Title
In: 1362
The “bigger” operations go first. Parenthesis are the exception, they always go first, but, for example, X^Y is a much more dynamic curve than X times Y which is more dynamic than X + Y.
>was it the result of higher math only making sense when equations are done in that order
If you think about it, you would realize that isn’t the case. We could just have parentheses around everything a hundred times to communicate whatever we want. Time if we were doing 5 * 2 + 3, we could do the 5 * 2 first by writing (5 * 2) + 3 or we could do the 2 + 3 first by writing 5 * (2 + 3). We just agree on doing PEMDAS in that order because it means that we can use less parentheses in most situations
When did it become PEMDAS instead of BODMAS? Or is this a UK / US thing?
I see a lot of folks saying it’s arbitrary, It’s just math and it doesn’t matter how we do it as long as we all do it the same. That is not correct. Math represents real life. You do pemdas because following this rule guarantees you will get real life results. Here’s the best example I’ve seen in the past (for this example forgive the strange farm that has octopus’ and consider their tentacles legs):
You go to a farm and there are 5 chickens, 3 cows and 2 octopuses. How many legs are there? Well if you count the legs you get 38. If you use math:
5×2+3×4+2×8 = 10+12+16 = 38 legs. This is why you must do multiplication first. It’s not arbitrary. Now the way we write this (symbols of + x etc and use of parenthesis, sure that’s arbitrary) but order of operations is required to have math match real life. There’s still confusion around other elements of pemdas, and memorizing rules is a terrible way to “understand” things. but the bottom line is, it’s not arbitrary. Source: I’m an engineer. Edited for clarity
My brother has a maths degree and explained it like this.
Imagine you have a sum, something like 8+8+8+8+2, for the sake of saving some space you could just write 8×4+2. The multiplication symbol here is just shorthand for all that extra additions, so it’s kind of like expanding the sum back to what it “actually” is by using PEMDAS
Now imagine 8+8+8+8+8+8+8+8+7+7+7+2
That can be considered
8×8+7×3+2
or to use another bit of shorthand
8²+7×3+2
You could write these with parentheses if you wanted to be extra doubly certain but PEMDAS means you can trust whoever is reading it won’t need them
TL;DR: expanding shorthand
No it’s not arbitrary.
All operations all just different and handy ways to add. And addition is a way to group things and count them.
So in order to calculate you must reduce everything to additions. And in order to reduce everything to additions you just start doing the most complicated things first.
So 3×2+2(1+3) = 3+3+1+3+1+3 = 16.
That’s it.
3^2 + 2×3+4/2 = 3×3+3+3+4×1/2 = 3+3+3+3+3+1/2+1/2+1/2+1/2=19
Latest Answers