6÷2(1+2)=? How do you solve this?

6÷2(1+2) is one of those order of operations problems that pops up on social media occasionally and causes people to disagree on the answer and get all angry about it 😉

The reason the disagreements occur is based in order of operations. Most of us know to complete the inside of the parenthesis before applying the other operators, but after doing this, we effectively go from 6÷2(1+2) to 6÷2(3), or 6÷2×3

Now, if we apply PEMDAS, we see M goes before D, so do the multiplication first and then apply the division, and this gives us an answer of 1. Done!

But wait- PEMDAS has this sneaky little misunderstanding- it actually has MD and AS grouped together. So really it should be PE(MD)(AS). Because we do Multiplication *and* Division in the same pass, from left to right. Same applies to Addition and Subtraction, but we’re not concerned with that right now. SO- solving from left to right gives us 9.

And 9.. is the correct answer.

Reference for PEMDAS – See the mnemonic section here: https://en.wikipedia.org/wiki/Order_of_operations
And the specific quote from the page is: “These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order ‘addition first, subtraction afterward’ would incorrectly evaluate the expression

So now you either owe your friends an apology, or it’s time to gloat.. but don’t go overboard if the latter, ok?