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Our public schools suck! Adults that cant do math...

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Engineer said:
That's not the way that the OP is stated. You are putting in a 2nd set of parenthesis which are not in the OP.

6/2(2+1) =

6 / 2 * (2 + 1)

6 / 2 * 3

3 * 3

9
Click to expand...

No. 6/2(2+1) is not the same thing as 6 / 2 * (2+1). If it was, it would be written that way.
 
disappoint said:
I'm going to give you the benefit of the doubt that you aren't just trolling. Multiplication and division orders are left to right. If division comes first it takes precedence over multiplication. Same with addition and subtraction. The answer to that problem is 9.
Click to expand...

division is just multiplication by the reciprocal. they're the same thing!
subtraction is just addition of a negative. they're the same thing!

so yeah, division shares order of precedence with multiplication.

subtraction shares order of precedence with addition.
 
Never even heard of "PEMDAS"... How bloody difficult is it to remember that multiplication and division have equal precedence that is greater than addition and subtraction, which also have the same precedence?
 
And why is there ambiguity in the OP's equation? Because we don't know what he is trying to accomplish. Were this a real-world problem, we would know for sure in which order the operations should be completed. And then we'd complete them with a fucking calculator.

Math, as taught by schools: useless.
 
I can see how people would get confused when divisions are involved, because there's different ways to write it. Not sure what the general approach is suppose to be but way I see it is if the division is on it's own then only treat it with the two numbers next to them like you do with multiplication.

So 6/2(2+1) would be 3(2+1)

But you could argue that it's actually suppose to be looked at like a fraction, as in 6 over 2(2+1). In that case, it should have been written that way, or brackets thrown in around 2(2+1).
 
Red Squirrel said:
I can see how people would get confused when divisions are involved, because there's different ways to write it. Not sure what the general approach is suppose to be but way I see it is if the division is on it's own then only treat it with the two numbers next to them like you do with multiplication.

So 6/2(2+1) would be 3(2+1)

But you could argue that it's actually suppose to be looked at like a fraction, as in 6 over 2(2+1). In that case, it should have been written that way, or brackets thrown in around 2(2+1).
Click to expand...

Same can be said for using parentheses. The distributive law should apply, no? 2(1+2) is a rewritten expression.
 
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Fayd said:
actually, it is the same thing.
Click to expand...

No, it's not.

When the distributive property is used, as in this case, it is an expression rewritten to show the same value. 2(a+b) has the same value as 2a+2b. 2(1+2) has the same value as (2*1) +(2*2). If you don't want the distributive law to apply, then don't write the equation that way.

Simplify this -

8 / (999999999*1+999999999*2+999999999*30+99999999*17+999999999*72)

You get 8 / 999999999(1+2+30+17+72). It's the same thing. You cannot break up a single expression.
 
JDawg1536 said:
No. 6/2(2+1) is not the same thing as 6 / 2 * (2+1). If it was, it would be written that way.
Click to expand...

Fayd said:
actually, it is the same thing.
Click to expand...

This.

It's the exact same thing. The * sign is unnecessary, and does not change the order of operations in the original equation.
It's 6/2(3) which equals 3(3) which equals 9.

I can see the confusion. Most want to immediately jump to the distributive property which involve parentheses, but that a) requires simplifying what is outside of the parenthesis if it must be done, and b) would require a variable in the parenthesis anyhow.

Most of the time, you see the distributive equation example with, say: 3 (z + 4). Perhaps you want to apply this to the other equation?
However, if it was 6/2 (z + 4), you would simplify the 6/2 before proceeding to distribute. A lot of the time, the equation wasn't made confusing in that manner.

This is why critical math is NOT written in plain-text format on the PC, it is always written in the proper subscript and superscript with proper symbols and formatting to ensure that, if understood, the order of operations is 100% clear.

I can see the confusion for the original, and why the internet is still in debate on it, even people debate mathematicians on the subject. In this case, you simply follow the order of operations, through and through. In this example, if you were truly going to make the 2 apart of the parenthesis to do that math before getting to the division, you must write it as such: 6/(2(2+1))
As it is written, it implies (6/2)(2+1), aka (3)(3) = 9. It can also be written as 6(2+1) / 2, which is simplifying a step I can't seem to put into text: it would look like 6 over 2, multiplied by (2+1) over 1. Which would then simplify to be 18/2.
You can envision it that way, or simply perform it as written, following PEMDAS.
If it were to be instructed to be performed in any other order, it would be written in a manner that made that clear. Additional parenthesis would be in order, most likely. Or, to be as clear as possible, text like
img
is how it would be communicated in a professional manner, removing all doubt of how it is supposed to look like. Plain text is truly a terrible means of communicating mathematical formula, because it is easily misinterpreted.
 
JDawg1536 said:
No, it's not.

When the distributive property is used, as in this case, it is an expression rewritten to show the same value. 2(a+b) has the same value as 2a+2b. 2(1+2) has the same value as (2*1) +(2*2). If you don't want the distributive law to apply, then don't write the equation that way.

Simplify this -

8 / (999999999*1+999999999*2+999999999*30+99999999*17+999999999*72)

You get 8 / 999999999(1+2+30+17+72). It's the same thing. You cannot break up a single expression.
Click to expand...

No you don't. And that's ignoring the incorrect assumption that you mix the 999999999 with the parenthesis before you address the division. Completely dropping the "8 /" part of the equation, those two second halves are not the same. Not at all.
 
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It's not that confusing. But if there is no standard rule about how to type the equation, then there will never be only one answer.
 
destrekor said:
No you don't. And that's ignoring the incorrect assumption that you mix the 999999999 with the parenthesis before you address the division. Completely dropping the "8 /" part of the equation, those two second halves are not the same. Not at all.
Click to expand...

Then simplify/rewrite (9a+9b+9c+9d+9e).
 
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JDawg1536 said:
No, it's not.

When the distributive property is used, as in this case, it is an expression rewritten to show the same value. 2(a+b) has the same value as 2a+2b. 2(1+2) has the same value as (2*1) +(2*2). If you don't want the distributive law to apply, then don't write the equation that way.

Simplify this -

8 / (999999999*1+999999999*2+999999999*30+99999999*17+999999999*72)

You get 8 / 999999999(1+2+30+17+72). It's the same thing. You cannot break up a single expression.
Click to expand...

Sorry, but you are wrong. If they are to be treated like a unit with precedence, they should have a parenthesis around them. Of course, it is not your fault your teachers were lazy and didn't include them, but it is your fault that you refuse to accept the order of operations.

There is a single solution to this problem, and the solution is nine.

The distributive law says that multiplication of the group is identical to multiplying with each member of the group separately. You seem to think this gives the number outside of the parenthesis some sort of immunity from the order of operations upon which it is bound, yet it is not.

The equation can be simplified like so, if you wish to see it in the context using distribution, and with some added parenthesis to help. Yea, I could have just went straight to 3 on that third step, but I wanted to make sure you understood what actually occurs:

6 / 2 (1 + 2)
(6 / 2)(1 + 2)
(6 / 2) * 1 + (6 / 2) * 2
3 * 1 + 3 * 2
3 + 6
9

Red Squirrel said:
But you could argue that it's actually suppose to be looked at like a fraction, as in 6 over 2(2+1). In that case, it should have been written that way, or brackets thrown in around 2(2+1).
Click to expand...

Yea, this is where the confusion lies. No brackets when written, it is wrong -- even if most math teachers would just take it as OK when handwritten for shorthand since the person writing it or the next step is going to yield their intention. Math ultimately comes down to the solution, so as long as the solution is right and it appears that what you wrote is correct based on how you have chosen to represent it, then it is going to be fine since they will just figure out what you meant in regards to the solution pretty easily.
 
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mrjminer said:
Sorry, but you are wrong. If they are to be treated like a unit with precedence, they should have a parenthesis around them. Of course, it is not your fault your teachers were lazy and didn't include them, but it is your fault that you refuse to accept the order of operations.

There is a single solution to this problem, and the solution is nine.

The distributive law says that multiplication of the group is identical to multiplying with each member of the group separately. You seem to think this gives the number outside of the parenthesis some sort of immunity from the order of operations upon which it is bound, yet it is not.

The equation can be simplified like so, if you wish to see it in the context using distribution, and with some added parenthesis to help. Yea, I could have just went straight to 3 on that third step, but I wanted to make sure you understood what actually occurs:

6 / 2 (1 + 2)
(6 / 2)(1 + 2)
(6 / 2) * 1 + (6 / 2) * 2
3 * 1 + 3 * 2
3 + 6
9



Yea, this is where the confusion lies. No brackets when written, it is wrong -- even if most math teachers would just take it as OK when handwritten for shorthand since the person writing it or the next step is going to yield their intention.
Click to expand...

I'm not ignoring order of operations, I'm arguing that the 2 next to the parenthesis means it is a single expression.
 
JDawg1536 said:
I'm not ignoring order of operations, I'm arguing that the 2 next to the parenthesis means it is a single expression.
Click to expand...

Incorrectly, you are. They are not a single expression without the parenthesis. Writing it without the parenthesis is just a shorthand method. See above.
 
MrRamon said:
6 / 2 (1+2) ....

What a joke. The answer is simply 9. If you wanted it to be one 6 / (2(1+2)).. booo
Click to expand...

Not really. Since you can't tell the difference when someone types the equation out, there are two answers. You can't tell if they mean (6/2)(1+2) or ---

6
-----------
2(1+2)
 
We already proven that those with ph.d in mathematics can get different results on this and that only an idiot would write it like that.
 
JDawg1536 said:
Not really. Since you can't tell the difference when someone types the equation out, there are two answers. You can't tell if they mean (6/2)(1+2) or ---

6
-----------
2(1+2)
Click to expand...

I understand where you are coming from, however, If you type it into any calculator or put it into c++ or java etc and compile, the answer will be 9 not 1 and not ambiguous. Left to right. This type of question was on my cop 3223 class. It would have been 9 as the compiler "understands" it. I can see where there could be two answers.
 
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