I have to say, the usual convention really seems to need typography with variable size superscripts to make sense. Ex: In e^{-x^2/2} the superscript 2 is doubly small, while in (e^x)^2 the superscript 2 is the same size as the x.
Parentheses are lovely. Inferred order of operations based on some convention is annoying and arbitrary.
What’s 48/2(9+3) ?
Rolling Dice…
2?
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Bad notation!
But yeah, order of operations is a convention for writing things down, not a rule of mathematics (unless I guess, you’re some kind of formalist). It isn’t really there to help use figure out what 2 + 5 * 8 is. It’s there to help us figure out what 3x7 - 6x2 - 7 is. The purely numerical expression might as well just be written 42, and if is really came down to it you could write 2 + (5 * 8).
But ((3(x7)) - (6(x2))) - 7? Not gonna do it.
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Multiplication and division are on the same level as each other, so I would do the parentheses first, then the operations from left to right:
48 / 2 * 12 = 24 * 12
… = 288
However this looks sketchy to me on some level, and I think the multiplication should actually come first, even though I have been told it doesn’t:
48 / (2 * 12) = 2
Because it’s debatable what the right answer is, and because division and subtraction are not commutative, I would use parentheses to avoid confusion.
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What about 3x2(x5 - 2) - 7?
Very true, although if I had written “is a/bc well defined?” I think many people would have assumed it was, without thinking too hard about it.
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I think it would be very reason to assume that meant a/(bc) because there’s no reason not to write ac/b if that’s what you mean. But in notation where you are using / as a divide symbol you should use * as a multiplication symbol.
Without order of operations thats (3((x2)((x5) - 2))) - 7
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But a/bc IS well defined. That’s WHY there is a rule that one does addition and subtraction operations from left to right as well as multiplication and division from left to right. So a/bc = (a/b)c ≠ a/(bc)
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I think it’s well defined in hand writing, but not on a computer screen, assuming the point is to know what was meant by the person who wrote it rather than to apply a rule. Like I said above, I can’t think of any reason in the world to not write ac/b if that’s what you meant, but if you are typing, you really, really ought to use a notation that clears up ambiguities.
Because really, without the context of this conversation, I’d interpret a/bc as a variable named ‘a’ divided by a variable named ‘bc’ every time if it is typed on a computer screen.
I would say that it is well defined, but confusing because, as you’ve said, that is an unusual way of writing that expression, and we’re not accustomed to it. But really, if there’s any chance of confusion adding parentheses is a good idea.
A police interaction with kids in the US and no shooty-bang-bang … I’m impressed.
Off-duty cop from Anaheim is probably already scheduled to do a re-training for his colleague B.J. Gruber from Marion, OH to set him straight on the proper procedures.
Maybe there’s the reason she posted to the PD’s FB page instead of asking in person.
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