48÷2(9+3) =

That really changes it. I think you forgot a digit.

 

That's what was bugging me. Mikewithaprius got it.
4÷2(1+1)=1
4÷2*(1+1)=4

Without the "*", The "2(1+1)" is a single expression.

 

Speaking of hockey....(Fair to assume you're a Canucks fan?)...if you count the posts, it was a tie.

 

It's cases exactly like this that prove our [ame="http://en.wikipedia.org/wiki/Infix_notation"]infix notation [/ame]is lousy. We should use [ame="http://en.wikipedia.org/wiki/Polish_notation"]prefix [/ame]or [ame="http://en.wikipedia.org/wiki/Reverse_Polish_notation"]postfix[/ame] instead.

Using prefix, if we said 48÷2(9+3) = 288, that would appropriately be represented as * ÷ 48 2 + 9 3. This directly tells you to divide 48 by 2, add 9 and 3, and multiply the two results.

On the other hand, if we said 48÷2(9+3) = 2, that would be appropriately represented as ÷ 48 * 2 + 9 3. This tells you to add 9 and 3, multiply that by 2, then divide 48 by the answer.

I won't get into postfix, since it makes things just as clear, it's only backwards from prefix. This removes any possible ambiguity or misunderstanding from the situation.

I still remember when i first found out about prefix and postfix back in my high school computer science class... Completely enthralled by the idea, and it was a lot of fun writing a program to convert between the three while performing the calculation.

PS. I learned it as PEMDAS, not BEDMAS...

 

No, it's not. Adjacent terms have an implied multiplication symbol. They are identical.

4÷2(1+1)≡4÷2*(1+1)

Tom

 

48/2(9+3)=
48/2(12)=
48/24=
2

 

48/2(12)=
24(12)=
288

You took the operators out of sequence. Infix notation is evaluated left to right for operators of the same precedence. The parentheses do not mean to first multiply 2*12. For that to be true they would have to be inside the parentheses, as in the following:

48/(2*12)

Tom

 

Well my high school son verified you are correct. Answer is 288. This type problem is used as a tool by their teachers.

 

and yet, we're losing in the poll. so much for improved math and science education in the u.s..

 

Using the logic that parentheses never imply multiplication first, I would solve the following question in the following way:

Solve 6÷2x when x = 2.
6÷2(2)
3(2)
6

In this case it's quite clear that's incorrect, though this is the procedure used to get 288 in the main example. Parentheses, besides coming first in PEMDAS, have a stronger case for multiplication than left to right. It is part of the simplification process.

6÷2x
6÷2(2)
6÷4
3/2 or 1.5

The method directly above is the way to solve that problem, and with that same logic, you get 2 for original problem.

 

The problem may be just how it written. I read 48 over 2(9+3)= Others read 48/2 x (9+3)= Sending this to school with the boy to see what the "Teachers" say for a laugh.

 

No, your first approach is correct. 6/2*2 is indeed 6. It should be very obvious by inspection that if you multiply and divide by the same number you get the original number. This particular case is commutative, so it doesn't matter what order you do the arithmetic:

6*2/2 = 6

6/2*2 = 6

2/2*6 = 6

You picked a poor example. You need to throw in some addition or subtraction to make a good example, but that is beside the point. Infix notation clearly doesn't work the way you claim.

Tom

 

i think the key point here is that infix notation sucks. Obviously people interpret it different ways depending on how they were taught (PEMDAS, BEDMAS, always go left to right when dealing with operands of equal importance, whatever), which leaves us in a situation where more than half the people in the poll don't pick the generally accepted (by the mathematics community) correct answer.

But that's America for you... why teach a method (like prefix or post fix notation) that is clear, concise, and impossible to misinterpret like this when we have a method that isn't clear, requires additional information (parenthesis) to ensure correct order of operations, and generally just causes problems?

 

Why would you say that? Parentheses can easily force multiplication to come first. Here is a simple example:

22+(4*7)

Of course the parentheses are not really needed, since multiplication comes before addition.

A better example would be this one:

4^(2*3)

In this case you would normally raise 4 to the power of 2 and then multiply by 3, but the parentheses force the multiplication to come first, so you get 4 raised to the power of 6.

This thread is really silly. What happened to basic math skills?

Tom

 

Probably the same thing that happened to basic writing skills, and basic reading skills, and critical thinking.

If sense were common, everybody would have some.

 

Hey, nobody told me there were going to be math problems on this site!

The way I was explained to me, while attending Moore Science High,
288.
Just ask Peorgie Tirebiter, he's a spy and a girl delighter.

 

You can't. He cut the soles off his shoes, climbed a tree, and learned to play the flute.

 

Why not consider the general case?

a÷b(c+d) is (a÷b)*(c+d)

not a÷(bc+bd)

Similarly,
a÷b*c is (a÷b)*c not a÷(b*c)

 

damn, y'all suck at math 288