Lets see how long it takes for someone to post a wrong answer.
9 - 3 ÷ 1/3 + 1 = ?
Your superficial understanding of PEMDAS is flawed, and you don't understand nuance. The problem you wrote is obviously designed for you to claim that people are wrong, by you sticking to an overzealous understanding of PEMDAS. A mathematician would look at that and say the answer is 1. The mathematician would also say that your expression is poorly and ambiguously written. Because of your spacing, and use of the division symbol ÷ right next to 1/3, no mathematician would claim that the interpretation of 3 divided by one-third is an incorrect interpretation, and that 3 divided by 1, then divided by 3 is a better interpretation.
Suffice to say, you probably have one of those Beavis and Butthead laughs when someone says the answer is 1, instead of the answer of 9 that you're going to claim is correct.