prefix notation doesn’t need parentheses either though, at least in this case. lisp uses them for readability and to get multiple arity operators. infix doesn’t have any ambiguity either if you parenthesize all operations like that.
How is PEMDAS 16? Multiply is before divide, so it’s 1. I was taught BEDMAS, divide before multiply, which makes it 16. I don’t know what is correct, just asking.
I don’t mean when they’re explaining “here’s how the order of operations works”. I mean in the basic way that they write more advanced problems and the answers they give for them.
This video, and the prequel to it linked in the description, go into some detail showing who uses what convention and why.
FWIW I went to school in Asia, using an internationally-focused curriculum, rather than going through the Australian curriculum here in Aus.
The video I linked includes some discussion with a calculator manufacturer who apparently is under the impression that teachers in North America are asking for strict BIDMAS, so the calculator manufacturer actually switched their calculators to doing that. Until they then got blowback from the rest of the world’s teachers, so they switched back to BIDMAS with juxtaposition being prioritised over division. The video also presents the case that outside of teachers—among actual maths and physics academics—prioritising juxtaposition is always preferred, even in North America.
That’s exactly where the calculators in the op differ. For more examples, Casio calculators do implicit multiplication first, while ti’s treat it the same as explicit multiplication and division. I think that the latter is more predictable personally, but really you just need to know your calculator.
My Casio calculators get this wrong, even the newer ones. BTW the correct answer is 16, right?
(8 ÷ 2) × (2 + 2)8 ÷ (2 × (2 + 2))2 2 + 8 2 ÷ × .(× (÷ 8 2) (+ 2 2))prefix notation doesn’t need parentheses either though, at least in this case. lisp uses them for readability and to get multiple arity operators. infix doesn’t have any ambiguity either if you parenthesize all operations like that.
How is PEMDAS 16? Multiply is before divide, so it’s 1. I was taught BEDMAS, divide before multiply, which makes it 16. I don’t know what is correct, just asking.
PEMDAS is actually (PE)(MD)(AS). Those that are grouped together have equal precedence and are evaluated left to right.
8 / 2 * (2+2)
8 / 2 * 4
4 * 4
16
Edit to fix formatting, maybe?
Yes
8 / 2 (2+2)
8 / 2 (4)
4 (4)
16
No
8 / 2 (2+2)
8 / 2 (4)
8 / 8
1
a(b) is a×b. Step 2 could be rewritten as 8 / 2 × 4. Working left to right, step 3 becomes 4 × 4.
No, because implicit multiplication binds more tightly than explicit. a/b© becomes a/(bש)
Says who?
Most maths textbooks written by mathematicians.
I don’t mean when they’re explaining “here’s how the order of operations works”. I mean in the basic way that they write more advanced problems and the answers they give for them.
This video, and the prequel to it linked in the description, go into some detail showing who uses what convention and why.
Interestingly I’ve wondered if this is regional, as a fellow Aussie I learned the same as you but it seems in other places they learn the other way
FWIW I went to school in Asia, using an internationally-focused curriculum, rather than going through the Australian curriculum here in Aus.
The video I linked includes some discussion with a calculator manufacturer who apparently is under the impression that teachers in North America are asking for strict BIDMAS, so the calculator manufacturer actually switched their calculators to doing that. Until they then got blowback from the rest of the world’s teachers, so they switched back to BIDMAS with juxtaposition being prioritised over division. The video also presents the case that outside of teachers—among actual maths and physics academics—prioritising juxtaposition is always preferred, even in North America.
Huh, I’ll be darned. I’m not as much of a math nerd as I thought
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That’s exactly where the calculators in the op differ. For more examples, Casio calculators do implicit multiplication first, while ti’s treat it the same as explicit multiplication and division. I think that the latter is more predictable personally, but really you just need to know your calculator.
Depends on the system you use. Most common system worldwide and in the academic circles (the oldest of the two) has 1 as the answer.
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