48÷2(9+3) = ????

[winders]

Go out there at look at the math and physics forums. There is no consensus......other than the equation could have been written with more clarity.

Scott

[BGCarrera32]

The answer is 288.

Order of ops is PEMA. Division is multiplication by the reciprocal and subtraction is addition of a negative number. Div/multiplication or add/subtract does not take precedence over the other in the given in example, and when that is the case evaluate left to right.

Verburg is correct.

[DARISC]

Originally Posted by winders

You are the windbag spewing bullsh**.

Look here:

Depending on whether one interprets the expression as (48/2)(9+3) or as 48/(2(9+3)) one gets 288 or 2.

The equation in question is written as NEITHER of the above equations.

The equation in question is 48/2(9+3)=n and there is no "interpretation" to be dealt with; it is what it is, is not ambiguous and when solved, using the unambiguous rules of math, the answer will be 288.

The equation (48/2)(9+3)=n is the same equation with superfluous parentheses added (they do nothing/don't belong there). So yes, the answer is still 288.

The equation 48/(2(9+3))=n is a DIFFERENT equation with an additional parenth that is NOT superfluous (it does something/belongs there). So yes, the answer is 2.

What don't you understand?

[winders]

Originally Posted by DARISC

...there is no "interpretation" to be dealt with; it is what it is, is not ambiguous and when solved, using the unambiguous rules of math...

And that is why there is so much debate even amongst those in the mathematics community.

The American Mathematical Society (AMS) says this:

"...multiplication indicated by juxtaposition is carried out before division."

This is multiplication indicated by juxtaposition:

2(9+3)

This is not:

2 x (9+3)

Like I have been saying all along, the equation is ambiguous.

Your "unambiguous rules of math", PEMDAS and BEDMAS, are actually called conventions. They are not hard and fast rules with proofs to back them up.

That equation is kind of like this sentence:

“Most of the time travelers worry about their luggage.”

Did the writer mean to put a comma after the word "time"?

Scott

[DARISC]

Originally Posted by winders

Like I have been saying all along, the equation is ambiguous.

Even if I were a time traveler I would say:
No it's not, or:
No, it's not, or:
No it isn't, or:
No, it isn't, or:
No it is not, or:
No, it is not and, besides not being ambiguous and/or open to interpretation, math is not English, nor is math notation based on/subject to the rules of English.

Yes, 2(9+3), by virtue of the fact that the 2 is juxtaposed to the parenth, says, "Multiply the sum of 9 and 3 by the number 2": 2(9+3)=24.

No, 2x(9+3) is not "multiplication indicated by juxtaposition", it is multiplication dictated by by the letter 'x', i.e., there is no need to consider "indication by juxtaposition": 2x(9+3)=24

However, the equation*2x(9+3) contains 'x', which is superfluous/not needed; without 'x', multiplication is indicated by juxtaposition.

Neither equation is ambiguous. The second has an 'x' inserted into it it that an eighth grade algebra teacher would fault a student for inserting.

The answer to the above, same equation, written two different ways, is 24.

Math is a universal language. A mathematician may not be able to speak a word of English but will still be able to solve 48/2(9+3)=???? and the correct answer will always be: ????=288.

Do you understand now?

[svandamme]

Originally Posted by winders

"...multiplication indicated by juxtaposition is carried out before division."

This is multiplication indicated by juxtaposition:

2(9+3)

This is not:

2 x (9+3)

There is no division to be carried out before the multiplication in this bit

it's just multiplication and parenthesis
stop changing things to what they are not

2(9+3) = 2x(9+3) = 2x(12) = 2x12 = 24

2(9+3) and 2x(9+3) are EXACTLY the same !

[DARISC]

Originally Posted by svandamme

...2(9+3) = 2x(9+3) = 2x(12) = 2x12 = 24

2(9+3) and 2x(9+3) are EXACTLY the same !

Was expecting you to chime in.

Originally Posted by DARISC

...The answer to the above, same equation, written two different ways, is 24...

I'm beginning to wonder if this winders guy is island911 reincarnated.

[Geary]

Can't believe this is still being debated ..

The following rule has likely been explained a dozen times in the past 27 pages, but I'll take one more stab at it ..

48÷2(9+3) = 48÷[2(9+3)] = 2 .. the only possible answer to the original equation.

48÷2x(9+3) = [48÷2]x[(9+3)] = 288 .. but this isn't the original equation.

Any time a number sits directly alongside a parenthesis, this number alone multiplies the sum within the parenthesis before moving outward to any other operation. Every time. It is not a matter of interpretation.

So no .. 2(9+3) and 2x(9+3) are obviously NOT the same within the original equation.

[sammyg2]

That's it.
As of now you're all on double-secret probation.


Earlier this year my (14 year old) son took a test called "The California state university/University of California Mathematics diagnostic testing project".

I was kind of surprised he missed a question and asked why, he said:
"it was a dumb question and was poorly formulated.
I knew the answer they were looking for but it wasn't the best answer for the question so I answered it right knowing they'd mark it as wrong".

[Pazuzu]

You're all wrong.



It's not:
48÷2(9+3) = 48÷[2(9+3)] = 2


It's:
48÷2(9+3) = (4*8)÷[2*(9+3)] = (32)/(2*12)=(3*2)/[2*(1*2)]=(6)/(4)=1.5

If you're going to play the juxtaposition game you must play it through to the end, no matter how bloody it gets.

[Bill Verburg]

here is the simplest example, 3 operators(1,2,x) and 2 operations(division, multiplication) no distractions, no confusion
1/2x

so since there are only 2 operations and one has to be done first, which one has to be done first? Think hard now. and remember division is not associative

[sammyg2]

3 traveling salesmen were headed to a convention and since money was tight, they agreed to share a room.
The hotel clerk told them it was $30 so they each kicked in $10

Later the hotel manager was looking at the books and realized the clerk had charged $30 for a $25 room.
He took five $1 bills from the register and headed up to the room to give a refund.
On the way he started wondering how he was going to split $5 three ways.
He was no math genius so he decided to refund each one of the salesman $1 and put the remaining $2 in his pocket, which he did.

So each saleman paid $10 and got one back, or $9 each.

3 times $9 is $27, plus the $2 in the manager's pocket is $29, where the heck did the other dollar go?







I know but it's fun.

[Bill Verburg]

We can make it even simpler

again 3 operands, 2 operations. Which has to be done first?

1/2*3

[Pazuzu]

Originally Posted by sammyg2

3 traveling salesmen were headed to a convention and since money was tight, they agreed to share a room.
The hotel clerk told them it was $30 so they each kicked in $10
where the heck did the other dollar go?

Inflation. Since the last time that there were three traveling salesmen together, who decide to share a room, and that room costs $30, was 1946.


Kids these days wouldn't even know what a traveling salesman was, much less how one finds a hotel that can hold three men in separate beds for $30 a night...

[DARISC]

Originally Posted by Geary

...Any time a number sits directly alongside a parenthesis, this number alone multiplies the sum within the parenthesis before moving outward to any other operation. Every time. It is not a matter of interpretation.

So no .. 2(9+3) and 2x(9+3) are obviously NOT the same within the original equation.

Johnny walked up to the blackboard where his 8th grade algebra teacher had written the equation 48÷2(9+3) = n and wrote 288 after the = sign. Johnny then turned and began to walk back to his seat with a satisfied smile on his cherubic face (Johnny somewhat resembled a cherub).

Johnny's algebra teacher sprang to his feet (he always had a spring to his step) and hollered at the top of his lungs, "STOP RIGHT WHERE YOU ARE, YOU LITTLE PUNK ASS MATH WHIZ WANNABE AND MARCH BACK UP TO THAT BLACKBOARD AND SHOW YOUR WORK!!!

Little Johnny (he was small for his age) stopped dead in his tracks, spun on his heel, walked back to the blackboard and wrote:

48÷2(9+3) = 48÷2(12) = 48÷2x12 = 24x12 = n = 288

Little Johnny's algebra teacher glared at the little punk ass math wannabe standing at the blackboard, noting the sardonic smile on his face (Algebra 101 was right after lunch and little Johnny had eaten a big sardone sandwich), slumped back into his chair behind his desk and said, "Very good Johnny. That is correct, you may return to your seat now".

NOW do you understand? LOL

[DARISC]

Originally Posted by Bill Verburg

We can make it even simpler

again 3 operands, 2 operations. Which has to be done first?

1/2*3

Division.

1/2*3=.5*3=288...

Just kidding, the answer is 2 (when using an '*' instead of an 'x', you always add .5 or 1/2).

[DARISC]

Originally Posted by Bill Verburg

We can make it even simpler

again 3 operands, 2 operations. Which has to be done first?

1/2*3

Oh, uh, wait a minute...MDAS; so, you multiply first, right?

1/2*3=1/6=.16666! NOW I unnerstan!

[winders]

No one wanting to be clear would write "1/2x". What did they mean?

1/(2x)?

(1/2)x?

Math Forum: Ask Dr. Math FAQ: Typing Math

Scott

[Bill Verburg]

Originally Posted by DARISC

Division.

.....
Just kidding, the answer is 2 (when using an '*' instead of an 'x', you always add .5 or 1/2).

hmm, I guess the problem is harder than I thought, did you use your calculator?
there are several ways to do it, you started well
1/2 is the same as .5 and .5*3 is ?

another way is to rationalize everything
1/2*3
is the same as


now what do you get?

[winders]

Huh?

1 / 2 * 3 is the same as 1 / 2 x 3....both equal 1.5.

By convention, division and multiplication have equal precedence. By convention, you start at the left.

Scott