6÷2(1+2)=?

[ojodelaplata]

ummm... ok...

[moxthemoron]

dahil ako nga ay alipin ng calculator,

x=1

Source: Solve function ng FX-570

pero gamit yung equation solver ng sharp el-9900,

x=-5/3

[chaos_knight]

for me the answer should be 1!

i'm not a math major but the reason that i see is because the omission of the multiplication sign between 2 and the parenthesis makes the number 2 a distributive factor for the whole parenthesis. therefore, regardless of the PEMDAS rule, you have to distribute 2 to the whole parenthesis first before you could solve the equation from left to right based on PEMDAS. i know there is no rule regarding this, but i think in most of the math equations that I've solved, if a number follows a parenthesis right away, then you have to distribute it to the whole number inside the parenthesis before you solve the equation from left to right.

hence, it makes 6÷2(1+2) not equal to 6÷2x(1+2), since with the multiplication sign in the 2nd equation you could solve the equation from left to right by following the PEMDAS rule

[dashingdevonair]

^ isn't it you always simplify what's inside the parenthesis?

That makes it three.

The question of three being a part of the denominator is the issue I faced. Since it is a part of the initial parenthesis I multiplied it with the denominator giving it 1 as a result.

I believe that we confronted with two operators of equal level, in this case division and multiplication, one would have to solve it from left to right, thus necessitating that we solve 6/2 first before multiplying it to three.

Of course this is purely based from what I was taught in grade school and high school. It is still mind boggling as to why some calculators still point out to 1.

We would need to understand the deeper explanation of the PEMDAS rule. There may be exceptions that we were not taught of in elementary.

[dashingdevonair]

We are looking for the case that leads to X=1.

Case 1: For those who claim that 9 is the answer

1. 6/2(x+2) = 9

PEMDAS rule states that operations of equal priority are to be solved from left to right.

Whether a multiplication sign exists or not is irrelevant as it is merely a symbolic preference.

Since it is impossible to solve X+2 alone even if it's inside the parenthesis, the parenthesis now signifies that x=2 should be treated as a single number.

÷ and / are the one and the same. It's merely a symbolic preference and in no way connotes a different concept.

Here the problem 6/2(x+2) = 9 can be seen in terms of A/B*C=9. Thus we divide first.

2. 3(x+2)=9

No PEMDAS here needed. The problem is basic algebra already.

3. x+2=3

4. x=1

Case 2: For those who claim that the answer is 1

6/2(x+2) = 1

Applying the same principles stated above.

3(x+2) = 1

x+2= 1/3

x= 1/3-2

Clearly erroneous since X should be 1.

We can conclude that the answer is indeed 9.

[dashingdevonair]

You may use the programming language C or C++ as well to verify that the answer is 9. Run the following code in the compiler in C

#include <stdio.h>
int main() {
int i;
i = 6/2*(1+2);

printf("%i", i);
}


The answer is consistently 9

[jaguarzxxx]

I therefore conclude that by using algebra as a verification tool, 1 is the answer to the equation of 6 divided by 2 (1+2).

I therefore conclude that by using algebra, PEMDAS is wrong.

To the guy who "disproved" PEMDAS with algebra, distribution has equal precedence with multiplication/division, because IT IS multiplication.

Plus, PEMDAS isn't a theory, it's an agreed upon convention. You can't disprove it.

[chaos_knight]

to those saying that the answer should be 9 based on PEMDAS, you should also note that the number 2 outside the parenthesis is still part of the parenthesis equation. if you could recall the distributive law, 2 has been factored out in the parenthesis based on this law: m(a+b) = (ma + mb)

hence, the number 2 was just factored out of the equation because of the distributive property. That is the reason why we don't see any multiplication sign between 2 and the parenthesis equation because they are considered as one term. As such, it is right to solve the 2(1+2) equation first because of the distributive law. By doing this, the answer should be 1.

[dashingdevonair]

to those saying that the answer should be 9 based on PEMDAS, you should also note that the number 2 outside the parenthesis is still part of the parenthesis equation. if you could recall the distributive law, 2 has been factored out in the parenthesis based on this law: m(a+b) = (ma + mb)

hence, the number 2 was just factored out of the equation because of the distributive property. That is the reason why we don't see any multiplication sign between 2 and the parenthesis equation because they are considered as one term. As such, it is right to solve the 2(1+2) equation first because of the distributive law. By doing this, the answer should be 1.

You cannot use the distributive property because a dividing operator exists in front of 2(1+2). This is where PEMDAS comes in.

m+n(a+b) is different from m/n(a+b). The distributive property you mentioned is only applicable to the first case and cannot be applied to the second case.

[dashingdevonair]

If you must use the distributive property, the equation would become

[(6/2)x1] + [(6/2)x2]

which still leads to the answer 9.

[ojodelaplata]

To the guy who "disproved" PEMDAS with algebra, distribution has equal precedence with multiplication/division, because IT IS multiplication.

Plus, PEMDAS isn't a theory, it's an agreed upon convention. You can't disprove it.

agreed-upon convention? Then, that means, we could change it to suit the needs of changing times. Do you think, someone who has little time but needs to do such an equation would belabor himself into using so many brackets and parentheses? As much as possible, he needs to do away with the brackets if he needs to save time.

I say, relax the freakin' rigid rules if we want to make it more useful to humankind. In fact, if it's not applied to reality, it's of no use. This is me, of course, saying as a layman as it's been a long time since I last had a math subject...

[dashingdevonair]

ojo, PEMDAS and brackets are there to make our lives easier and to avoid misinterpretation on the part of the reader.

They may seem utterly useless in short elementary equations such as this one, but I can assure you that they come in handy in extremely long equations found in calculus or physics.

[aquarian21]

1 ang sagot. 6/2(1+2).
Meron tayong tinatawag na distributive property di ba? so 6/(2+4)
6/6=1

[jaguarzxxx]

Ojo, why the heck are you so hell bent on changing the rules and disproving things? :P This is a question designed to get a discussion going. We are meant to argue with each other, not with math itself and it's rules.

Yes, it's a convention that can be changed to suit new needs. And maybe you can't see it applied to reality. But to us, it's working just fine. So maybe you can make your own convention to suit your own needs. Just don't expect the rest of the world to agree with you. :P

Just to keep the thread going, isn't a(b+c) the same as a*(b+c)?

So why the heck should one get a higher precedence over the other? Distribution is just fancy multiplication.

[ojodelaplata]

Ojo, why the heck are you so hell bent on changing the rules and disproving things? :P This is a question designed to get a discussion going. We are meant to argue with each other, not with math itself and it's rules.

Yes, it's a convention that can be changed to suit new needs. And maybe you can't see it applied to reality. But to us, it's working just fine. So maybe you can make your own convention to suit your own needs. Just don't expect the rest of the world to agree with you. :P

are you starting a fight with me? peace tayo, bro...

[ubermensch]

agreed-upon convention? Then, that means, we could change it to suit the needs of changing times. Do you think, someone who has little time but needs to do such an equation would belabor himself into using so many brackets and parentheses? As much as possible, he needs to do away with the brackets if he needs to save time.

I say, relax the freakin' rigid rules if we want to make it more useful to humankind. In fact, if it's not applied to reality, it's of no use. This is me, of course, saying as a layman as it's been a long time since I last had a math subject...

Why would someone have so little time that he wouldn't have time to use grouping symbols? There's efficiency, and there's also making sure you are clearly understood. If you leave things ambiguous, the reader's gonna waste a lot of time figuring out what you meant, when all you had to do was use a pair of grouping symbols.

The rules are fine. People just don't know how to use the rules.

[TTJed]

^ LOL.

[ojodelaplata]

Why would someone have so little time that he wouldn't have time to use grouping symbols?

Why wouldn't?

There's efficiency, and there's also making sure you are clearly understood. If you leave things ambiguous, the reader's gonna waste a lot of time figuring out what you meant, when all you had to do was use a pair of grouping symbols.

I doubt if there would really be efficiency when using brackets over and over again. It just makes things more complicated.

Re ambiguity: look how PEMDAS made things ambiguous? Had there been any exception or clarification, this thread would have not started! NOtice that calculators aren't even in consonance with their answers!

The rules are fine. People just don't know how to use the rules.

And you think the rules are fine but people just don't know how to use the rules? There has to be some clarifications there to erase the ambiguities. I say the rules aren't perfect. Just like in legal matters, laws are amended when they are subsequently found out to be imperfect. Sure, these are agreed-upon conventions. But who agreed with whom? When was PEMDAS established? Did they ever consider that this kind of ambiguity would arise? Should another group of mathematicians resolve this ambiguity? If so, how? And what clarifications should be done?

[rabii]

Makigulo nga dito.
Based on PEMDAS rule, my answer is 9.
kung susundin ang convention, ganito ang instruction or intrpretation sa given na expression or equation:
get the quotient of the expression 6/2 first, then get the sum of 2+1, then multiply the quotient with the sum. In simpler term, the reader should interpret the equation like this: multiply the quotient of 6/2 with the sum of 2+1

Yong mga nagsasabi na ang sagot ay 1 ay tama sila kung yong equation was presented thsi way:

6/(2(2+1)).

Yon naman mga nagsasabi na yong number 2 outide the parenthesis should be interpreted as part of the expression(2+1) as a factor dahil walang multiplication symbol and should be treated as a group or a single expression ay wala akong alam na rule or convention para isipin na ganito dapat ang treatment. Pwede rin kasi i-interpret na yong 6/2 was originally part of the equation inside the parathesis and the expression(fraction 6/3 ) was taken out of the equation as a factor. bakit kasi hindi na lang mag stick sa rule at sundin yong convention habang hindi pa naman ito pinapalitan.

[rabii]

correction : (fraction 6/2) dapat.