48÷2(9+3) = ???

[frankenbeemer]

I'm having a similar argument with my friend. He insists .99999... (.999 repeating) is equal to 1. When it is in fact, not.

Did he get mad and turn your car upside down?

[frankenbeemer]

I'm having a similar argument with my friend. He insists .99999... (.999 repeating) is equal to 1. When it is in fact, not.

Perhaps not in arithmetic, but in calculus it is.

[Danny]

I'm having a similar argument with my friend. He insists .99999... (.999 repeating) is equal to 1. When it is in fact, not.

[frankenbeemer]

I'm trying to prove it's incorrect to just take the 8 from 8(2+3), just as it's incorrect to just take the 2 from 2(9+3).

I told you it wouldn't work. Your pedantic assertions are becoming boring. Conki is right. You are insisting on a convention that is not universally accepted.

The evidence of this fact is in several places in the thread, including this very page.


:yawn:

[reelizmpro]

No.
1/(5(1+2)/8(2+3)) = 8/(5(1+2)(2+3)) = 8/((5)(3)(5)) = 8/75 = 0.10667

What you proposed, (8(2+3)/5(1+2)), eqauling 24, is wrong.

You are incorrect. (5(1+2)/8(2+3)) is a fraction in the denominator. To write in proper form, you multiply the entire thing by 1 or (8(2+3)/8(2+3))...cancel out and get (8(2+3)/5(1+2)) which is the reciprocal.

What you did is multiply top/bottom by 8 only...but that still leaves 5(1+2) being divided by (2+3). It magically disappears in your work and somehow becomes multiplied together? What's multiplied on the bottom must also be multiplied on top, just like the 8 which is why you multiply top and bottom by 8(2+3). The 8(2+3) on bottom cancels but remains in the numerator. In the end, when you multiply both fractions together you get 1. This is the essence of the reciprocal property.

Plug it in here...

http://www.algebra.com/algebra/homework/Inverses/FIND-reciprocal-of-a-FRACTION.solver

It's proven...

Now what's the reciprocal of 2(9+3)? 1/(2(9+3)) or 1/24 * 48 = 2.

I'm trying to prove it's incorrect to just take the 8 from 8(2+3), just as it's incorrect to just take the 2 from 2(9+3).

[alpinweiB]

i'm glad we all agree it's 288

[frankenbeemer]

You forgot to quote this part:

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)

[BrewCity11]

I go back to my initial comment that 48 / 2(9+3) is not the same as 48 /2 * (9+3)

Forty-eight divided by two OPEN PARENS the sum of nine and three CLOSE PARENS.

Corrected.

Here is pretty much the same thing, some quotes taken from it, the first being the most important.

"This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing."

"because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division"

"That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication"

The last example at the bottom: http://www.purplemath.com/modules/orderops2.htm

[Conki]

Well then, write the OP's math probelm as it would be read out loud then.

Forty-eight divided by..................................

Forty-eight divided by two times the sum of nine and three.

[BrewCity11]

A written out mathematical expression should not be misinterpreted. It doesn't matter what sign leads you to think what, you are wrong and you fail at a single math problem.

Well then, write the OP's math probelm as it would be read out loud then.

Forty-eight divided by..................................

[Conki]

if you write it like this 2 makes more sense. As a fraction.

48
______

2(9+3)

But that's not how it's written. If you want to write that ^ fraction in a one line configuration for programming languages or for calculators, it has to be written like

48/(2(9+3)),

which is not what we have in the title of this thread.

[5Toes]

if you write it like this 2 makes more sense. As a fraction.

48
______

2(9+3)

[Conki]

Right...which is (8(2+3)/5(1+2)) after you multiply top and bottom by 8(2+3). Wouldn't you do the same with 2(9+3)? and it's reciprocal is 1/(2(9+3)). So...

48 / 2(9+3) = 48 * 1/(2(9+3)) which equals 2.

Although I'm making arguments for the answer 2, with the way the problem is presented I can't say for sure that 288 is wrong either. As mentioned before, it depends on what you believe takes priority and whether or not you solve to get rid of parentheses or just simplify what's inside. My friend says that we are trying to apply algebra rules to a 3rd grade elementary problem.

No.
1/(5(1+2)/8(2+3)) = 8/(5(1+2)(2+3)) = 8/((5)(3)(5)) = 8/75 = 0.10667

What you proposed, (8(2+3)/5(1+2)), eqauling 24, is wrong.

I'm a Math tutor. I make mistakes occasionally, but these are pretty simple calculations:)

My friend says that we are trying to apply algebra rules to a 3rd grade elementary problem.

I knew about algebra rules in 3rd grade. This is math. A linear equation can only have one answer, there shouldn't be a debate about this.

In a nutshell, the question is easily misinterpreted. That division sign the OP used in the problem leads me to think of it not as a fraction, thus he answer=2.

A written out mathematical expression should not be misinterpreted. It doesn't matter what sign leads you to think what, you are wrong and you fail at a single math problem.

[reelizmpro]

The reciprocal of 5(1+2)/8(2+3) is 1/(5(1+2)/8(2+3))

Right...which is (8(2+3)/5(1+2)) after you multiply top and bottom by 8(2+3). Wouldn't you do the same with 2(9+3)? and it's reciprocal is 1/(2(9+3)). So...

48 / 2(9+3) = 48 * 1/(2(9+3)) which equals 2.

Although I'm making arguments for the answer 2, with the way the problem is presented I can't say for sure that 288 is wrong either. As mentioned before, it depends on what you believe takes priority and whether or not you solve to get rid of parentheses or just simplify what's inside. My friend says that we are trying to apply algebra rules to a 3rd grade elementary problem.

[BrewCity11]

basically what it comes down to is that nobody is going to write out the equation that way. if its written on a piece of paper it will be written one of the two ways we are all seeing it. and that will clarify any confusion as to how the problem should be solved.

This is the only answer in here that is undeniable.

Here is how I see it, hear it.

Written the way the OP posted it, with the division sign, read out loud, is 48 divided by..........let's say X.

Now since the next number (2) is touching a parenthesis, that whole expression 2(9+3) is X, and you must first apply the distributive property to simplify it. Then you take the answer (24) and put inplace of X or 48 divided by 24.

The other way it could be interpreted, if it had been written correctly or even asked/spoken correctly, is:
48 halves times the sum of 9 plus 3. This obviously being 288.

The latter, is saying the "48 divided by 2" or 48/2, is actually a fraction, or better yet, the multiplier for whatever is in the parenthesis.

In a nutshell, the question is easily misinterpreted. That division sign the OP used in the problem leads me to think of it not as a fraction, thus the answer=2.
If had been read to me as 48 halves times...... or if it was written as a top/bottom fraction next to parenthesis, then the answer would be 288.