6÷2(1+2)=?

If you want to know the truth there is really only multiplication and addition - no division nor subtraction

(I know you can't handle the toof )

division such as 6 ÷ 2 is really 6 * (1/2) that is six times one half.

Or even 6 * 2 ^-1. six times 2 to the minus one.

subtraction 3 - 1 is really 3 + (-1) that is three plus negative one.

and when ever you see 3 (Y + 1) it is really 3 * (Y + 1) or 3 * Y + 3

stick to those rules and there will never be a problem interpreting.

6 ÷ 2 (1+2) ÷ 9 = 6 * (1/2) * (1 + 2) * (1/9) = 1

paste into google 6 ÷ 2 (1 + 2) ÷ 9. How else would you do it?

so .... 6 ÷ 2 (1 + 2) = 9 = 6 * (1/2) * (1 + 2)

this page may be of some help (note rules 1 thru 3 there)

www.mathgoodies.com...

also subtraction

from the above wiki article ...

In mathematics, it is often useful to view or even define subtraction as a kind of addition, the addition of the additive inverse. We can view 7 − 3 = 4 as the sum of two terms: 7 and -3. This perspective allows us to apply to subtraction all of the familiar rules and nomenclature of addition. Subtraction is not associative or commutative—in fact, it is anticommutative and left-associative—but addition of signed numbers is both.

I would argue that a similar thing may be said of division and that by using inverse multiplication all confusion would cease to exist.

have fun kids ....

9

Originally posted by xxsomexpersonxx
My spin on this:
6÷2(1+2) is the same as 6÷2*(1+2)
2(1+2) is no different than 2*(1+2), just like 2X = 2*X

so 6÷2*(3) = 9

The answer is 9, but it's a simple oversight to cause it to look like one.

edit on 2-5-2011 by xxsomexpersonxx because: (no reason given)

actually, you almost had it on line #2 ... you are correct that 2(1+2) is no different than 2*(1+2)
however, the answer to both is 6 and 6 divided by 6 only equals 1

2(1+2) = 2*(1+2) = (2*1)+(2*2) = (2+4) = 6

Originally posted by grey580
For example: 6÷2×3 = 9, not 1. 6-2+3 = 7, not 1.

many of us were educated long before the citations of wiki existed ... hint: wiki has been wrong more than once.
for the record, your linear equation of 6/2x3 = 9 does and will always = 9
however, the expression as printed is NOT and i repeat it is NOT a linear problem.

what everyone seems to be overlooking is the fact that although, both division and multiplication are on the same 'level' of processing ... the sum of the addition within the parenthesis is "ordered" by a multiplier -2 (higher level) and must be performed UPON the sum before division can be properly or sequentially applied.
the only Correct answer is "1".

Originally posted by Honor93

Originally posted by grey580
For example: 6÷2×3 = 9, not 1. 6-2+3 = 7, not 1.

the sum of the addition within the parenthesis is "ordered" by a multiplier -2 (higher level) and must be performed UPON the sum before division can be properly or sequentially applied.

Simply not true. No such thing. Convention must be accepted. Here is the convention.

www.mathgoodies.com...

Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Like I said 6 * (1/2) * (1+2) = 9

rule 1: 6 / 2 (3)
rule 2: 3 * 3

Originally posted by MegaMind

Originally posted by GobbledokTChipeater

Originally posted by MegaMind

Let me ask you what is 1/3 (X + Y) distributed?

x/3 + y/3 correct?

or

(X + Y)/3

or

(X + Y)

Actually, I read it as

1 / (3X + 3Y).

Now you mention it this way, I distinctly remember this problem from my uni text books. If I can find it tomorrow, I will scan the relevant pages up and post.

You are violating the rules with that.

A (B + C) = AB + AC

A = 1/3

therefore,

1/3B + 1/3C

Basic algebra

same as (X + Y)/3 or (B + C)/3

edit on 2-5-2011 by MegaMind because: (no reason given)

edit on 2-5-2011 by MegaMind because: (no reason given)

and you are making rules up as you go along ...
never is any problem which starts with 1 divided by ... figured as x or y divided by 3 ... never ever.
your equation reads (distributes / defines) as ... 1 divided BY the sum of 3 times x+y
do you really transpose orders and numbers at leisure?

reply to post by IamBoon


I got 2 different answers from two different calculators. What gives?

Originally posted by MegaMind
reply to post by IamBoon

 

Simply doesn't matter.

A = 6/2, B = 1, C =2

A (B + C) = AB + BC

6 / 2 (1 + 2) = 9

(1 + 2) is NOT a denominator PERIOD. If it were it would be 6 / (2 (1 + 2)) but it is NOT.

no and no and no again ... A never equals the equation unless in brackets
a = 6 period ... not 6 divided by 2
in this equation, a=6 b=2(c) and c=(1+2)
try that and see if you get 9

reply to post by Honor93


A (B + C) = AB + AC

1 / 3 (B + C) = (1/3)B + (1/3)C

is that clear? what don't u get? A = 1/3, or 6/2 or whatever the hell else you want it to be.

Originally posted by Honor93
in this equation, a=6 b=2(c) and c=(1+2)
try that and see if you get 9

This statement you made above about the equation A (B+C) = AB + AC and 6 / 2 (1 + 2) clearly shows you do not have even a basic grasp of algebra.

Originally posted by MegaMind

Originally posted by Whatsreal
Is this really still going... the answer is 1... just drop it... the idiots saying 9 are idiots...

DISTRIBUTIVE RULE.... so many people are saying 2(2+1) ..... that the 2 doesn't need to be distributed after doing whats inside the parenthesis???.... well you're wrong, just because you simplified whats in the parenthesis they do not magically disappear.... and you can still distribute the 2 before hand and get the same answer....

6/2(2+1)

6/(2*2 + 1*2)

6/(4+2)

6/(6)

1

please stop confusing the young lad who originally asked the question...

the distributive rule is A (B + C) = AB + AC

therefore,

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

A = 6/2 --- NOT --- 2

please pay attention to what you are writing ... your thought pattern seems to be on the mark but your writing leaves much to be considered.

A does not equal 6/2
a = 6
b = 2 times the sum of c
c= (1+2)
which calculates to the answer 1, only.

reply to post by MegaMind


I cannot take anyone seriously who says 15y/5y = 3yy.

Originally posted by Honor93

please pay attention to what you are writing ... your thought pattern seems to be on the mark but your writing leaves much to be considered.

A does not equal 6/2
a = 6
b = 2 times the sum of c
c= (1+2)
which calculates to the answer 1, only.

you are simply wrong. WRONG!!!

A (B + C) = AB + AC

according to your substitution from above the eq yields.

6 (2 * (1+2) + (1+2)) This is just garbage.

the correct substitutions for the equation are

A = 6/2 (a fraction get over it)
B = 1
C = 2

6 / 2 (1 + 2)

Originally posted by MegaMind

Originally posted by knightseifer

but for 6÷2(1+2) , we cannot use 6÷2 as A

Sure you can! "A" can be any damn thing you want!!!

A ( B + C) = AB + AC

edit on 2-5-2011 by MegaMind because: (no reason given)

only in your fantasy land or mind apparently.
a = a .. in this case 6
b = b .. in this case 2
c = c .. in this case (1+2)
if the sum of c times 2 divided by 6 = 9 ... then i need another drink.

Originally posted by IamBoon
reply to post by MegaMind

 

I cannot take anyone seriously who says 15y/5y = 3yy.

I never did! It is 3 just 3!!!

If standard notation applies this would generally be interpreted as (15 * y) / (5 * y) = 3

Originally posted by Honor93

Originally posted by MegaMind

Originally posted by knightseifer

but for 6÷2(1+2) , we cannot use 6÷2 as A

Sure you can! "A" can be any damn thing you want!!!

A ( B + C) = AB + AC

edit on 2-5-2011 by MegaMind because: (no reason given)

only in your fantasy land or mind apparently.
a = a .. in this case 6
b = b .. in this case 2
c = c .. in this case (1+2)
if the sum of c times 2 divided by 6 = 9 ... then i need another drink.

No ... I give up you have no concept of algebra at all!

reply to post by MegaMind


YOu cannot get rid of y!!!!!!! It doesn't disappear. No matter what y is the equation will ALWAYS be equivalent to 3*y! or 3y!

If you write the equation 6/2(1+2) like a sentence, you will automatically know how it is supposed to be solved.

Six divided by two "times" one plus two equals.

- Six divided by two equals three.

- Three "times" one plus two equals nine.

Originally posted by IamBoon
reply to post by MegaMind

 

YOu cannot get rid of y!!!!!!! It doesn't disappear. No matter what y is the equation will ALWAYS be equivalent to 3*y! or 3y!

Go back to your school and demand a refund!

15 * y
--------- = 3
5 * y

"y"s cancel

Originally posted by Honor93

Originally posted by grey580
For example: 6÷2×3 = 9, not 1. 6-2+3 = 7, not 1.

many of us were educated long before the citations of wiki existed ... hint: wiki has been wrong more than once.
for the record, your linear equation of 6/2x3 = 9 does and will always = 9
however, the expression as printed is NOT and i repeat it is NOT a linear problem.

what everyone seems to be overlooking is the fact that although, both division and multiplication are on the same 'level' of processing ... the sum of the addition within the parenthesis is "ordered" by a multiplier -2 (higher level) and must be performed UPON the sum before division can be properly or sequentially applied.
the only Correct answer is "1".

I graduated in HS in 1990. By no means a math wiz.
And of course Wikipedia can be wrong. It has people involved with it. No one is perfect.
And not just using Wikipedia as a source. I've gone to several websites that explain PEMDAS.
From what I can gather using solely PEMDAS the answer to this problem is 9.

NOW WITH THAT BEING SAID!

Solely using PEMDAS to solve this problem you get an answer of 9.

Several of you are applying Distributive Properties to this equation that is a function of algebra. Giving an answer of 1.

Now the real question here is and that someone has yet to answer IS THIS AN ALGEBRA PROBLEM?

If this is algebra then the answer is 1.
If it's not algebra then the answer is 9.

NO ONE HERE HAS YET TO ANSWER THIS QUESTION.

And it's just mental masturbation to sit here and try to answer the problem before setting the ground rules of the question.

The way I'm seeing it is that the question can not be answered properly because.
6 / 2(1+2) IS AN AMBIGUOUS STATEMENT.

This is the most annoying thread ever.