48÷2(9+3) = ?

[Altherion]

4 / 3 * 5 means, to Wolfram Alpha, (4 / 3) * 5. (It means nothing to me.) Left to right.

1 / 2x means, to Wolfram Alpha 1 / (2x). (It means that to me as well.) Not left to right.

Yes, that is annoying -- when used without any indications of multiplication, I would tend to treat the entire "2x" expression as a single entity. However, any indication of multiplication changes things. For example, 1/2(x) is x/2 and so is 1/2*x.

That said, when used with numbers, there is no ambiguity because that trick is not possible: you can't do 2x with x being 3 by writing 23 and any indication of multiplication breaks the union (e.g. 1/2(3) is 3/2).

[Cantabile]

The reason that Wolfram doesn't process 1/2x as 1÷2*x, I imagine, is because most people don't mean that when they type it in, they just mean 1 as the numerator, and 2x as the denominator. If you put a space between the 2 and the X then it parses it using order of operations instead.

But there are no variables in the equation at hand; it's pure arithmetic. So I think it's fair to say we can just settle upon the method that all the calculators and engines use, which gives us 288.

[Shryke]

HE nailed it a few pages back, basically going into more detail on what I mentioned earlier:

This whole expression is shitty and unclear and thus, terrible.

Math is about conveying information. Not using brackets here just makes it needlessly more ambiguous to people reading it. It's about clarity.

If this was programming, you'd probably get shit for making your expression overly opaque for no good reason.

[Bronn Stone]

So if I have read this correctly, the solution to 1 ÷ 2x = ½x.

This does not compute for me.

[Altherion]

So if I have read this correctly, the solution to 1 ÷ 2x = ½x.

This does not compute for me.

1/2x is ambiguous because 2x is ambiguous -- it's hard to say whether it is the product of two numbers or a single symbol that stands for this product. 1/2*x and 1/2(x) are unambiguous because it's clear that you're multiplying.

[Bronn Stone]

1/2x is ambiguous because 2x is ambiguous -- it's hard to say whether it is the product of two numbers or a single symbol that stands for this product. 1/2*x and 1/2(x) are unambiguous because it's clear that you're multiplying.

So the original proposal was equally ambiguous, no?

[ErikConrad]

It can be both 2 or 288.

I immediately said 2. I can tell you 99 out of a hundred math/phys students in the Netherlands would answer 2.

Hundred out of a hundred would not have written it like that in the first place...

[MinDonner]

So if I have read this correctly, the solution to 1 ÷ 2x = ½x.

This does not compute for me.

Why not? 1 ÷ 2 = ½, after all.

[Seli]

In the civilized sciences we use units to try and avoid this mess. That, and use properly formatted formulas.

[Mya Stone]

Parentheses does not change the answer on this one, it simply helps people separate it into two separate terms in their mind. (48÷2)(9+3) is the same as 48÷2(9+3). If you write the division as a fraction it might be easier to get.

To get 2 it'd need to be written 48÷[2(9+3)] which is what most of you are doing.

And if anyone needs further proof that it's 288, the computational engine agrees.

Holy shit. Cantabile and I agree on something. Mark this momentous day on the calendar, guys. ;)

[Happy Ent]

To expand on what Shryke said:

mathematical notation is about precise communication.

3/2(9+3) is not an example of that.

Teaching people (even children) completely arbitrary “rules” about how an ambiguous collection of symbols “ought to be” parsed to “get it right” is sinful. It reduces maths to a collection of arbitrary rules. For not good reason. It’s exactly what maths shouldn’t be.

Thus, this entire thread is in a state of sin. And everyone who intones sagely about right or wrong ways of parsing the gobbledigooky expression adds to his own damnation. The only useful and valid opinion that can be ventilated, as usual, is mine: the expression is ambiguous. No mathematician would write it, and if you handed it code that was written like that to me, I’d throw it right back at you.

[Scuba Steve]

Why not? 1 ÷ 2 = ½, after all.

Because the assumption Bronn is making in his example is that 2x is a single expression that forms the denominator of the fraction. The fraction could be re written as 1/2*1/x, but it cannot be rewritten as 1/2*x because you that would create the expression x/2, which is not equivalent to the original fraction.

[Shryke]

To expand on what Shryke said:

mathematical notation is about precise communication.

3/2(9+3) is not an example of that.

Teaching people (even children) completely arbitrary “rules” about how an ambiguous collection of symbols “ought to be” parsed to “get it right” is sinful. It reduces maths to a collection of arbitrary rules. For not good reason. It’s exactly what maths shouldn’t be.

Thus, this entire thread is in a state of sin. And everyone who intones sagely about right or wrong ways of parsing the gobbledigooky expression adds to his own damnation. The only useful and valid opinion that can be ventilated, as usual, is mine: the expression is ambiguous. No mathematician would write it, and if you handed it code that was written like that to me, I’d throw it right back at you.

Indeed. It's important to remember that BEDMAS and shit like that exist to clarify the order of operations, not as some sort of divine rule.

If we changed BEDMAS around to like BEASMD, math doesn't break down. You just need to right your expressions differently to mean the same thing.

[Mya Stone]

Also, people that think it's 2 eat babies and are responsible for the dinosaurs going extinct. Do not trust them.

Dammit, Cantabile! This should teach me not to post anything without reading the whole thread. We do not agree on everything, then. :P

[aeu]

Link to what 1/2x means to Wolfram Alpha: http://www.wolframalpha.com/input/?i=1%2F2x

It means the same to me (but I’d never write it like that). Unfortunately, I can’t give you a URL to my brain.

It seems Wolfram Alpha cannot make up its mind:

http://www.wolframalpha.com/input/?i=1+%2F+2+x

[Balefont]

To expand on what Shryke said:

mathematical notation is about precise communication.

3/2(9+3) is not an example of that.

Teaching people (even children) completely arbitrary "rules" about how an ambiguous collection of symbols "ought to be" parsed to "get it right" is sinful. It reduces maths to a collection of arbitrary rules. For not good reason. It's exactly what maths shouldn't be.

Thus, this entire thread is in a state of sin. And everyone who intones sagely about right or wrong ways of parsing the gobbledigooky expression adds to his own damnation. The only useful and valid opinion that can be ventilated, as usual, is mine: the expression is ambiguous. No mathematician would write it, and if you handed it code that was written like that to me, I'd throw it right back at you.

:bowdown:

[Mudguard]

Error, does not compute!

I think my brain exploded back on page 3.

[Altherion]

So the original proposal was equally ambiguous, no?

No. The original expression is 48/2(12) which, while hideous, is unambiguous.

mathematical notation is about precise communication.

3/2(9+3) is not an example of that.

Teaching people (even children) completely arbitrary “rules” about how an ambiguous collection of symbols “ought to be” parsed to “get it right” is sinful. It reduces maths to a collection of arbitrary rules. For not good reason. It’s exactly what maths shouldn’t be.

So how would you handle it? Put parentheses everywhere? In this case, I personally would never write it this way because I know that this leads to confusion -- I'd write (3/2)(9+3) -- but you can save yourself a lot of parentheses with a single rule (e.g. evaluation from left to right). Would you also insist on writing 3-2-1 as (3-2)-1?

No mathematician would write it, and if you handed it code that was written like that to me, I’d throw it right back at you.

But the compiler would understand (although come to think of it, I always use parentheses just in case).

[Cantabile]

31 User(s) are reading this topic

We all need lives.

[ErikConrad]

...

Thus, this entire thread is in a state of sin.

...

I agree with your technical outcome 100%, but how is this thread sinful? Apparently a lot of people don't know what they are talking about, adamantly claiming 2 or 288 as truth...

Lets educate!