Longhornmaniac
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48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:15 pm

Here's a (simple) math problem for you guys. This should spur some heated discussion, if the responses in here are like other places I've seen it.

Cheers,
Cameron
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Cadet985
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:18 pm

The answer is 288.

Marc
 
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:18 pm

288, is it not?

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aa61hvy
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:19 pm

I came up with .5

2(9+3)/48

(18+6)/48
24/48
=
.5

Go easy on me if I screwed this up. I haven't taken a math course in 8 years.  

Edit: or is it 2?
same equation but 48/24 instead.....

[Edited 2011-04-13 12:20:55]
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canoecarrier
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:20 pm

You do division before multiplication right? I'm going to say 288

Basically:

48/2 * (12)
24 * 12
288

[Edited 2011-04-13 12:24:03]
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Cadet985
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:21 pm

You do the work in the parenthesis first.

9+3=12
48/2=24
24*12=288

Marc
 
AR385
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:23 pm

It is 288

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aa61hvy
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:25 pm

Quoting Cadet985 (Reply 5):
You do the work in the parenthesis first.

9+3=12
48/2=24
24*12=288

Ah makes sense to me now.

I was always better in sciences anyhow.  
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Cadet985
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:27 pm

Quoting aa61hvy (Reply 8):

Just be glad there weren't variables in this problem...Lord knows I suck at algebra.

Marc
 
Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:28 pm

[Devil's Advocate]

Could you not interpret it as:

48 ÷ 2(9+3)

=

48 ÷ 2(12)

=

48 ÷ 24 =

2?

[/Devil's Advocate]

For the record, I also got 288, but there are a lot of people, including some very smart ones, who believe the answer is 2.

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Cameron
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casinterest
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:33 pm

Please Excuse My Dear Aunt Sally.

Parenthesis, Exponents, Multiply, Divide, add , then suptract.


The answer is 2.
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Ken777
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:34 pm

Quick look for me is 48 ÷ (2(9+3)) because of the spaces on both sides of the ÷ sign.

That leaves you with an answer of 2.

Unless, of course, you are trying to calculate a tax deduction before Tax Day, in which case it is acceptable to come up with an answer of 288.  
 
auntie
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:35 pm

This ..................

Quoting Longhornmaniac (Reply 10):
48 ÷ 2(9+3)

=

48 ÷ 2(12)

=

48 ÷ 24 =

2?

............is exactly how I would have done it!!!!

Although I too, haven't done maths in a loooong time!
 
Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:37 pm

Quoting Ken777 (Reply 12):
Quick look for me is 48 ÷ (2(9+3)) because of the spaces on both sides of the ÷ sign.

I wasn't implying anything by the spaces, just spacing it out to make it look prettier.   

Quoting Ken777 (Reply 12):
Unless, of course, you are trying to calculate a tax deduction before Tax Day, in which case it is acceptable to come up with an answer of 288.

  

Now we're starting to get some competing answers! Hehe.

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Cameron
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Moose135
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:39 pm

I came up with 2 as well.
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atrude777
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:41 pm

I got 288.

You always go from Left to Right in order of what comes up first.


Quoting canoecarrier (Reply 4):
You do division before multiplication right? I'm going to say 288

Only if it shows up first.

In this case it did so yes 288 is correct.

A lot of people used that PEMDAS formula which is right...but it ignored the fact you still must work from left to right. Since divide came up before multiply in this problem, the PEMDAS formula does not apply.



Alex

[Edited 2011-04-13 12:43:05]

[Edited 2011-04-13 12:43:29]
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DocLightning
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:46 pm

48/2(9+3) is expressed as:


48 48
------ = ----- = 2
2(9+3) 24

Order of operations. Learned it in 6th grade.

First do what's in parentheses (following order of ops within the parenthesis if applicable).

48
---
2x12

Then do exponents. (N/A)
Then multiply.

48
----
25

Then divide.

=2

Then add. Then subtract. (N/A)

Quoting casinterest (Reply 11):
Please Excuse My Dear Aunt Sally.

Why, did she fart?   
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einsteinboricua
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:54 pm

The answer is 288. Order of operation: parenthesis, exponents, and from left to right multiplication and division, and then from left to right again addition and subtraction.

For the answer to be 2, the equation would have to read: 48 ÷ (2*(9+3)), so that in better terms is 48/(2*(9+3)).

If in doubt, Excel can always help us. Excel says it's 288.

Quoting aa61hvy (Reply 8):
I was always better in sciences anyhow.

Well...unless you're studying basic sciences where it's only theory with no equations, you SHOULD be better in math.

Quoting atrude777 (Reply 16):
Only if it shows up first.

Actually you go from left to right regardless of whether a division or a multiplication appeared first. So if you had, for instance, 1/3*3, it would give the same answer as 1*3/3. One will give you a decimal which is then multiplied by an integer and the other gives you an integer in all steps.

As long as parenthesis and exponents are all done, you sweep from left to right doing both mult. and div. in the order they appear.
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:56 pm

Quoting aa61hvy (Reply 3):
Quoting Longhornmaniac (Reply 10):

48 ÷ 2(9+3)
=
48 ÷ 2(12)
=
48 ÷ 24 =
2?
Quoting casinterest (Reply 11):
Quoting Ken777 (Reply 12):
Quoting auntie (Reply 13):

That's what I got as well.

Do the stuff in parentheses first: 9+3 = 12
2(9+3) = 24
48 ÷ 24 = 2.

I looked at it as a fraction, with 48 as the numerator and 2(9+3) as the denominator.

Quoting Longhornmaniac (Reply 14):
I wasn't implying anything by the spaces, just spacing it out to make it look prettier.

Even without the spaces, I would have separated the two parts anyway. Unless the 48 ÷ 2 portion was in parentheses on its own, I would consider the 2 as a multiplier of the (9+3) before dividing.

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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:57 pm

Quoting Longhornmaniac (Thread starter):
48 ÷ 2(9+3)=?  

48 ÷ 2(9+3)=?  
48 ÷ 2 * (9+3)=?  
48 ÷ 2 * 12=?  

is either 288 or 2, depending on your view whether you use the ltr rule or the multiplication over dividing.

Oh and for this reason equations with a ÷ in it should be banned. In science papers i've read the last few years I've not often seen the ÷ sign.

How difficult can it be?   

[Edited 2011-04-13 13:02:39]
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 7:59 pm

Quoting casinterest (Reply 11):
Please Excuse My Dear Aunt Sally.

Parenthesis, Exponents, Multiply, Divide, add , then suptract.

This is true but I also remember a catch to this as well - if the functions in the equations are opposites (multiple & divide or add & subtract) then you work from left to right. I honestly forgot how it's carried out if there are more functions though.
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UAL747
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:00 pm

I got two as well. Always do stuff in parentheses first, then multiply, divide.

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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:02 pm

I'm honestly shocked at the amount of people who are getting this wrong. 288?

Please Excuse My Dear Aunt Sally

48 / 2(9+3)

48 / 2(12)

48 / 24

= 2

Edit... I guess I was wrong Big grin

[Edited 2011-04-13 13:35:40]
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Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:02 pm

Some common misconceptions:

Multiplication does not receive a higher priority than division. They are equal priority, and are read from left to right.

Same goes for addition and subtraction.

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Cameron
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GAIsweetGAI
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:05 pm

It's funny, I just "stumbled" across the following picture yesterday - it's always better with a picture:



Or am I just spoiling the fun?   
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UAL747
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:05 pm

Quoting Longhornmaniac (Reply 24):
Multiplication does not receive a higher priority than division. They are equal priority, and are read from left to right.

Same goes for addition and subtraction.

Correct, however division and multiplication are > addition and subtraction
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aa61hvy
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:09 pm

Quoting JetsGo (Reply 23):
I'm honestly shocked at the amount of people who are getting this wrong. 288?

Please Excuse My Dear Aunt Sally

48 / 2(9+3)

48 / 2(12)

48 / 24

= 2

Alright, my second guess was correct!  
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unattendedbag
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:09 pm

Quoting Longhornmaniac (Thread starter):
48 ÷ 2(9+3)=?

48 ÷ 2(9+3)=?

first step
(9+3) = 12

second step
2(12) = 24

third step
48 / 24 = 2

the answer is 2

Quoting einsteinboricua (Reply 18):
For the answer to be 2, the equation would have to read: 48 ÷ (2*(9+3)),

the 2(9+3) implies 2 * (9+3) ie. 2 * 12 . any number outside and attached to the () is multiplied by the sum inside the (). The /*-+ inside the () is always completed first. Then you move away from the ().
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Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:10 pm

Quoting UAL747 (Reply 26):

Correct.

Quoting GAIsweetGAI (Reply 25):

Haha. You're the second person that's posted that when I raised this question.

Carry on!

Cheers,
Cameron
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ArmitageShanks
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:11 pm

This same thread has about 200 views on another forum I frequent.

Any NN fans here?
 
dragon6172
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:15 pm

I see the "Friday Stupid Thread" has arrived early this week.
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dragon6172
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:17 pm

By the way... when in doubt put it into the ol' TI-89 exactly as it is written in the thread starter... answer is 288.
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Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:25 pm

Look at the first reply on this thread:

http://www.shaggybevo.com/board/show...hread.php/87280-48%C3%B72%289-3%29

You'll see not all calculators give the same result.

Cheers,
Cameron

Edit: there's plenty of offensive language on that site!

[Edited 2011-04-13 13:26:19]
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DeltaMD90
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:34 pm

It is 288. I made the same mistake and got 2.

Please Excuse My Dear Aunt Sally, so:

48 / 2 (9+3) IS REALLY 48 / 2 * (9+3)... so you do the parenthesis first so its 48 / 2 * (12) aka 48 / 2 * 12 which, going from left to right, is 48 / 2 = 24 times 12 equals 288.

Edit: Also, if you want to distribute, you don't only distribute the 2 into the (3+9), you also distribute the 48. In other words, you distribute 48/2 into (3+9) equaling (72+216) = 288

[Edited 2011-04-13 13:36:59]
 
Derico
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:37 pm

The key is to always remember that when a parenthesis has operations inside, you do them first with any multiplying or dividing FIRST from left to right, once you are out of those, addition and subtraction from left to right.

Once there is only ONE number inside the parenthesis, it becomes just another simbol for multiplication.

Step by step:


1. Parenthesis first: You first do any multiplication / division left to right, and then any addition / substraction left to right INSIDE parenthesis BEFORE ANYHING OUTSIDE. ALWAYS!!!!

48 / 2(9 + 3) ... lets imagine the 9 in the parenthesis was expressed as 3*3, thus

48 / 2( 3*3 + 3).

Parenthesis first = (3*3 + 3)
multiplication or division left to right inside parenthesis first = 3 times 3? = 9 .... (9 + 3)
addition or subraction inside parenthesis first = 9 plus 3? = (12)

Now, there are no more OPERATIONS inside the parenthesis.

Now you have 48 / 2(12)

The only trick here is that the parenthesis now becomes equal to a multiplication problem and NOT a symbol to do it first!! Remember that:

2 x 12 is the same as 2*12 is the same as 2(12)

So you do not do 2(12) first just because it is a parenthesis. There are no more operations inside, thus the parenthesis is now just another way of showing multiplication relationship. Since that is the case, you simply now multiply or divide left to right:

48 / 2 = 24 ... 24 (12) or 24*12 = 288
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UAL747
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:39 pm

For people getting 288, you are forgetting that ANY number touching a parenthesis by multiplication or division, whether it's on the inside or out should be part of the first step of any operation. The calculator pictures show a calculator that needs to be taken to the store and returned.

1. Any operation involving a Parenthesis (a. inside, b. outside)
2. Multiply/Divide
3. Add/Subtract

UAL
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Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:42 pm

Quoting UAL747 (Reply 36):

Tell that to a linear algebra professor at my school who says 288 is the right answer.   

Can you provide a source that says any number touching a parenthesis is included in part of the "Parenthesis" category in the order of operations?

Cheers,
Cameron
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Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:43 pm

Quoting UAL747 (Reply 36):
The calculator pictures show a calculator that needs to be taken to the store and returned

And just to make sure you're aware, those are 4 different calculators.

Cheers,
Cameron
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unattendedbag
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:44 pm

Quoting Longhornmaniac (Reply 33):
You'll see not all calculators give the same result.

If you choose to use a calculator to solve the math problem, your calculator must be in scientific notation. Only a calculator in scientific notation will follow PEMDAS and the order of operations. A non-scientific calculator will yield an incorrect answer.


Read more: How to Solve a Math Problem Using PEMDAS | eHow.com http://www.ehow.com/how_4449191_solv...em-using-pemdas.html#ixzz1JRDlkKut
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Derico
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:49 pm

Quoting UAL747 (Reply 36):
For people getting 288, you are forgetting that ANY number touching a parenthesis by multiplication or division, whether it's on the inside or out should be part of the first step of any operation. The calculator pictures show a calculator that needs to be taken to the store and returned.

1. Any operation involving a Parenthesis (a. inside, b. outside)
2. Multiply/Divide
3. Add/Subtract

No, that is not so. You are confusing the distributive property which you assign as ''b. outside''

if the problem was 48 + 2(9 +3) THEN YES, you would do the following:

48 + 2(12)
48 + 24 = 72

Because again, parenthesis once it has only one number in it, is just another symbol to multiply. So in my example you do the parenthesis first because there is a PLUS after 48, and you do mutiplication or division left to right FIRST before the plus sign.

But it is 48 DIVIDIED by 2(12) or in other words 48 / 2 x 12. Since multiplication and division are equal, by convention it is done left to right.

[Edited 2011-04-13 13:51:10]
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canoecarrier
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:53 pm

Quoting dragon6172 (Reply 31):
I see the "Friday Stupid Thread" has arrived early this week

I think that's a little harsh. Out of curiosity I googled the equation and found this thread on a physics forum where it's getting just as much attention and discussion as we have here.

http://www.physicsforums.com/showthread.php?t=488334

I also haven't seen the division symbol used like it is in this equation in ages.
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UAL747
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:58 pm

Also, the division sign is simply the line in a written fraction. 1/2 is 1 divided by 2. Thus, wouldn't this just be read like a fraction, with 2(9+3) on the bottom? After all, 48/2(9+3) is the same thing as written above.

UAL
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dragon6172
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 8:59 pm

Quoting dragon6172 (Reply 31):
I see the "Friday Stupid Thread" has arrived early this week.
Quoting canoecarrier (Reply 41):
I think that's a little harsh.

Maybe so... I actually have never checked out the Friday Stupid Thread so I do not really know what they are all about. Maybe I should have said:
"I wonder if the number of posts on this thread will match that of the famous aircraft taking off from a treadmill thread"
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JBirdAV8r
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:05 pm

       Epic thread!!

For the record, I'm not a math-oriented person and I got 288. I'm reading explanations with interest...
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Longhornmaniac
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:06 pm

Quoting UAL747 (Reply 42):

Indeed, but then, is it read as:

48/(2(9+3))

OR

48/2(9+3)

The top answer gives 2, the bottom answer gives 288.

Cheers,
Cameron
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canoecarrier
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:09 pm

Quoting Longhornmaniac (Reply 45):
48/(2(9+3))

And, the equation he posted is not written like that.

Quoting Longhornmaniac (Reply 45):
48/2(9+3)

I'm in the camp that this is how it should correctly be calculated. 48/2(12) to (24)(12) = 288
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BAKJet
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:09 pm

Quoting JetsGo (Reply 23):
m honestly shocked at the amount of people who are getting this wrong. 288?

Please Excuse My Dear Aunt Sally

48 / 2(9+3)

48 / 2(12)

48 / 24

= 2

Me Too! And you're one of them! In order of operations, multiplication and division are "equal" therefore you go from left to right.

So 48/2 *(9+3)
48/2 *(12)
24 *(12)
answer is 288. definitely.

Put it into a calculator or Google, you'll get 288.
http://lmgtfy.com/?q=48%2F2(9%2B3)

[Edited 2011-04-13 14:12:43]
 
Derico
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:12 pm

This is the same confusion people get with the following kinds of problems:

7 + -( -4 x 3)

This equals 19 and not -5

The minus outside the parenthesis kills even differencial equation people, that's what a professor I had says, so it's no wonder the ''physicists'' are flummoxed by these problems. This is my way to solve these, though most people will get a headache:

The easiest way for me is to make everything an addition problem, even if I add negatives, and place negatives in parenthesis to remember the minus is part of the number.

So 7 + - (-12)

We should know a negative times a positive is a negative thus:

7 + (-1) x ( -12)



7 + 12 = 19

Edit: I butchered the signs, now it's right. I just made up this problem, sorry...
[Edited 2011-04-13 14:35:27]

[Edited 2011-04-13 14:45:59]
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dragon6172
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:14 pm

Quoting Longhornmaniac (Reply 33):
You'll see not all calculators give the same result.

Interesting that using my TI 89 when I put:
48/2(9+3)

the answer is 288

When I put:
48/y(9+3)

the answer is 48/(y(12))

And finally, when I put:
48/y*(9+3)

the answer is 576/y
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Jetsgo
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RE: 48 ÷ 2(9+3)=?

Wed Apr 13, 2011 9:16 pm

Quoting BAKJet (Reply 47):
Me Too! And you're one of them!
Quoting JetsGo (Reply 23):
Edit... I guess I was wrong

[Edited 2011-04-13 13:35:40]

Hmmm... a little late there!   
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