Submitted by TheManNamedPeterPan t3_z8c5vf in explainlikeimfive
Graega t1_iyb40dl wrote
Reply to comment by MagicSquare89 in ELI5 why we first multiply, then add by TheManNamedPeterPan
To put that in even simpler terms, imagine you have 5 boxes of 12 eggs, and an extra 2. That's 2 + 5 x 12. But if you add first, you'd have a lot more complicated way of trying to express that. It's not a law of nature, but there is a practical use case that made selecting multiplication first a clear choice.
Walty_C t1_iybftk5 wrote
Why couldn’t you just write it 5 x 12 + 2 and solve it all left to right? Or just stick with parentheses as the operator. (5x12) + 2. Could math not be simplified in this way or would it fall apart with more complex equations?
bovisrex t1_iybhjf5 wrote
You can and should. A large function in algebra (including basic mathematics) is in making a long problem easier to understand. The problem you wrote could also be written 12 + 12 + 12 + 12 + 12 + 2, but writing it as 5 x 12 + 2... or (5 x 12) + 2... makes it understandable at first glance. This is all that is meant by the common math problem "Simplify this equation."
Agreeing on a convention to write math problems a certain way just removes ambiguity and makes it possible for any person familiar with the relatively simple Order of Operations rule to understand any other problem written by someone. My biggest problem with the order of operations "riddles" that swarm Facebook from time to time is that they'll intentionally write them in a confusing way in order to trick people. It's the same as posting a scribbled rough draft of a paragraph and then making fun of people who misinterpret it.
Salindurthas t1_iybms9m wrote
>Why couldn’t you just write it 5 x 12 + 2 and solve it all left to right?
Well, what if you are writing down the eggs you see, as you see them?
What if you spot 2 eggs, so you write that down, and then spot 2 cartons of a dozen, so you write that down.
Oh, dang, now you've written 2+ 5x12, and under your convention, that isn't what I meant (I've written 7x12, but I mean 2 more than 5x12).

Or, what if you have a formula like: "D = 2*x/y + 5*z^2"
You might be working in a lab, , and your assistant tells you "I've measured x & y, they are 7 and 3.5 respectively."
You're waiting for them to measure z, and figure that you'll simplfiy your equation, and you work out the left term happens to be 4 (2*6/3.5=4).
So you write "D = 4 + 5*z^2" to keep your equations easy to read and lined up.
Oh, dang again! That isn't what you meant, you need to change the order around!

I think it is better to have a convention where the order you write addition in doesn't matter, so that you can add things as you discover them/calculate them, rather than needing to reorder your equation every time.
You *could* do it, but I think if society did, we'd have more errors than using our current convention.
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