this post was submitted on 03 Dec 2023
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PEMDAS is what they teach school children to help them learn. Like most such rules, it's oversimplified and doesn't quite work all the time.
The proper way is to write a fraction top and bottom. Thus, 8(2+2) / 2 = 16, while 8 / 2(2+2) = 1. The implicit multiplication simply does not work if they're split across the fraction.
PEMDAS sucks as a mnemonic, we can agree on this.
Try 8/2(2+2) on an actual calculator that's used by scientists.
Something like a Ti-83 would show 16, not 1.
Replace (2+2) with x:
8 / 2x = 4 / x = 4 / (2+2) = 1
Implicit multiplication takes priority over division.
My Casio fx-991 gives 1. If I put in an explicit multiplication, then I get 16.