why in algebra class they teach the order of operations (PEMDAS) in that order. Is this just an arbitrary standard everyone agreed on or was it the result of higher math only making sense when equations are done in that order?

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In: 1362

Answer 1

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