48÷2(9+3) = ?

[Al]

Originally Posted By: crinkles
I can't see how this can go wrong when using RPN.

Have you used a calculator with RPM? I have. When I switched to the present generation of calculators..I thought I died and went to heaven.

It really won't make any difference. You still need to decide if (9+3) is in the numerator or denominator.

 

[Quattro Pete]

Originally Posted By: kender

purplemath.com says....2
They say that a multiplication indicated by a number to the left of a "(" is "stronger" than a regular "x" . Therefore you would multiply 2(9+3) before you divide 48 by the result. GOOGLE is wrong.

That's the first time I've read that there are different strengths of multiplication and some take precedence over division.

Not saying it's wrong, but I wonder whether the professional mathematician community agrees with this view.

Maybe we can ask Watson?

 

[Vikas]

Nobody interprets "one over two ex" as "one over two and then multiplied by ex" EXCEPT a computer That is the difference between a human and a robot.

- Vikas

 

[Al]

Originally Posted By: Vikas
Nobody interprets "one over (two ex)" as "one over two and then multiplied by ex" EXCEPT a computer That is the difference between a human and a robot.

- Vikas

Fixed

 

[KrisZ]

Without reading any responses I got 2.

Other than for philosophical discussion you wouldn't write the equation the way OP did.


48
---- = no wiggle room
2(9+3)


48
------ x (9+3) = again no wiggle room
2

 

[motorguy222]

I got 2 also.If you look at the equation in algebraic terms,which it seems to be written in,the answer 2 seems to be the only answer that would be correct.

 

[Quattro Pete]

Originally Posted By: motorguy222
I got 2 also.If you look at the equation in algebraic terms,

What does that mean?

 

[Reelizmpro]

Originally Posted By: Drew99GT
Here is the correct answer. The original equation is written incorrectly. It's either one depending on how you interpret it. Using correct algebra expressions, it can be either one. I hope this doesn't interrupt the space time continuum...

The second image is incorrect. (9+3) should be DIVIDED into 48 as well. Simplify the first expression. It becomes 24 / (9+3). Think about it. It's not hard.

"The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3).

So this can be rewritten as:
48 / (2*9 + 2*3)

Which leaves us with

48 / 24 = 2

Answer = 2.

Lastly for those using Google or any other online calculator. These do not understand many theorems or properties so you must explicitly explain what you mean. There is a difference between 48 / 2 * (9+3) and 48 / 2(9+3). The first notation reads 48 / 2 * 1(9+3) while the second reads 48 / (2*9+2*3). Be very careful with your signs."

As a EE who has worked with many scientific calculators and programs like MATLAB, etc. The guy I quoted above is right. Have to be careful of signage and calculators are very picky on how you input it.

In summary, parentheses first. The problem is people think parentheses means multiply well that's not the whole story. 2 is a factor of what's inside the parentheses. It's to be distributed into the parentheses. Either way 2(12) or (18+6) the parentheses remain until distribution or addition occur leaving only 24 UNDER 48 which is 2.

The left to right rule is the most elementary and doesn't apply to this type of problem. Parentheses first gentleman.

 

[Al]

Originally Posted By: Reelizmpro
that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.

Show me that in a textbook.

You are saying 2* (3+4) does not equal 2(3+4) or (2+4)(5+3) does not equal (2+4)*(5+3)

And again you better write Texas Instruments and tell them they are wrong.

Not knocking you. I'd like proof. Until I get it I'll trust TI

 

[Reelizmpro]

Looking at the "288" example...the way they inputed the problem can also be written as 48(9+3) / 2 which is incorrect and a completely different problem than 48 / 2(9+3) and that's the way the calculator is interpreting the problem. IF it were (48/2) (9+3) where it was explicitly stated that (48/2) then it's 24(9+3) =288.

So Al, parentheses first. 48 / 2(12) then distribution due to parentheses still being there gives 48 / 24 = 2. Make sense?

Since 2 is a factor, you can simplify 48/2 and get 24 in the NUMERATOR but it's still divided by (9+3). To do it cleanly 48 / [2(9+3)] = 2 ; If you don't use double parentheses or brackets the calculator is assuming (48/2)(9+3) = 288.

 

[bigmike]

This thread is epic.

 

[Vikas]

Straight from the horse's mouth

==============================================================

Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators?

Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper.

This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the TI-Nspire™ Handheld in TI-84 Plus Mode. Implied and explicit multiplication is given the same priority.

 

[morris]

this is from my son, so of course it right. and iam sure it is the same as other posts. but he is my son, and thats special. LOL.

288 is the correct answer. The reason is the order of operations rule to go from left to right. Here are the steps:
1. we do what is in parentheses first (9+3) = 12
2. the remaining two operations are first divide then multiple, because these operations are at the same level in the order of operations tree we invoke the left to right rule, thus we evaluate the following left to right:
48 / 2 * 12
for the claculation we do:
48 / 2 = 24
then
24 *12 = 288
QED

For more info on order of operations see: https://secure.wikimedia.org/wikipedia/en/wiki/Order_of_operations
For more info on the left to right rule see: http://www.purplemath.com/modules/orderops.htm

 

[Vikas]

Let us see how many of you get this right.

If a circle has circumference of 1 meter, what is the radius of the circle? Please show all the steps.

To refresh your middle school math, "two-pie-are" is the circumference.

- Vikas

 

[Blaze]

Originally Posted By: Vikas
Let us see how many of you get this right.

If a circle has circumference of 1 meter, what is the radius of the circle? Please show all the steps.

To refresh your middle school math, "two-pie-are" is the circumference.

- Vikas
Funny.... I was just going outside to grab some 12 ft panels to build a round pen. I was wondering how many I need to build a round pen that was 30 ft in diameter?

 

[Quattro Pete]

Originally Posted By: Reelizmpro

"The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire statement and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it. You do NOT compute this expression from left to right until you use Algebra to simplify the statement 2(9+3).

Is this really taught in modern day math text books?

 

[cp3]

Originally Posted By: Vikas
Let us see how many of you get this right.

If a circle has circumference of 1 meter, what is the radius of the circle? Please show all the steps.

To refresh your middle school math, "two-pie-are" is the circumference.

- Vikas


I'll throw my hat in again....lol

0.15915494309189533576888376337251

 

[motorguy222]

I use the 'algebraic' term to mean that if you look at it strictly as an equation to be solved using algebra.

In algebra,that is,the way it was taught years ago,you would solve this problem as such:

48/2(9+3)=

1.You take the 48 and leave it alone for this first step.
2.You take the 2 and multiply it first by 9 which is 18.
3.You take the 2 and multiply it by 3 which is 6.
4.You now have 48/24 which equals,2.

This is why I said it was an 'algebraic' equation.Algebra teaches,or did,that when you have parentheses next to a number that you multiply said number by what is in the parentheses,such as 2(5+4)=,this would equal,18.

You would multiply 2X5 and add that to 2X4,this totals,18.

 

[mechanicx]

That is the crux of the debate whether or not you distribute or multiply what is in paranthesis by the 2 first. I haven't seen any rule provided from a legitimate source and don't remember ever being taught that a number in front of paranthesis takes precedence over PEMDAS. I think another way of looking at it is the 2 was factored out so that changes the order of operation to division first.

 

[Reelizmpro]

Look closely...

48/2(9+3)
48/2(12)
2 is actually DISTRIBUTED into parentheses as it's the only way to get rid of parentheses at this point. Which is not the same as 2x12. Technically, it's multiplication through distribution.
48/24
2

another way to do it...

48/2(9+3)
48/(18+6) 2 is Distributed into parentheses but they remain UNTIL the two terms have been added! This takes priority over the DIVIDE symbol.
48/24
2

yet another way to do it...
48/2(9+3)
24/(9+3) expression is simplified by the factor 2. Parentheses still remain!
24/12
2

You must resist the temptation to divide into 48 without first getting rid of the parentheses.

Mechanix, even with the 2 factored out, the parentheses still remain and must be simplified BEFORE dividing.