Most of these answers are incorrect. It isn’t PEMDAS simply because some mathematicians decided that’s how it should be, PEMDAS is there because that’s how math works naturally.
For example, 1 + 3 x 4 = 13. This is objective, not subjective depending on what mathematicians agreed to follow. This is because 3 x 4 is just addition on its own, ie 3 x 4 = 3 + 3 + 3 + 3 or 4 + 4 + 4, both equal 12. This is also why multiplication is reversible.
Mathematicians DID just use multiplication in order to shorten the equation though, it’s much easier to write 3 x 4 rather than adding 4 3s together.
To put this in a real life term, let’s say you are having a party, you invited 3 people and each of them is bringing 3 friends. So in essence each of your friend groups total 4 people, 1 + 3 x 4 = 13 total people, which is correct for the attendance. 1 (yourself) + 3 (groups of friends) x 4 (people per friend group) = 13 total people. If you added 1 and 3 first you’d get 16 total people and your party would be a let down with less people coming.
Mathematicians can’t just change it by all agreeing and saying add the 1 + 3 first and still result in a correct answer.
kylitobv t1_iyb46yf wrote
Reply to ELI5 why we first multiply, then add by TheManNamedPeterPan
Most of these answers are incorrect. It isn’t PEMDAS simply because some mathematicians decided that’s how it should be, PEMDAS is there because that’s how math works naturally.
For example, 1 + 3 x 4 = 13. This is objective, not subjective depending on what mathematicians agreed to follow. This is because 3 x 4 is just addition on its own, ie 3 x 4 = 3 + 3 + 3 + 3 or 4 + 4 + 4, both equal 12. This is also why multiplication is reversible.
Mathematicians DID just use multiplication in order to shorten the equation though, it’s much easier to write 3 x 4 rather than adding 4 3s together.
To put this in a real life term, let’s say you are having a party, you invited 3 people and each of them is bringing 3 friends. So in essence each of your friend groups total 4 people, 1 + 3 x 4 = 13 total people, which is correct for the attendance. 1 (yourself) + 3 (groups of friends) x 4 (people per friend group) = 13 total people. If you added 1 and 3 first you’d get 16 total people and your party would be a let down with less people coming.
Mathematicians can’t just change it by all agreeing and saying add the 1 + 3 first and still result in a correct answer.