Solve 48÷2(9+3)

[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.