this post was submitted on 03 Dec 2023
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There's quite a few calculators that get this wrong. In college, I found out that Casio calculators do things the right way, are affordable, and readily available. I stuck with it through the rest of my classes.
Casio does a wonderful job, and it's a shame they aren't more standard in American schooling. Texas Instruments costs more of the same jobs, and is mandatory for certain systems or tests. You need to pay like $40 for a calculator that hasn't changed much if at all from the 1990's.
Meanwhile I have a Casio fx-115ES Plus and it does everything that one did, plus some nice quality of life features, for less money.
TI did the same thing Quark and Adobe did later on – got dominance in their markets, killed off their competition, and then sat back and rested on their laurels thinking they were untouchable
EDIT: although in part, we should thank TI for one thing – if they hadn’t monopolized the calculator market, Commodore would’ve gone into calculators instead of computers
https://en.wikipedia.org/wiki/TI-99/4A
It was a huge failure, but they tried.
Huge failure my ass. Come at me on munch man, Alpiner, or Tombstone City. Or coding vaguely racist things like Mr. Bojangles, one of the first codes in the early books.
Had one at home and used the hell out of it, don't get me wrong. Was my first computer. Played the Zork series on that thing. But, it had issues and wasn't a financial success.
It had fewer issues than almost anything I've owned since. I bet it would still work if I got the right adaptors. Wasn't a huge financial success though. They seemed content with early coding and games, and didn't move into word processing etc.
If you're lucky, you can find these TI calculators in thrift shops or other similar places. I've been lucky since I got both of my last 2 graphing calculators at a yard sale and thrift shop respectively, for maybe around $40-$50 for both.
The TI equivalent to the Casio fx-115ES Plus is the TI-36X Pro, and they both cost $20 at Walmart.
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.
There isn't any ambiguity even if you don't.
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?
When you added the multiply you changed the answer, because the (2+2) is now in the numerator instead of in the denominator.
You added brackets and changed the answer. 2(2+2) is a single term, and if you break it up then you change the answer (because now the (2+2) is in the numerator instead of in the denominator).
The only right answer
Nope, 1 is the only correct answer.
Except they don't. This isn't a notation problem, it's a people don't remember the rules of Maths problem.
Yes
8 / 2 (2+2)
8 / 2 (4)
4 (4)
16
No
8 / 2 (2+2)
8 / 2 (4)
8 / 8
1
No. Order of operations is left to right, not right to left. 1 is wrong.
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(c) becomes a/(b×(c))
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.
I'm an Australian teacher who has also taught the U.K. curriculum (so I have textbooks from both countries) and, based on these comments you mention, have also Googled some U.S. textbooks, and I've yet to see any Maths textbooks that teach it "the other way". I have a very strong suspicion that it's just a lot of people in the U.S. claiming they were taught that way, but not actually being true. I had someone from Europe claim the way we (and the U.K.) teach it wasn't taught there (from memory it was Lithuania, but I'm not sure now), so I just Googled the curriculum for their country and found that indeed it is taught the same way there as here. i.e. people will just make up things in order not to admit they were wrong about something (or that their memory of it is faulty).
Huh, I'll be darned. I'm not as much of a math nerd as I thought
Here is an alternative Piped link(s):
This video
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I'm open-source; check me out at GitHub.
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.
Write it out on paper, with numerator above the denominator. You'd have to write 8(2+2), 2(2+2) can only be written if both are in the denominator.
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.
No, the correct answer is 1.
Casio calculators FTW. I got one that could do polar conversions, was basically essential for engineering.
Ditto for Sharp. It's really only Texas Instruments that is the ongoing exception to the rule.
Sharp as well.