48÷2(9+3)

[Nephthys]

For those using a calc or in most cases (google) and programming languages Remember by default the program/ calculator will change the equation to (48/2) (9+3)=
because as Eris says the equation is wrongly written. which in fact is not the same equation as 48/2 (9+3)=
Generally yes since Multiplication and Division have equal precedence you would work the problem from left to right. However the asker of the question did not specify the equation to either ( 48/2)*12 or 48/(2*12). If specified. (48/2)*12 =288 and 48/ (2*12)= 2

[zansa]

I used to fall asleep in algebra.

[Wio]

I used to fall asleep in algebra.

This is arithmetic.

[OminousCloud]

Calculations are worked from left to right.
Brackets and parentheses are worked first
Powers and roots are worked out next (often referred to as exponents or orders)
Multiplication and division are worked next as they occur from left to right
Addition and subtraction are worked last from left to right.


The answer is 2.

The original equation is 48÷2(9+3).
2(9+3) is one complete term and cannot be split up. This term already comes with an order of operations! It must be worked out first before solving from left to right.
48÷2(9+3) = 48÷2(12), the bracket has not gone away and brackets take precedence.
= 48÷24
= 2

Proof:
Let (9+3) = x and let our solutions be (1) 2, and (2) 288:

(1)
48÷2(x)=2
expand the bracket first 48÷2x=2
48= 2*2x
48= 4x
x=12. 9+3 = 12

(2)
48÷2(x)=288
48= 288*2x
48=576x
x=0.083, but we know that x was (9+3)

[ExitNine]

answer is 8.666667 when first distributing the 2 and then following the order of the operations.

2(9+3) = 18 + 6

so you would have: 48 / 18 + 6 --> 2.666667 + 6 --> 8.666667

Yay me

[Wio]

Proof:
Let (9+3) = x and let our solutions be (1) 2, and (2) 288:

(1)
48÷2(x)=2
expand the bracket first 48÷2x=2
48= 2*2x
48= 4x
x=12. 9+3 = 12

(2)
48÷2(x)=288
48= 288*2x
48=576x
x=0.083, but we know that x was (9+3)

(1)
48÷2(x)=2
expand the bracket first 48÷2x=2
x = 2÷(48÷2)
x = 2÷24
x= 0.08333333...

(2)
48÷2(x)=288
48÷2x=288
x = 288 ÷ (48 ÷ 2)
x = 288 ÷ 24
x = 12. 9+3 = 12



1/2x is bad form, but when push comes to shove it should be parsed as 1 * 2 ^ -1 * x = (1/2)x and not 1/(2x). This is according to your own left to right rule. By the way, a term is basically what you get when you separate an expression on addition or subtraction. So 48÷2(9+3) altogether is a term. Also, parenthesis does not mean that multiplication near parenthesis must come first. 2(2) = 2 * (2). You wouldn't say 10 - 2 + (3) should be 10 - 5 just because the parenthesis is near the plus operation.

[Nephthys]

answer is 8.666667 when first distributing the 2 and then following the order of the operations.

2(9+3) = 18 + 6

so you would have: 48 / 18 + 6 --> 2.666667 + 6 --> 8.666667

Yay me

how does 48/ 18 + 6 = 2.666667?

[ExitNine]

48 / 18 + 6 = 8.666667

[Furore]

Normally I don't advocate stuff like this, but at this point I think the only correct course of action is to shoot the person that asked the question in the face.
Twice to be sure.

[Cantelope]

Looking at it from an infix point of view, I see 48 / 2 (9+3)

Evaluate parenthetical statements first, (9+3) = 12, pop that back into the stack:

48 / 2 * (12)

and then in computer fashion, crunch left to right; 288. If I parse right to left though, I get 24/48 or 1/2. OH NOES, ORDERS OF OPERATION BE DAMNED. Off-topic, do people in countries like China/Japan do math right->left in the same fashion they read, or no?

[Vaishu]

The answer is 2 as,
=48/2(9+3)
=48/2=24,9+3=12
=24/12
=2

[-GAZKUL-]

only remember chunks of maths from Int 2 (failed) but came up with 4.4, reasoning?

9+3=11: brackets first
2x11=22: something vauguly about brackets being first
48/11=4.4:I think.....

[Ranshiin]

Wait ... how does 9 + 3 = 11? >_>

288 is one answer, it is correct if you interpret the expression in one of the two possible ways.
2 is another answer, it is correct if you interpret the expression in one of the two possible ways.

If someone shows you this expression, you shouldn't pick an interpretation, you should slap them in the face and tell them to write unambiguous expressions. The very fact that this discussion exists is evidence enough that this is a terrible way of writing whatever it is supposed to mean, especially as there completely non-ambiguous ways of writing both possible interpretations.

I'm a graduate student in theoretical physics, so I have a fair share of mathematical experience too.

Once again, I owe you a touché. xD


And now looking back on this thread, the equation's output is basically just showing the method in which people work through math. People who use the PEMDAS rule end up with 2, whilst people who use BODMAS end up with 288.

Ambiguous with reason? Obvious observation is obvious?

[Furore]

In Australia, we don't use those stupid abbreviations and instead just solve it left to write prioritising what we need to.
We must do something right though as our method will get the exact answer machines that calculate such things get.

[Eris]

Wait ... how does 9 + 3 = 11? >_>

You assume 3 to be small.

Normally I don't advocate stuff like this, but at this point I think the only correct course of action is to shoot the person that asked the question in the face.
Twice to be sure.

Now you're thinking like a mathematician.

[Capitán]

9 + 3 = 12.
2 x 12 = 24.
48 / 24 = 2.

The answer is 2. Or 42.

[Nephthys]

it's been 7 months since this thread, and now I cannot comprehend any of my theories I gave for this equation. I'm getting dumber!!

[Hanamaru Kunikida]

it's been 7 months since this thread, and now I cannot comprehend any of my theories I gave for this equation. I'm getting dumber!!

[Nesh]

Fisrt:
9+3=12
Second:
It's 48÷2=24 and not the other way around
and finaly:
24x12=288

....and that's all folks

[GameGeeks]

People, that aren't me, need to let this die. Should have stayed dead seven months ago.

[Derrick Remon]

I say it's ambiguous, as I take multiplication and division to have the same precedence. You could either mean

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

If ever you write an expression that's ambiguous like this, your problem isn't how do I evaluate it, it's that you've written an ambiguous expression.

For sanity's sake, write out the fraction (instead of using ÷ or /) if it's more than just a fraction of two numbers.

I wanted to scream this, but I didn't want to start some debate over basic expression.

[Eris]

This is an old thread. Let it rest.