\pi f} { m} g$$ you would almost certainly write it as $$ z = \dfrac{2\pi f g} { m} $$ or $ z = 2\pi f g/ m $ when written on a single line.
TL;DR The division operator makes us think that we're looking at single line version of a stacked fraction and gets us confused and uncertain. People who aren't trying to intentionally confuse us will use parentheses to be clear.