this post was submitted on 31 May 2025
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[–] [email protected] 11 points 2 days ago* (last edited 2 days ago)

The "why" goes a little further than that.

In actuality, it's because of fundamental properties of operations

  • Commutation

a + b = b + a

a×b = b×a

  • Association

(a + b) + c = a + (b + c)

(a×b)×c = a×(b×c)

  • Identity

a + 0 = a

a×1 = a

If you know that, then PEMDAS and such are useless because they're derived from those properties but do not fully encompass them.

Eg.

3×2×(2+2) = 3×(4+4) = 12+12 = 24

This is a correct solution that is improper if you're strictly adhering to PEMDAS rule as I've done multiplication before parenthesis from right to left.

I could even go completely out of order by doing 3×2×(2+2) = 2×(6+6) and it will still be correct