Solve 48÷2(9+3)

[Lukie]

... if you think my point is that the people saying that the answer is 288 are wrong, than you clearly don't know anything.

I answered that it was 288.

... if you think I believe they all came to the same conclusion by coincidence than I am left to only believe that I am not talking to an actual human being.

I wish I wouldn't read any further through your post and I now feel like I owe spoon something because he's right about how awesome it is that argument spreads on the internet because of this question.

If you are saying that it is mathematically ambiguous, given that there is basically always 1 way to interpret basic mathematical equations, then by default 288 is not correct, or less correct, or however else you want to put it that there can be varying degrees of correctness in basic algebra.

[a500lbgorilla]

If you are saying that it is mathematically ambiguous, given that there is basically always 1 way to interpret basic mathematical equations, then by default 288 is not correct, or less correct, or however else you want to put it that there can be varying degrees of correctness in basic algebra.

There is no basically always 1 way to interpret basic mathematical equations as evidenced by the following basic mathematical equation:

48÷2(9+3)

[Lukie]

There is no basically always 1 way to interpret basic mathematical equations as evidenced by the following basic mathematical equation:

48÷2(9+3)

Ok then, logic problem:

Situation A: we follow the order of operations strictly, meaning terms inside brackets, then orders, then division and multiplication left to right, and subtraction and addition left to right. We do not give special preference of varying degrees to mutliplication via juxtaposition against brackets.

Situation B: we (by we, I mean generally a large following of people) give arbitrary special emphasis of varying degrees to such multiplication via juxtaposition, such that seemingly simple problems can be interpreted in multiple ways, and nobody can seemingly agree on anything.

Which makes more sense?

Quoting myself from an earlier post which should even more clearly demonstrate why option B is much murkier:

Example that I am coming up with right here:

3(2*2.5)^2

Do you do the 3* as in left to right (same as parenthesis), before the exponent, after the exponent but before other multiplication, or simply left to right?

[a500lbgorilla]

Ok then, logic problem:

Situation A: we follow the order of operations strictly, meaning terms inside brackets, then orders, then division and multiplication left to right, and subtraction and addition left to right. We do not give special preference of varying degrees to mutliplication via juxtaposition against brackets.

Situation B: we (by we, I mean generally a large following of people) give arbitrary special emphasis of varying degrees to such multiplication via juxtaposition, such that seemingly simple problems can be interpreted in multiple ways, and nobody can seemingly agree on anything.

Which makes more sense?

Quoting myself from an earlier post which should even more clearly demonstrate why option B is much murkier:

It should be situation A: Order of operations say multiplcation by juxtaposition will be treated as any other multiplication.

Situation B: Multiplcation by juxta takes precedence over multiplcation or division by other means.

Both make perfect sense.

[Lukie]

It should be situation A: Order of operations say multiplcation by juxtaposition will be treated as any other multiplication.

Situation B: Multiplcation by juxta takes precedence over multiplcation or division by other means.

Both make perfect sense.

Ok... this is good. I feel like we are getting somewhere here.

My initial interpretation for the '2' crowd was that because the factor was juxtapositioned against the bracket, that it would get the bracket level in order of operations.. which is why I posed the following question:

3(2*2.5)^2

Why multiplication against a bracket goes after exponents but violates the otherwise-in-effect left to right for multiplication and division doesn't make any sense to me and seems completely arbitrary. The real tipping point is that it adds confusion and ambiguity in mathematics where usually there is none.

So with that, I'm most likely exiting this thread for good, unless I see something I find particularly disagreeable.

[a500lbgorilla]

I love it when rilla reminds us how smart he is.

My blood delights.

Why multiplication against a bracket goes after exponents but violates the otherwise-in-effect left to right for multiplication and division doesn't make any sense to me and seems completely arbitrary. The real tipping point is that it adds confusion and ambiguity in mathematics where usually there is none.

My blood dances.

It is completely arbitrary and it doesn't make sense to me either. But that is beside the point. Because there exist mathematicians in this world who don't agree with the order of operations we have learned, and because there exists no authority to step in and say which of us is most correct, we are left to take the steps of including extra brackets or parens to make our mathematical statements clear.

By the way, under both sets of rules, I'm pretty sure it solves your problem the same way. 3(2*2.5)^2=3(5)^2=3(25)=75

But someone could just as easily define multiplication by juxtaposition as dominant over even exponents and be allowed to write 3(2*2.5)^2=3(5)^2=15^2=225.

That's the power of math. It's capable of describing great things and flexible enough to be delivered in many ways.