48÷2(9+3) = ?

[Reelizmpro]

Originally Posted By: 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


Be careful...
48 / 2(12) NOT 2*12. You don't see a multiplication symbol in the problem do you? Distribute the 2 into 12 by multiplication. This takes precedence over left to right which is elementary and shouldn't be used in algebraic expressions unless they are in simple form. Parentheses remain until the 2 is multiplied with 12. This detail is often overlooked but it changes the order of operations. Only then do you get 24 as a denominator. If you do it on paper...cleanly it'll make more sense.

 

[Shannow]

I (vaguely) remember a math teacher telling me that a number next to a parentheses "married" it to the parentheses for all intents and (mathematical) .purposes

I'm sure that she would poke me in the gut with a red pen, call me Mergatroid (ye olde English sp) and give me the correct(ed) answer

 

[Al]

Originally Posted By: Reelizmpro
Look closely...

Let me summarize your argument: 2* (3+9) is not equal 2(3+9)

24 does not equal 24

Follow up..What would the answer be if the question were written:
48/2*(9+3)

 

[Al]

Originally Posted By: 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.


Thank you for the info.

 

[Scienceman]

Guys, come on. 48 Divided by 2 (9+3)

(9+3) is done first. The answer is 12
48 divided by 2 is 24
Multiply 24*12
=288

 

[kender]

Originally Posted By: Al
Originally Posted By: Reelizmpro
Look closely...

Let me summarize your argument: 2* (3+9) is not equal 2(3+9)

24 does not equal 24

Follow up..What would the answer be if the question were written:
48/2*(9+3)


You're using 2 different equations above. Obviously, they both equal 24. When you add to the equation the order of operations may change.
48/2*(9+3)=288
48/2(9+3)=2

2* is not the same as 2(

 

[Vikas]

Once again before there were computers and calculators and precedence rules for languages, the world used 1/2Pi to really mean 1/(2Pi). When said it aloud, it was said as "One over two pie". There are lots and lots of expressions and formulas in engineering where such nomenclature is used involving constants such as Pi, Omega, Eee etc. Only after calculators which started taking "algebraic" input, this confusion came by.

Fifty years ago, C language was yet to be invented. Written expression usually did not suffer because they were written in two dimension and you wrote big horizontal bar rather than the little slash.

HOWEVER, spoken expression such as "One over Two Pie" were never mistaken to be "0.5Pie".

I am amazed at how many forums this has gone to now. Many geek forums (e.g. ubuntu) and jock forums are buzzing with this topic. Whoever started this better cash in it by getting on to one of the late night show and hiring a ghost writer quickly to do a screen play. A new blockbuster is in making

- Vikas

 

[Vikas]

Now to answer my circumference problem:-

2 Pi R = 1

therefor R = 1 / 2 PI

Since I don't know what I am doing, I just blindly input this in my calculator

Since it is smarter than me, it knows what I really meant by that expression and it gives me the CORRECT answer violating all of the rules which you thought were cast in stone.

Is your calculator as smart as mine?

- Vikas

 

[Hokiefyd]

Originally Posted By: Al
2* (3+9) is not equal 2(3+9)


That is correct. 2*(3+9) <> 2(3+9)

Edit: the result of this expression, by itself, will equal 24 both ways. But the way you evaluate it, in the context of a larger expression will differ. In the first version, the 2 is not "married" to the 3+9 in the brackets, and PEMDAS would go, by convention, left to right. In the second version, as others have stated, the 2 is married to the brackets, and you must distribute that 2 when evaluating the brackets.

Originally Posted By: Al
24 does not equal 24


No, 24 = 24.

Originally Posted By: Al
Follow up..What would the answer be if the question were written:
48/2*(9+3)


If the expression were written as 48/2*(9+3), the answer is 288.

 

[Steve S]

Originally Posted By: 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?
I draw a 30 ft circle and start adding the panels.

 

[Al]

Originally Posted By: Vikas
Now to answer my circumference problem:-

2 Pi R = 1

therefor R = 1 / 2 PI

Since I don't know what I am doing, I just blindly input this in my calculator

 

[Vikas]

My calculator beats your calculator

 

[KrisZ]

I want to conduct a little poll.

So let's see what is your answer and how were you thught math (only written form vs using the calculator)?


My answer is 2.

I was forbidden to use the calulator in math and physics classes all the way through high school, you got an automatic 0 if you were caught using calculator.

 

[Vikas]

When I was in school, we never had these type of expressions entered in a single line. The divisor line was always explicit.

 

[d00df00d]

Originally Posted By: Vikas
When I was in school, we never had these type of expressions entered in a single line. The divisor line was always explicit.

Ditto.

 

[Warstud]

IIRC

48÷2(9+3) =
24 brackets mean x(12)=
or 24x12=288

 

[mechanicx]

Originally Posted By: 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.


I completely understand your argument. But again, I'm saying I don't necessarily believe the order of operation states the 2 most be distributed first. Maybe they do maybe they don't but I'd be just taking your word for it. You say the only way to get rid of the parenthesis is by multiplying the 2. But that's not really true since you can just multiply the product of 48/2 by the product in parenthesis and get an answer. Ie, 48/2(12)=24(12)=288. I think 2(12) does equal 2x(12) equals 2x12. I could be wrong but it's a matter of whether or not the order of operation follows the order you are proposing. No one has presented a definitive source other than stating their personal knowledge or belief. So far, we all agree the rules state what's in parenthesis must be factored first, but the rules of distributing the number in front of the parenthsis aren't so certain. Actually you violate that rule in your second example. You seem to be saying the distributive property takes precedence but my understanding of the distributive rule is it just explains how multiplication works and not necessarily the order since the order doesn't really change the product,ie, 2(9+3)=2(12)=18+6=24.

 

[Warstud]

Originally Posted By: Warstud
IIRC

48÷2(9+3) =
24 brackets mean x(12)=
or 24x12=288


Wrong^^^^

Correct:
48÷2(9+3) =

48÷2(12)=

48÷2x12=

48÷24=

=2

 

[mechanicx]

Originally Posted By: Warstud

IIRC

48÷2(9+3) =
24 brackets mean x(12)=
or 24x12=288


Wrong^^^^

Correct:
48÷2(9+3) =

48÷2(12)=

48÷2x12=
I'm with you so far.

48÷24=

=2

But this violates the rule to divide and multiply from left to right.

 

[Warstud]

Remember: PEDMAS

P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)