6÷2(1+2)=?

reply to post by Lysergic


This thread is definitely a classic.

Wish I could have been around when it was originally created.

It's that damned "/" symbol that caused all the problems with people using calculators and coming up with an answer of 1 on some calculators and 9 on others. Some calculators reading it as a fraction bar and some reading it as a division sign.

... and then of course we have the self-imposed brainiacs making illegal assumptions and reading more into the equation than the way it was actually written.

So... 27 pages later.

Originally posted by CranialSponge
6÷2(1+2)=?

I'm wondering why people are implying that the 2 is an exponent and therefore causing the equation to read as if it were a fraction because they're implying that the 2 then must be calculated before the 6 ??


You are forcing a fraction bar (between the 6 and 2) by implication.

This is an illegal mathematical move...

No. The illegal math move is forcing a multiplication operator where there is none. I explained this already. 2(2+1) is one operand, ie (4+2), showing a GCF of 2 outside the parentheses. The 2 is also a coefficient of the 2(2+1), which binds it to it. You can't use a coefficient of a literal as an operand without the rest. THAT my friend, is illegal.

Originally posted by CranialSponge

So basically, we are now looking at the equation as if each number is in it's own parenthesis: (6) ÷ (2) x (3)

Not basically, and completely incorrect. You changed the coefficient of (3) from a 2, to a 1, ie:
(6) ÷ (2) x (3) = (6) ÷ (2) x 1(3)
Illegal.

The incorrect answer is 9.

What is so hard to understand about "6 divided by two 2+1's" ?
That is exactly what is written...

to get 9, you change the equation to "6 divided by 2 times (2+1)" ie, 6 ÷ 2 * (2+1)
If you want to make a substitution, CONTAIN IT PARENTHESES. You are ignoring this rule.
EG:
Expression: 2(2+1).
I want to replace with: 2 * 2(2+1)
Original equation: 6 ÷ 2(2+1)
Now with subsstituted expression: 6 ÷ [2 * (2+1)]

I also forgot to mention that, not only can you not change the coefficient of 2, to a 1, ... you can't change it to (1/2) either.
WRONG INTERPRETATION: 6 ÷ 2(2+1) = 6 * (1/2)(2+1)
The coefficient magically changed to (1/2).

**A group of coefficients and literals are ALL ONE OPERAND.

Here are few links to solving division equations with groups of operands:

Originally posted by mathman26cstl.syr.edu...
www.wisc-online.com... (Slide 4)
www.math-mate.com... (This whole page is good, especially the notes on factorizing and expanding parentheses)

I noticed how no one has attempted any of the other simple expressions I posted, for instance:
1a ÷ 1a and 4xyz ÷ 2xz

Originally posted by ASeeker343
reply to post by Kody27

 

It is correct to solve left to right after following order of operations. In PEMDAS the M and D, multiplication and division are done at the same time before any addition or subtraction. Addition and subtraction are again done concurrently left to right. You dont go through and do all the addition first and then subtraction, same concept with multiplication and division.

[link]http://www.math.com/school/subject2/lessons/S2U1L2GL.html[link]

The correct answer is 9. You are multiplying out of order if you get 1.

Yes this is correct, the answer is 9, in most cases. There are only exceptions within the context of the lesson being taught at the time of the problem.

answer?


9


always was, always will be ...