48÷2(9+3) = ????

[raijin-xiii]

lmao I guess this "David M." guy is just full of crap everywhere he goes.

[Tony-R32]

wait...so this isn't science?

[archaeic_bloke]

I think I see why there is controversy....

the way it is written is 100% mathematically 288, not 2, and theres a law that governs that, honestly! It's called "order of Operations" or sometimes known in highschool as BEDMAS. http://en.wikipedia.org/wiki/Order_of_operations

It refers to the very strong point that it does not matter what's written in front of the brackets, you MUST compute the brackets first, it is the law! lol Brackets then Exponents and only then can you commence Division or Multiplication.

so following the real math laws you do 9+3 first which is of course 12... then you may divide or multiply at your choice, it won't affect the outcome at this point.

I saw this originally on a special type of forum for anonymous ppl... LOL'd when i thought to myself how sneaky it is.

Holy crap, just realized how long this thread has been here, I thought it said 7 posts not 7 pages! hahahah, oh well, my response is still valid

[archaeic_bloke]

DAMN going over this my mind just blew up!

BEDMAS, yes you will do the brackets first, but you do the division and multiplication before any add or sub. if there are both division and multiplication in the same equation, then you do which ever one comes first by reading it left to right.

1.Brackets: (9+3) = 12 eq: 48/2(12)
2.Division: 48/2 = 24 eq: 24(12)
3.multi: 24*12= 288

but if it is written
48
-----
2(9+3)

then the 48 gets reduced to 24 and the 2 is gone. because there are 24 times 2 goes into 48 so...

24
------=2
12

written (48/2)(9+3) you get 288

BUT if you take the derivative of the equation you get 0 so thats really what counts.

Actualy its not a zero deriviative either, you get something undefined! can't divide by zero.

[our_kid]

Actually, I worte that answer last week on Yahoo. I've also written it in similar forms on this forum and 4 other places. And no, I don't use my real name or location anywhere online.

In regards to Google calulator saying it's 288; all calulators will go left-to-right. If you type this expression into Google, you get:

(48 ÷ 2) * (9 + 3) = 288

That's not how the original question is written. It's written as 48÷2(9+3), meaning he 2 is exclusive to the bracket. It is written that way to show that the 2 is factored from (9+3), and therefore is one complete operand. In English, that equation means "forty-eight divided by twice the sum of nine plus three." It does NOT mean 'forty-eight divided by two times the sum of nine plus three'. That would be written as 48÷2x(9+3).

You can go on and on about doing multiplcation and division left-to-right all you want, but that '2' written with no operator (i.e., operation sign) between itself and the bracket, meaning that is has been factored from the bracket and therefore must be reapplied to the bracket before carrying out any further operations. I'm looking at 6 other examples of this right now.

Here's another of thinking of it. You could write out the original question as:

48
----
2(9+3)

You wouldn't solve that by doing 48 ÷ 2 then multiply that by (9+3). You would solve the denominator then divide the numerator by the denominator.

lmao I can't believe you ripped this right off of yahoo answers.

it says right in that link that "it makes no difference whether you add two or more terms together first, and then multiply the results by a factor, or whether you multiply each term alone by the factor first, and then add up the results."

THE WHOLE EQUATION IS A SINGLE TERM. Terms are separated by addition or subtraction... this is still one term because the would-be "entire term" that "you" speak of is actually separated by a division sign.

You wanna use distributive property? ok, sure.

48÷2(9+3)
=24(9+3)
=(24x9)+(24x3)
=216+72
=288

Again, THIS EQUATION ONLY HAS ONE TERM AND BEDMAS STILL APPLIES WHETHER YOU WANT TO USE DISTRIBUTIVE PROPERTY OR NOT. Like the quote above says taken from the link "you" gave us, IT DOESN'T MATTER BECAUSE THE SAME ANSWER WILL COME UP.

The only reason distributive property exists is to handle UNKNOWNS in the equation, also quoted in that link:

"This is kinda cool, but you might wonder what possible use it might be. I mean, really, why wouldn't you ALWAYS add the terms together first, and avoid all that yukky multiplication? Well, the answer is: It comes in very useful when you have terms that cannot be added together first, because they are not like terms."

math teacher that plagiarizes wrong answers...? This is like grade 11 all over again where I had to teach the class half of the time because the teacher didn't know what the hell they were talking about.

[raijin-xiii]

Actually, I worte that answer last week on Yahoo. I've also written it in similar forms on this forum and 4 other places. And no, I don't use my real name or location anywhere online.

In regards to Google calulator saying it's 288; all calulators will go left-to-right. If you type this expression into Google, you get:

(48 ÷ 2) * (9 + 3) = 288

That's not how the original question is written. It's written as 48÷2(9+3), meaning he 2 is exclusive to the bracket. It is written that way to show that the 2 is factored from (9+3), and therefore is one complete operand. In English, that equation means "forty-eight divided by twice the sum of nine plus three." It does NOT mean 'forty-eight divided by two times the sum of nine plus three'. That would be written as 48÷2x(9+3).

You can go on and on about doing multiplcation and division left-to-right all you want, but that '2' written with no operator (i.e., operation sign) between itself and the bracket, meaning that is has been factored from the bracket and therefore must be reapplied to the bracket before carrying out any further operations. I'm looking at 6 other examples of this right now.

Here's another of thinking of it. You could write out the original question as:

48
----
2(9+3)

You wouldn't solve that by doing 48 ÷ 2 then multiply that by (9+3). You would solve the denominator then divide the numerator by the denominator.

it's one term. there is no magical mathematical function that happens to numbers that are beside brackets; it's plain old multiplication.

This isn't the correct input that you're claiming is right:

48
----
2(9+3)

this equation is another way of writing 48÷[2(9+3)]. Notice the double brackets.

it is written this way:

as in, do the division and then multiply.

again, you're clearly confused about what a term is and you're convinced that saying 2x(9+3) is different than 2(9+3) because this magical distributive property thing exists. it's not. stop it. seriously. You're just confused because any examples you find don't have multiplication or division before doing the distributive property.

Here's a breakdown-of-a-solution calculator in action:

Yes, this is an algebra calculator that is designed specifically to do these types of "friggin complicated" equations.

I couldn't use division to explain it because of this error:


but if you tell me that
48*2(9+3)
=48*2(9)+2(3)
=48*12
=576
I'll ******* smack you because it doesn't mean the same thing as this

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

that's right. division sign doesn't mean CUT THE WHOLE DAMN EQUATION IN HALF because if it could do it, so could multiplication.

but yeah, thanks to that error I got to show you another ounce of proof that you do the division (or in this case, multiplication) before you do anything to the numbers in the brackets.

admit you're wrong now and salvage some respect. I'm begging you.

[frankiman]

^^ this

[MarusGTR]

http://knowyourmeme.com/memes/48293

The only thing I can say about this thread is that some people like to belittle/patronize others.

Some calculators have shown the answer as 2 (check the bottom pictures)

As for me, MATHCAD says 288 for the exact symbolically imputed equation, which is fine, I agree that the nomenclature and structure calls for a left to right progression with the brackets being called in the end. I thought it was 2 at first because im used to big formulas being correcly represented and I always solve the factors first. I didn't give it much thought since I knew there was a catch.

For people who code and said they knew structure well I found the comment odd since I personally know from MATLAB (which itself runs on Visual Basic code) that I can't input the formula without explicitly giving the multiplier before the bracket. Seems like they made sure to prevent ambiguity.

So some ppk think I don't know my math because I called 2 as an answer? Fine.

[Snake556]

How has this thread hit 7 pages...?

[frankiman]

How has this thread hit 7 pages...?

i lol'ed

[MarusGTR]

How has this thread hit 7 pages...?

I dunno but I'm hoping my link is going to /end thread

[our_kid]

You made an error with this calculation:

48*2(9+3)
=48*2(9)+2(3)
=48*12
=576

It should be

48*2(9+3)
=48*(2*9 + 2*3)
=48*24
=1152

Which is the same as saying

48*2(9+3)
=48*2(12)
=48*24
=1152

Which is the same only because you're multiplying everything and it therefore follows associative properties which states that when two or more numbers are multiplied together, the product is the same regardless of the grouping of the factors:

48*2(9+3)
=96(12)
=1152

Division is a different operation than multiplication.

Wolfram is just reading the equation left-to-right (like I said, just about all digital calculators do), and is not taking more complex theorems into account. Distribution properties do exist. I swear I'm not making them up. It's taught in the Ontario grade 9 academic math course. I swear I'm not making this up.

I should be able to factor a 3 out of the bracket and it should still give me the same answer, because all I'm doing is moving a common factor outside the bracket

48 ÷ 2(9 + 3) = 48 ÷ 2(3(3 + 1)) because (9 + 3) can be written as 3(3 + 1).


Following BEDMAS and proper distribution properties:

48 ÷ 2(3(3 + 1))
= 48 ÷ 2(9+ 3)
= 48 ÷ 2(12)
= 48 ÷ 24
= 2

OR

48 ÷ 2(3(3 + 1))
= 48 ÷ 6(3 + 1)
= 48 ÷ 6(4)
= 48 ÷ 24
= 2

OR

48 ÷ 2(3(3 + 1))
= 48 ÷ 6(3 + 1)
= 48 ÷ (6x3 + 6x1)
= 48 ÷ (18 + 6)
= 48 ÷ 24
= 2

The way it's written in the question, written as 2(9 + 3) represents a factored form of the expression. It's the same as saying (2 + 0)(9 + 3). They are a single statement and need to be simplified first (using distributive properties or F.O.I.L.) and then calculated.

Let's look at this questions algebraically. If we replace any of the numbers in the expression with a a letter, like 'x', then we should be able to rearrange and solve and get that original number.

Let's replace the 48 with x and start with setting the expression equal to 288 as you suggest:

288 = x ÷ 2(9 + 3)
288 = x ÷ 2(12) -- simplify first
288 = x ÷ 24
288 x 24 = x
6912 = x


Now setting the expression equal to 2 and solving for 'x':

2 = x ÷ 2(9 + 3)
2 = x ÷ 2(12) -- simplify
2 = x ÷ 24
2 x 24 = x
48 = x

which is what was in the original expression.

So, following algebra rules, 288 doesn't work as an answer.

it's one term. there is no magical mathematical function that happens to numbers that are beside brackets; it's plain old multiplication.

This isn't the correct input that you're claiming is right:

48
----
2(9+3)

this equation is another way of writing 48÷[2(9+3)]. Notice the double brackets.

it is written this way:

as in, do the division and then multiply.

again, you're clearly confused about what a term is and you're convinced that saying 2x(9+3) is different than 2(9+3) because this magical distributive property thing exists. it's not. stop it. seriously. You're just confused because any examples you find don't have multiplication or division before doing the distributive property.

Here's a breakdown-of-a-solution calculator in action:

Yes, this is an algebra calculator that is designed specifically to do these types of "friggin complicated" equations.

I couldn't use division to explain it because of this error:


but if you tell me that
48*2(9+3)
=48*2(9)+2(3)
=48*12
=576
I'll ******* smack you because it doesn't mean the same thing as this

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

that's right. division sign doesn't mean CUT THE WHOLE DAMN EQUATION IN HALF because if it could do it, so could multiplication.

but yeah, thanks to that error I got to show you another ounce of proof that you do the division (or in this case, multiplication) before you do anything to the numbers in the brackets.

admit you're wrong now and salvage some respect. I'm begging you.

[our_kid]

Also, here's an example from a high school textbook:

Simplify the following expression:

20 ÷ 2[8 – 3(4 – 2)] + 1

= 24 ÷ 2(10 – 6) + 1
= 24 ÷ 2(4) + 1
= 24 ÷ 8 + 1
= 3 + 1
= 4

It goes on to say:

"Even though multiplication and division are usually treated equally according to BEDMAS, parentheses outrank the division...multiplication that is indicated by placement against a parenthesis is carried out before other multiplication."

I don't know how it was taught years ago, but as long as I've been going to school and as far as teaching math goes today, numbers against and parenthesis outrank numbers multiplied together with an 'x' or '*' in between. So, the way the original question is written, you have to apply the 2 to the bracket before dividing the 48, making the correct answer 2. Period. Case closed.

[Joker]

"Even though multiplication and division are usually treated equally according to BEDMAS, parentheses outrank the division...multiplication that is indicated by placement against a parenthesis is carried out before other multiplication."

I don't know how it was taught years ago, but as long as I've been going to school and as far as teaching math goes today, numbers against and parenthesis outrank numbers multiplied together with an 'x' or '*' in between. So, the way the original question is written, you have to apply the 2 to the bracket before dividing the 48, making the correct answer 2. Period. Case closed.

That!

[MarusGTR]