master_shake_
Diamond Member
wait i got it.
we need some common core in this shit
🙂
we need some common core in this shit
🙂
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Our public schools suck! Adults that cant do math...
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No. 6/2(2+1) is not the same thing as 6 / 2 * (2+1). If it was, it would be written that way.
Fayd
Diamond Member
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.
Fayd
Diamond Member
actually, it is the same thing.
Carson Dyle
Diamond Member
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?
ralfy
Senior member
From 2006:
"New Study of the Literacy of College Students Finds Some Are Graduating With Only Basic Skills"
http://www.air.org/news/press-relea...s-finds-some-are-graduating-only-basic-skills
"New Study of the Literacy of College Students Finds Some Are Graduating With Only Basic Skills"
http://www.air.org/news/press-relea...s-finds-some-are-graduating-only-basic-skills
phucheneh
Diamond Member
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.
Math, as taught by schools: useless.
Red Squirrel
No Lifer
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).
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).
Same can be said for using parentheses. The distributive law should apply, no? 2(1+2) is a rewritten expression.
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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.
ThatsABigOne
Diamond Member
It's 9 and I am studying in a field of engineering mathematics.
So is my friend, and I just sent him the problem. He said it's 1.
destrekor
Lifer
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
destrekor
Lifer
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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Then simplify/rewrite (9a+9b+9c+9d+9e).
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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. 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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I'm not ignoring order of operations, I'm arguing that the 2 next to the parenthesis means it is a single expression.
Incorrectly, you are. They are not a single expression without the parenthesis. Writing it without the parenthesis is just a shorthand method. See above.
So then you're saying 6/2(1+2) is a shorthand method of writing 6/2*(1+2)?
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)
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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