Math Help - When one divides 2x by 2, why isn't the x part divided by 2 as well?

1. When one divides 2x by 2, why isn't the x part divided by 2 as well?

When one divides 2x by 2, why isn't the x part divided by 2 as well?

I was thinking that maybe it's because 2x is one term only but it can also be written as x+x and I think that if one were to divide x+x by 2, one would have to divide both x's. So clearly in 2x, one must divide the x's. I looked at the math later and realized that this makes 1x. Okay so then what makes 2x a single term and its equivalent, x+x, two terms?

Thanks for feedback.

2. Originally Posted by bournouli
I was thinking that maybe it's because 2x is one term only but it can also be written as x+x and I think that if one were to divide x+x by 2, one would have to divide both x's.
Correct. Then you'd get (x/2) + (x/2) = x, the same as if you had just divided the 2x by the 2. Naturally, you should get the same result either way!

So clearly in 2x, one must divide the x's. I looked at the math later and realized that this makes 1x. Okay so then what makes 2x a single term and its equivalent, x+x, two terms?
The addition symbol or lack thereof.

3. Originally Posted by Ackbeet
Correct. Then you'd get (x/2) + (x/2) = x, the same as if you had just divided the 2x by the 2. Naturally, you should get the same result either way!

The addition symbol or lack thereof.

Yet, since 2x=2*2, then why doesn't the presence of the multiplication sign create two terms in 2x?

4. Originally Posted by bournouli
Yet, since 2x=2*2,
That's only true if x = 2. Do you know that in advance?

then why doesn't the presence of the multiplication sign create two terms in 2x?

5. Originally Posted by Ackbeet
That's only true if x = 2. Do you know that in advance?

Sorry, I meant x+x.

And likewise x+x is the correct phrasing. Also, I take it that the presence of an operator like, "+", determines what is a term. If that's true, then why isn't 2x two terms by virtue of it being equal to x+x?

6. Originally Posted by bournouli
Sorry, I meant x+x.

And likewise x+x is the correct phrasing. Also, I take it that the presence of an operator like, "+", determines what is a term. If that's true, then why isn't 2x two terms by virtue of it being equal to x+x?
By definition. x and x (in the expression x + x) are like terms; so you could add them together to just get one term. I'm not sure this answers your question, but I think I understand better what the question is.

7. terms and factors

Yes, you are correct about needing to know how to identify terms and factors. This is the area that most arithmetic and algebra students make their mistakes. Yet, most instructors do not make a big deal about this!
Terms are separated by addition and subtraction signs not inside parenthesis. Once you have a single term you can now talk about its factors. Factors are separated by multiplication and division signs not inside parenthesis.
EACH term must be divided by the WHOLE denominator.
Why is 2x/2 = x and not x/2. Think about what 2x/2 says in words! It says to double some number or to multiply some number by 2 and then divide this result by 2. Do you see that the multiplication by 2 and dividing by 2 cancel out leaving the original number x? 2 times 7 is 14 and 14 divided by 2 is 7. Another example: (4times4) divided by 2. 1st the correct answer will be 16/2 or 8. Now if we divide both 4s by 2 we will be left with 2times2 or 4, not 8! On the other hand, (4+4)/2 = 8/2 = 4. But (4 + 4)/2 does not equal (2 + 4) = 6 (I divided the 1st 4 by 2 only). If we divide both 4s by 2 we get 2+ 2 =4, the correct result.

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8. Another point: yes, if you write 2x as x+ x, then you must divide each x by 2:
(x+ x)/2= (x/2)+ (x/2)= x as before.