48÷2(9+3) = ??

92CelicaHalfTrac wrote: I'll look... but mtn would be better to ask for the actual law.

Nope, I don't know it. I'm just trying to play out all sides of this; the only concrete answer that actually exists is that this is an equation with incredibly poor notation. Anybody actually asking/writing it would know better than to put write it as it is, they would either make it a fraction or add in another set of parenthesis.
Also, I think that for just about any practical application (not a math test), it would be pretty obvious which one is correct.

mtn wrote:

92CelicaHalfTrac wrote: I'll look... but mtn would be better to ask for the actual law.

Nope, I don't know it. I'm just trying to play out all sides of this; the only concrete answer that actually exists is that this is an equation with incredibly poor notation. Anybody actually asking/writing it would know better than to put write it as it is, they would either make it a fraction or add in another set of parenthesis. Also, I think that for just about any practical application (not a math test), it would be pretty obvious which one is correct.

But basically... it is true that (9+3) actually has a "1" in front of it, yes?

I'm trying to find something that formally says that, but i'm failing so far.

As for which one being correct is obvious... iono about all that. Seems to be a 50/50 split across the internet. Both sides think it's obvious. I'd say the only thing truly obvious is that 50% would come up with the wrong answer, depending on which side you're on.

92CelicaHalfTrac wrote:

mtn wrote:

92CelicaHalfTrac wrote: I'll look... but mtn would be better to ask for the actual law.

Nope, I don't know it. I'm just trying to play out all sides of this; the only concrete answer that actually exists is that this is an equation with incredibly poor notation. Anybody actually asking/writing it would know better than to put write it as it is, they would either make it a fraction or add in another set of parenthesis. Also, I think that for just about any practical application (not a math test), it would be pretty obvious which one is correct.

But basically... it is true that (9+3) actually has a "1" in front of it, yes? I'm trying to find something that formally says that, but i'm failing so far. As for which one being correct is obvious... iono about all that. Seems to be a 50/50 split across the internet. Both sides think it's obvious. I'd say the only thing truly obvious is that 50% would come up with the wrong answer, depending on which side you're on.

Yes, I was taught that everything has a "1" in front of it, but I am not sure if it is an actual law or not.

The closest thing i can find right now has to do with simplifying algebraic equations. Which, as far as i'm concerned, is relevant.

http://www.jamesbrennan.org/algebra/intro%20to%20algebra/simplifying_algebraic_expression.htm

Parentheses · Parentheses must be multiplied out before collecting like terms You cannot combine things in parentheses (or other grouping symbols) with things outside the parentheses. Think of parentheses as opaque—the stuff inside the parentheses can’t “see” the stuff outside the parentheses. If there is some factor multiplying the parentheses, then the only way to get rid of the parentheses is to multiply using the distributive law. Example: 3x + 2(x – 4) = 3x + 2x – 8 = 5x – 8

Negative signs in front of parentheses A special case is when a minus sign appears in front of parentheses. At first glance, it looks as though there is no factor multiplying the parentheses, and you may be tempted to just remove the parentheses. What you need to remember is that the minus sign indicating subtraction should always be thought of as adding the opposite. This means that you want to add the opposite of the entire thing inside the parentheses, and so you have to change the sign of each term in the parentheses. Another way of looking at it is to imagine an implied factor of one in front of the parentheses. Example: 3x + 2(x – 4) = 3x + 2x – 8 = 5x – 8

mtn wrote:

92CelicaHalfTrac wrote:

mtn wrote:

92CelicaHalfTrac wrote: I'll look... but mtn would be better to ask for the actual law.

Nope, I don't know it. I'm just trying to play out all sides of this; the only concrete answer that actually exists is that this is an equation with incredibly poor notation. Anybody actually asking/writing it would know better than to put write it as it is, they would either make it a fraction or add in another set of parenthesis. Also, I think that for just about any practical application (not a math test), it would be pretty obvious which one is correct.

But basically... it is true that (9+3) actually has a "1" in front of it, yes? I'm trying to find something that formally says that, but i'm failing so far. As for which one being correct is obvious... iono about all that. Seems to be a 50/50 split across the internet. Both sides think it's obvious. I'd say the only thing truly obvious is that 50% would come up with the wrong answer, depending on which side you're on.

Yes, I was taught that everything has a "1" in front of it, but I am not sure if it is an actual law or not.

It kindof has to be. Because anything directly in front of parantheses is a factor. If there's nothing, it's a factor of 1. If it's not 1, then it's something else. If you say that there isn't a 1 there if left blank, then everytime there isn't anything in front of parantheses, anything inside will be equal to zero, because something multiplied to a factor of zero... is zero.

Please read through the proof I provided, and investigate the definitions of 'Division' and the 'Commutative Properties of Multiplication'. It's all right there.

In the link I provided before (here it is again: http://www.purplemath.com/modules/orderops.htm), they tell that division and multiplication have the same rank, and, as such, you do them in order.

Oh and you're retort of "It should be a÷bc. " Can you tell me what is happening between the 'b' and the 'c'? There is no implied parentheses but there is an implied multiplication. The definition of division is the multiplication of the inverse. Using the commutative property allows you to rearrange the equation to any order.

In reply to 92CelicaHalfTrac:

That's only relevant when you have dissimilar terms inside the parentheses. All of the examples you've snagged have a variable and integer inside.

If you have similar terms, say "2(x-3+5)", you'd simplify the parenthetical before you distributed, i.e. 2(x+2).

RossD wrote: Please read through the proof I provided, and investigate the definitions of 'Division' and the 'Commutative Properties of Multiplication'. It's all right there. In the link I provided before (here it is again: http://www.purplemath.com/modules/orderops.htm), they tell that division and multiplication have the same rank, and, as such, you do them in order. Oh and you're retort of "It should be a÷bc. " Can you tell me what is happening between the 'b' and the 'c'? There is no implied parentheses but there is an implied multiplication. The definition of division is the multiplication of the inverse. Using the commutative property allows you to rearrange the equation to any order.

You're skipping over the Distributive Property/Law.

If i simplified the original equation even further, and made it 48÷2x, where x=(9+3), what would you simplify it to from there?

If i say that a÷bc, you would multiply b and c. But notated as such, they are one value. You would read it as "a" OVER "bc." Yes. There's implied multiplication. There's also implied factors when talking about parantheses. Can't ignore one just because you want to use the other.

I'm aware of the laws and definitions you posted.... basic arithmetic wasn't hard for me back in 3rd grade, and it isn't now. My point is that the order of operations is subject to many other variables especially when you get into Algebra. Like now.

I'm still looking, i'm not dismissing what you're saying.

In return, i'd like you to prove that in this example: 48÷(9+3), that there is NOT a 1 in front of the (9+3). Or at least investigate.

ReverendDexter wrote: In reply to 92CelicaHalfTrac: That's only relevant when you have dissimilar terms inside the parentheses. All of the examples you've snagged have a variable and integer inside. If you have similar terms, say "2(x-3+5)", you'd simplify the parenthetical before you distributed, i.e. 2(x+2).

So you're saying that you would work the equation completely different if it were 48÷2(x+3) vs. 48÷2(9+3)?

Or are you saying that there is not a "1" in front of the parantheses in this example? 48÷(9+3)

(Not attacking, just asking )

Serious question:

What is in front of the following expression?

(9+3)

A) Nothing
B) 1

for multiplicative identity to work, the assumed 1 must also be in an assumed (). therefore: (9+3) = 1(9+3) only if 1(9+1) is an isolated expression. If not isolated, it must be noted as (1(9+3))... or you risk breaking order of operations. which is exactly where this all started.

ps - for the ultimate answer, go ask a lobster.

nderwater wrote: for multiplicative identity to work, the assumed 1 must also be in an assumed (). therefore: (9+3) = 1(9+3) only if 1(9+1) is an isolated expression. If not isolated, it must be noted as (1(9+3))... or you risk breaking order of operations. which is exactly where this all started.

This kindof smells to me again like the "if you saw 48÷2x, how would you read it?"

Would it be "48 over 2, times "x"? Or "48 over 2x?"

The only reason the parantheses exist in this case is because you can't just write it as "212" after the 9+3 is resolved.

I'm having a hard time understandin why 1 isn't a factor of (9+3) when it's written as (9+3), and that 2 isn't a factor of (9+3) when it's written as 2(9+3).

Hah! Just saw your edit.

Dear Lobster: How do i grow stronger?

You raise a valid point.

I think the confusion comes in as you're looking at 48 / 2(9+3) as "48 over 2(9+3)" instead of "48 over 2, times 9+3"

By lumping the whole of "2(9+3)" in as the denominator, you're inferring parentheses around it, i.e. 48/(2[9+3]).

But the way it's written, it could also be 48/2 * (9+3).

And I don't think either is a provably wrong interpretation.

What is the answer to: 48÷2÷(9+3)

Conversely: 48÷2*(9+3)

The answer cannot be the same.

RossD wrote: What is the answer to: 48÷2÷(9+3) Conversely: 48÷2*(9+3) The answer cannot be the same.

First is 2.

Second is 288.

I think i see where you're going with this...

My proof really does hold water.

All that 'put a one in front of everything' was just muddying the waters.

RossD wrote: My proof really does hold water. All that 'put a one in front of everything' was just muddying the waters.

Yet you still haven't answered any of the questions i asked, and neither does your proof...

Putting a one in front of the paranthetical expression doesn't muddy the waters, it just demonstrates the function of "2" in this case.

Oh well. Moving on.

I'll go with my answer of 2 which is what I got when I first read the problem. In words it is 48 divided by twice 12.

Ahem... I just wanted to point out that I became a powerdork at the top of this page!!!

mtn wrote: Ahem... I just wanted to point out that I became a powerdork at the top of this page!!!

NNNNEEEEEEEEEERRRRRRRRRDDDDDDDDD!!!!!!!!

RossD wrote: My proof really does hold water. All that 'put a one in front of everything' was just muddying the waters.

I can do that too.

DILYSI Dave wrote:

RossD wrote: My proof really does hold water. All that 'put a one in front of everything' was just muddying the waters.

I can do that too.

I'm ROFLing... I wanted to do that, but i couldn't figure out how to modify that thing because i'm techno-dumb.

RossD wrote: What is the answer to: 48÷2÷(9+3) Conversely: 48÷2*(9+3) The answer cannot be the same.

Again, please.