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.
Different compilers have robbed me of all trust in order-of-operations. If there’s any possibility of ambiguity - it’s going in parentheses. If something’s fucky and I can’t tell where, well, better parenthesize my equations, just in case.
In some countries we’re taught to treat implicit multiplications as a block, as if it was surrounded by parenthesis. Not sure what exactly this convention is called, but afaic this shit was never ambiguous here. It is a convention thing, there is no right or wrong as the convention needs to be given first. It is like arguing the spelling of color vs colour.
BEDMAS: Bracket - Exponent - Divide - Multiply - Add - Subtract
PEMDAS: Parenthesis - Exponent - Multiply - Divide - Add - Subtract
Firstly, don’t forget exponents come before multiply/divide. More importantly, neither defines wether implied multiplication is a multiply/divide operation or a bracketed operation.
Exponents should be the first thing right? Or are we talking the brackets in exponents…
afair, multiplication was always before division, also as addition was before subtraction
Multiplication VS division doesn’t matter just like order of addition and subtraction doesn’t matter… You can do either and get same results.
Edit : the order matters as proven below, hence is important
8÷2(2+2)=2(2+2)÷2(2+2)
alternatively if 8÷2(2+2)=16 that means 2(2+2)=8÷16 in other words 8=0,5 which it isnt
your first line is correct, but while it looks like 1 (and it might be under different conventions), evaluating according to standard rules (left to right if not disambiguated by pemdas) yields
2(2+2)/2(2+2) = 2(4)/2(4) = 2*4/2*4 = 8/2*4 = 4*4 = 16
Using implicit multiplication in quotients is weird and really shouldn’t happen, this would usually be written as 8/(2*(2+2)) or 8/2*(2+2) and both are much clearer
Your second argument only works if you treat 2(2+2) as a single “thing”, which it looks like, but isn’t, in this case
not much to refute in the argument of whether its 16 or 1 as its all a matter of convention in the end and ultimately the root of the argument is poor formatting of the expression, im used to implicit multiplication taking precedent and that 2(2+2)===2*(2+2) and that for my first argument having the same expression on 2 sides of a division sign automatically equals 1, but how come you find implicit multiplication in quotients weird? seeing as it happens literally all the time in equations, unless thats a difference in school systems or similar im unaware of
for fun also rewrote the expression into powers of 2 and indeed depending on how you go about implicit multiplication i end up with either 2⁰ or 2⁴, so for the sake of sanity i figure its best to just say x₁=1; x₂=16
It’s weird because usually the people writing the expressions want to communicate clearly, and stuff like 1/2x is not immediately clear to everyone, so they write the 1/2 as a fraction.
The same expression on both sides of the division sign only reduce to one if they actually bind to the division sign, which is rarely an issue, but that is exactly the thing that is in question here. I think it’s clear that 1 + 1/1 + 1 is 3, not 1, even though 1+1 = 1+1.
But as you said, of course, the evaluation order is just convention, you can just as well write everything in https://en.m.wikipedia.org/wiki/Reverse_Polish_notation
The correct answer is 16. Multiplication and Division happen at the same level of priority, and are evaluated left-to-right.
