Here's a problem that can easily be solved incorrectly if the order of operations is not used properly.

6 divided by 2(1+2)

The
answer is 9, some might think it's 1, but really it's 9. Do the work
in parenthesis first, so you have 6 divided by 2(3).. Now in the order
of operations multiplication comes before division.. IF you do it that
way you would get 1 because you'd multiply 2 and 3 to get 6, then 6
divided by 6 is 1. But the order of operations also states
multiplication and division is done from left to right, so the division
is first... IF the problem was 6/[2(1+2)] THEN it would be 6/[2(3)] =
6/6 = 1. But the problem doesn't state this.

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