6 divided by 2(1+2)=?

[NicoleMarie]

In Algebra and above, whatever is below the division sign (the denominator of a fraction) is done first, as if in brackets, but no brackets are needed.

 

6

---------- = 1

2(1+2)

 

When the problem says 6 divided by 2(1+2), I do see that as 6 divided by the whole expression, as if it were in the denominator of a fraction. The fact that the expression is written algebraically (without the "times" sign) strengthens that assumption.

 

I agree that if it were written as a simple arithmetic problem, it should be 6 divided by 2 times (1+2), which would result in 6/2*(1+2) = 9

 

^^^ This is how I saw it.

I say the answer is 1.

[Paula in MS]

 

 

If it is 6/2x=1, the answer is x=1/3. If it is 6 divided by 2x=1, then the answer is x=3. If there were brackets around 2x, then the answer would be 3 in 6/[2x]=1.

 

No, it can never be 1/3. If you divide 6 by 2, you must also divide 6 by x which would give you an answer of x=3. You will never see brackets around a 2x. It will be implied that 2 and x go together. Always. 6/2x will never be simplified 3x. It is simplified 3/x or 3 over x.

[Joker]

nm

[Barb_]

The three would still be in parentheses after 1 + 2 is done first due to order of operations. The parentheses must be eliminated before the division can take place. Therefore, the 2 must be distributed to the three. This gives an answer of six and then it is six/six.

 

Most people are skipping that fact that parentheses was NOT eliminated simply by doing the addition. That answer would still be inside the () 2(3) must be solved before the simple division outside of (). Essentially, 2(1+2) is all one unit or exp<b></b>ression. It is a simple issue of order of operations, but it is easy to overlook that fact that after adding the two numbers, the answer is still in ().

 

Dh has a bachelor's in mathematics and agrees with me. The answer is one.

 

Faith

 

 

You almost had me until I happened to think it really isn't the 2 that you are distributing but the 6 over 2 (six halves...set up like a fraction). That's why you never see a division sign in algebra. It's always a fraction. You can distribute the fraction as a three or you can distribute the 6/2 as a fraction. Either way the result is 9. Unless of course the 2(2+1) is actually intended to remain as a unit in the denominator of the fraction, that is, 6 over the result of 2(2+1). At that point all bets are off. It's like that brainteaser drawing that looks like an old lady from one perspective and a young woman from another.

[jbuggie]

The answer is 9. You use PE(MD)AS

 

6/2(1+2)=x

 

You do what is inside the parentheses first, do not distribute.

 

6/2(3)=x

 

Then you do from left to right so you divide first

 

3(3)=x

 

Then you multiply

 

X=9