PEMDAS Is NOT The Correct Order Of Operations
Every now and then a math exercise of the style of 6 ÷ 2(1+2) goes viral. Some people get one result while others get another. And then there is controversy. Why is there conflict? Because school has taught us wrong. If you were a good student, you would try to solve the exercise by using the order of operations known as PEMDAS. This is the mnemonics of Parenthesis, Exponentials, Multiplications, Divisions , Additions and Subtractions. All read it from left to right. So, this is what you surely will try:
6 ÷ 2(1 + 2) = 3(1 + 2) = 3(3) = 9 ✗
Why is this wrong? Because the exercise was written using juxtaposition. That means it was written without explicitly using the multiplication symbol. This is important because 2(1 + 2) is not the same as 2 × (1 + 2). The difference is that when you use juxtaposition, you are indicating that the expression works as a unit:
2(1 + 2) = (2 × (1 + 2))
On the other hand, the multiplication symbol is separating two different units:
2 × (1 + 2) = (2) × (1 + 2).
Therefore, the exercise is correctly resolved like this:
6 ÷ 2(1 + 2) = 6 ÷ (2 × (1 + 2)) = 6 ÷ (2 × 3) = 6 ÷ 6 = 1 ✔
Thus, the correct order of operations is PEJMDAS. Now, if you want to check if what I had written makes any sense by using a calculator, you will meet the problem that some calculators use PEMDAS while others use PEJMDAS. You will need to read the manual to know which one it is.
The funny thing is that as no scientists or engineers use PEMDAS, as it is only used in school, they are told on the internet that they are doing basic math wrong by people only at school level. This can be really frustrating when it happens in conjunction with most sites assuming PEMDAS is right, even sites written by experts.
Now, if the original exercise were 6 ÷ 2×(1 + 2), with explicit multiplication, then the correct answer would be 9:
6 ÷ 2 × (1 + 2) = 6 ÷ (2) × (1 + 2) = 3 × (1 + 2) = 3 × 3 = 9 ✔