Hiper Calc is the calculator app that I use. It’s very good. When I ran this equation, it actually notified me how the operands should be grouped (weak or strong) and provided two answers. Honestly the whole issue can be avoided if you use more parentheses
There isn’t a multiplication symbol though. By your logic something like 8÷2x would mean (8÷2)*x because order of operations
Or if you read 8÷2√x as (8÷2)*√x
Just notate 8÷2(2+2) as 8÷2x; x=(2+2) and you get it, you can substitute any complete expression with a variable in an equation and the logic stays the same.
I’m with the right answer here. / and * have same precedence and if you wanted to treat 2(2+2) as a single unit, you should have written it like (2*(2+2)).
It’s pretty common even in academic literature to treat implied multiplication as having higher precedence than explicit multiplication/division. Otherwise an expression like 1 / 2n would have to be interpreted as (1 / 2) * n rather than the more natural 1 / (2 * n).
A lot of this bullshit can be avoided with better notation systems, but calculators tend to be limited in what you can write, so meh. Unless you want to mislead people for the memes, just put parentheses around things.
That’s fair. Personally, I just have a grudge against math notation in general. Makes my programmer brain hurt when there’s no consistency and a lot of implicit rules.
Then again, I also like Lisp so I’m not exactly without sin.
As a musician, can I just say: I would give my right nut for a musical notation system that is as clearly defined as mathematical notation. The worst part is that everyone that attempts to fix musical notation, just creates a new standard of notation.
I know what video you linked even without clicking lol. Yeah, I can agree there. Although my only experience with music was “try to learn guitar, get distracted because ADHD”.
I started with piano, technically, but I was 3-4 years old, and don’t remember any of it. I can sit a piano and make it sound good, but I can’t play sheet music on it. I switched to violin in second grade, and then just learned how to play everything except for rhythm guitar, and piano. Chords mess with my fingers. Strangely enough my ADHD allowed me to super focus, but I never got the hang of sight reading, so I mostly play by ear, but no one can tell.
I can even play a didgeridoo, and that required me to learn circular breathing.
Even guitarhero/rockband will help you with using your fingers and will help when you want to try a real guitar. Muscle memory might not be great but for someone who is just doing it for fun it will be helpful getting your fretting and strumming coordination. And them being games might help fend off the adhd enough to keep you motivated to pick it up again after putting it down
The problem is whether or not that rule is taught depends on when and where you learned it. Schools only started teaching that rule relatively recently, and even then, not universally. Which of course makes for ideal engagement bait on your hellsite of choice.
Unfortunately, it’s the best calculator I could find so far (for my own needs). I paid to remove the ads though, ads bother me way too much to use something infested with them.
If you’re willing to pirate (or legally generate) a TI calculator ROM, then Graph 89 is probably what you’re looking for. This is what I use as my daily driver calculator with a TI-89 ROM.
My mom’s a mathematician, she got annoyed when I said that the order of operations is just arbitrary rules made up by people a couple thousand years ago
It’s organized so that more powerful operations get precedence, which seems natural.
Set aside intentionally confusing expressions. The basic idea of the Order of Operations holds water even without ever formally learning the rules.
If an addition result comes first and gets exponentiated, the changes from the addition are exaggerated. It makes addition more powerful than it should be. The big stuff should happen first, then the more granular operations. Of course, there are specific cases where we need to reorder, or add clarity, which is why human decisions about groupings are at the top.
“Math” is a mass noun. You can’t have “a math”. It’s like blood or love. You can have more blood or less blood. There might be units in which blood is measured that you can have a certain number of (“a gallon of blood”), but you can’t have, unqualified, a blood or two bloods (well, not in that sense of the word, anyway).
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
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.
Afaik the order of operations doesn’t have distributive property in it. It would instead simply become multiplication and would go left to right and would therefore be 16.
If you agree that parenthesis go first then the equation becomes 8/2x4. Then it’s simply left to right because multiplication does not take precedence over division. What’s the nuanced talk? That M comes before D in PEMDAS?
In this more sophisticated convention, which is often used in algebra, implicit multiplication is given higher priority than explicit multiplication or explicit division, in which those operations are written explicitly with symbols like x * / or ÷. Under this more sophisticated convention, the implicit multiplication in 2(2 + 2) is given higher priority than the explicit division in 8÷2(2 + 2). In other words, 2(2+2) should be evaluated first. Doing so yields 8÷2(2 + 2) = 8÷8 = 1. By the same rule, many commenters argued that the expression 8 ÷ 2(4) was not synonymous with 8÷2x4, because the parentheses demanded immediate resolution, thus giving 8÷8 = 1 again.
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