like how does it make sense? why is it correct compared to just solving equations left to right? what are some scenarios that prove PEMDAS to be the absolute truth and necessity? @_@
In: Mathematics
As everyone has mentioned, PEMDAS isn’t baked into math but rather it is just how we agreed to write the math. Here is a concrete example.
Say we have the equation 4 x 5 + 10.
Let’s pretend there is no order of operations. This could mean one of two things.
You have four buckets and each bucket has five apples in it. You have ten apples in the side not in a bucket. How many apples do you have? You have 30 apples.
You have four big buckets. Each of these buckets were advertised as being able to hold ten more apples than the previous buckets. How many apples can you now carry? You can now carry 60 apples.
There are some parts of PEMDAS that aren’t arbitrary. MD and AS have to stick together. This is because they are the same things.
5 ÷ 6 is the same as 5 x 1/6. Likewise 3 – 5 is the same as -5 + 3. Since M & D, and A & S are the same they need to be fine together.
E doesn’t make any sense without PEMDAS because it would become arbitrary where it goes. If the order was ASE then 4^2 + 5 would be the same as 4 + 5^2 since in both cases you would add 4 & 5 first.
P likewise makes even less sense as, without being first, it becomes meaningless.
You could do some alternative to PEMDAS like go from left to right but this would make many complex problems impossible or at least extremely difficult.
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