Maths Question

[Pyro Paul]

If you've taken basic math and only basic math the answer is 288.

If you've taken basic algebra or any more mathmatics beyond basic math then the answer is 2.

48 / 2(9+3)

n(x+y) is an simplified expression using coefficents.
unsimplified it is ((n*x)+(n*y))

so unsimplified the equation is written

48 / ((2*9)+(2*3))

48 / 24

2

n(x+y) is the basis of all more complex mathmatic, functions, and graphing seen through Algebra to statistics to complex theoritical math.

---

On the Other hand...
if you use only 'Basic math' (ie- What most all computer programs use)
the equation should be split up
48/2*(9+3)

24*(12)

288

Google calculator will give you this answer.

i will point out, Google calculator isn't the end all-be-all answer to everything.

example:
2^3^4

to google calculator will show the answer 24 septillion... (2.4 x 10^24)
however, using standard order of operations... you should get the answer 4096

 

[Pyro Paul]

There is no real answer because it's been written in a purposefully retarded way with no clarification.

This. The actual discussion here is being treated as two different expressions: (48/2)(9+3) and 48/(2(9+3)).

For the sake of argument, let's simplify (9+3) to (12) and set 2 equal to the variable a (a = 2). Now we have the expression 48/a(12). So how do you simplify it? As 4/a (= 48/(12a)), or as 576/a (= (48*12)/a)? Without explicit separation and grouping of the terms, the question just simply becomes stupidly ambiguous.

No, it can't be treated as 48/(2(9+3)) because that isn't the problem. You can't just add parenthesis and say is ambiguous. As it stands, it is extremely easy to solve so long as you understand the order of operations.
I honestly don't know how we can be debating what the answer is.

I understand order of operations, but it doesn't make the question suddenly less ambiguous. Expressions in math that follow the format of a(b+c) can be treated as (ab+ac), and this is where the hangup on this question lies.

Out of curiosity, how would evaluate 14/7(a) when a = 2? As 4 or 1?

14/7(2)
14/7*2
2*2
4
Multiplication and division have equal priority so its done from left to right. There is no operation within the parenthesis so it serves no real purpose.

14 / 7(2)

14 / (7*2+7*0)

14 / 14

remember. Coefficents.

7(a) is the same as 7(a+0).
7(a+0) is the simplified form of (7*a+7*0)

 

[Pyro Paul]

There is no real answer because it's been written in a purposefully retarded way with no clarification.

This. The actual discussion here is being treated as two different expressions: (48/2)(9+3) and 48/(2(9+3)).

For the sake of argument, let's simplify (9+3) to (12) and set 2 equal to the variable a (a = 2). Now we have the expression 48/a(12). So how do you simplify it? As 4/a (= 48/(12a)), or as 576/a (= (48*12)/a)? Without explicit separation and grouping of the terms, the question just simply becomes stupidly ambiguous.

it is better if you Imagine (9+3) = (x+y)

now lets solve for x.
288=48/2(x+y).

distribute 2.

288=48/(2x+2y)

remove the deminominator by multiplying both sides by (2x+2y)

288*(2x+2y) = 48

distribute 288.

576x + 576y = 48

subtract 576y

576x = 48 - 576y

divide by 576.

x = (48/576) - y

plug in known variables. x=9 y=3.

9 = .083 - 3
9 = -2.719

incorrect.

now lets go through the same process with 2.

2=48/2(x+y)
2=48/(2x+2y)
2(2x+2y)=48
4x+4y=48
4x=48-4y
x=12-y

known variables x=9, y=3

9=12-3
9=9

Correct.

 

[Tharwen]

Bloody hell. We've had the same maths problem posted here twice now in about a week.

The answer is 288. It has been for about 3000 years. It isn't subjective, it isn't hard. You learn this when you're 10.

 

[Cerdog]

To everyone using algebra to show that the answer is two, distribution does not take priority if you don't have any unknowns. If you know all the values on one side, you do everything in order of BIDMAS, which gives an answer of 288.

 

[Heart of Darkness]

And then what happens when I rewrite the equation without the parentheses, as 14/7a? Still 4?

Yes.

Welp, there goes all the algebra I ever learned.

Actually not, though. The point of contention with that problem, along with the problem shown in the OP, is actually an issue with how we're taught multiplication in algebra, mainly multiplication by juxtaposition. The people here that see equates OP's equation as equal to 2 implicitly groups 2(9+3) as one group, because that's how we're used to seeing these things in algebra. Similarly, they are also going to equate 14/7a to 1 when a=2 because of the whole multiplication by juxtaposition concept. Let's look at another example that's equally as ambiguous as the one in the OP;

5a/2a = y, a = 3

So what's y? If we group together (5a) and (2a) based on multiplication by juxtaposition, we'll get 2.5, regardless of what a is. If we apply strict PEMDAS to the equation, y = 22.5 when a = 3 (5 * 3 / 2 * 3 = 15 / 2 * 3 = 7.5 * 3 = 22.5).

It's this point of contention that makes the equation in the OP ambiguous, and both answers are right depending on whether you keep 2(9+3) as a single term (24) or rewrite it as two (2*12). Either way, it's ambiguous, and the expression is begging for clarification via an extra set of parentheses.

It's actually raised a lot of discussion either way [http://www.google.com/search?hl=en&biw=1366&bih=612&q=%2B48/2%289%2B3%29&nocalc=1], so it definitely means that this expression isn't as straight-forward as it appears. I do like the discussion on this subject that arose on Wall Street Oasis [http://www.wallstreetoasis.com/forums/48%C3%B7293], though, as people have posted pics in that thread of calculators coming up with different answers for the expression 48/2(9+3), as well as having Excel throw out an error using that same exact notation. One of the posters from that same forum ,manbearpig, also raised an interesting point on if there's a difference between the notations x* and x at the top of page 3 (I'd link to it, but the link's a little wonky).

As a side note, researching this expression wasn't exactly what I had planned for my Sunday...

 

[Pyro Paul]

There is no real answer because it's been written in a purposefully retarded way with no clarification.

This. The actual discussion here is being treated as two different expressions: (48/2)(9+3) and 48/(2(9+3)).

For the sake of argument, let's simplify (9+3) to (12) and set 2 equal to the variable a (a = 2). Now we have the expression 48/a(12). So how do you simplify it? As 4/a (= 48/(12a)), or as 576/a (= (48*12)/a)? Without explicit separation and grouping of the terms, the question just simply becomes stupidly ambiguous.

No, it can't be treated as 48/(2(9+3)) because that isn't the problem. You can't just add parenthesis and say is ambiguous. As it stands, it is extremely easy to solve so long as you understand the order of operations.
I honestly don't know how we can be debating what the answer is.

I understand order of operations, but it doesn't make the question suddenly less ambiguous. Expressions in math that follow the format of a(b+c) can be treated as (ab+ac), and this is where the hangup on this question lies.

Out of curiosity, how would evaluate 14/7(a) when a = 2? As 4 or 1?

14/7(2)
14/7*2
2*2
4
Multiplication and division have equal priority so its done from left to right. There is no operation within the parenthesis so it serves no real purpose.

And then what happens when I rewrite the equation without the parentheses, as 14/7a? Still 4?

Yes.

and with that comment, you prove that you've never taken anything beyond basic algebra.

Solving for a with the answer 1 and 4.
we know a=2

4=14/7a
4*7a=14
7a=14/4
a=3.5/7
a=.5
2=/=.5

1=14/7a
1*7a=14
a=14/7
a=2
2=2

 

[googleit6]

BEDMAS: Brackets, exponents, division, multiplication, addition, subtraction.

Brackets first makes it 48/2(12)

Next, division. 48/2 = 24

24(12)= 288

That's just my two cents though. I'm sure I made a mistake in there somewhere.

Its 288.

Do it in order of BODMAS.

Brackets Order Division Multiplication Addition Subtraction.

I learned three of them over my time in school BOMDAS, BIMDAS & BIRDMAS they stood for: Brackets Of/Indexes Multiplacation Division Addition Subtraction, and BIRDMAS stood for Brackets Indexes Routes Division Multiplacation Addition Subtraction as for the equation the answer is 288

Yeesh those all sound pretty complicated. I'll just stick with BEDMAS- it's pretty simple, and I need simple in math.

 

[Heart of Darkness]

Also, this seems relevant:

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

* Simplify 16 ÷ 2[8 ? 3(4 ? 2)] + 1.

16 ÷ 2[8 ? 3(4 ? 2)] + 1
= 16 ÷ 2[8 ? 3(2)] + 1
= 16 ÷ 2[8 ? 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!

(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!)

Source [http://www.purplemath.com/modules/orderops2.htm]

 

[Daystar Clarion]

As someone who is terrible at maths, this thread has made my brain implode, then explode, then implode again except this time, the theme tune from Danger Mouse was playing.


I'm really bad at maths.

 

[Link_to_Future]

Guys, seriously, this again?

It could be written better because it can be misinterpreted at a glance. 288 is technically correct but I got 2 the first time because I didn't really look that closely.

Also, people who say 288: Yes, you are correct. No, this unusual sense of self-entitlement is not warranted. Cut it out.

 

[halfeclipse]

Barring brackets and exponents (Or the equation being written as a fraction.), division and multiplication occur in the order they appear.

So 48/2(9+3)= is read as the quotient of 48 and 2, multiplied by the sum of 9 plus 3:

48/2(9+3)=
=48/2(12)
=24(12)
=288

while 2(9+3)/48= is read as the product of 2 and the sum of 9 and 3, divided by 48:

2(9+3)/48=
=2(12)/48
=24/48
=0.5

and 48*2/(9+3) is read as the product of 48, and 2, divided by the sum of 9 and 3:

48*2/(9+3)=
=48*2/12
=96/12
=8



Now if it was written as 48
.......................................--------=
.......................................2(9+3)

Then it's read as the quotient of 48 and the product of 2 and the sum of 9 and 3
...48
--------=
.2(9+3)

....48
=--------
...2(12)

....48
=--------
....24

=2

Which is the same as 48/(2(9+3))=



Make sense?


Edit: Ignore the periods, the forums don't preserve spaces so they're just there to center everything.

 

[ProfessorLayton]

Yeah there was already a thread about this. It's 288. There is no reason you would multiply before you divide. They're the same priority so you would divide before you multiply. Type it, as is, into any calculator.

I hate to seem rude but this is literally 7th grade math. It's embarrassing to see this argued about across the internet.

48/2(9+3)

->
I open the bracket
48/18+6

->

8.66666667

I suck at math so tell me what i did wrong

... opening the brackets...

-snip-

I see what you're trying to point out, except that only works if it is in that form. If it was meant to be a fraction, the problem should read "48/(2(9+3))" because you're supposed to do it first... see what I mean?