Hello guys I need help with solving this combining like terms problem. OK -1/2a+3a-1/2+3/4

Question

anonymous · Answer

I get 11/4 + a squared

mathstudent55 · Answer

Do you know what like terms are?

anonymous · Answer

Yes I do

mathstudent55 · Answer

Ok, now look at the expression you have, which terms are like terms?

anonymous · Answer

Well you have the fractions and the variables

mathstudent55 · Answer

Let me give you an example without variables to explain like terms.
Let's say you have 5 oranges and 2 apples.
I give you 3 oranges and 4 apples.
What do you have now?

mathstudent55 · Answer

Your problem is to combine like terms in this expression:
5 oranges + 2 apples + 3 oranges + 2 apples
What is the sum?

anonymous · Answer

8 oranges + 4 apples but you would have 12 fruits

mathstudent55 · Answer

Yes, you are correct in both statements.
In math, though, we keep the variables separate.
If you have 
5a + 3b + 2a + 4b, 
you can combine the terms with a together, and you can combine the terms with b together, but you can't combine terms with a and be together.
So 
5a + 3b + 2a + 4b
= 5a + 2a + 3b + 4b
= 7a + 7b
There is no more you can do.

mathstudent55 · Answer

Now let's get back to your problem.

mathstudent55 · Answer

Like terms have exactly the same variable parts.
Terms with a are like terms and can be combined.
Terms with no variable are like terms and can be combined.
Terms with a and terms without a variable are NOT like terms and CANNOT be combined toghether.

mathstudent55 · Answer

This is your problem, correct?

$ \dfrac{1}{2}a+3a-\dfrac{1}{2}+\dfrac{3}{4} $

mathstudent55 · Answer

The first two terms have the variable a. They are like terms and can be combined together.
The last two terms have no variable. They are like terms and can be combined together.

anonymous · Answer

So is it 7/2 a -1/4?

anonymous · Answer

But actually the textbook is telling me that 1/2 a is 1/2 * a

mathstudent55 · Answer

Since we have fractions, we need common denominators.

$\dfrac{1}{2}a+3a-\dfrac{1}{2}+\dfrac{3}{4}$

$= \dfrac{1}{2}a+\dfrac{3}{1}a -\dfrac{1}{2}+\dfrac{3}{4} $

$= \dfrac{1}{2}a+\dfrac{2}{2} \times \dfrac{3}{1}a -\dfrac{2}{2} \times \dfrac{1}{2}+\dfrac{3}{4} $

$= \dfrac{1}{2}a+\dfrac{6}{2}a -\dfrac{2}{4}+\dfrac{3}{4} $

$= \dfrac{7}{2}a +\dfrac{1}{4} $

anonymous · Answer

Well I got - 1/4 so yes I was right except for the sign well thank you :-) for helping me mathstudent!

mathstudent55 · Answer

You were close. Good effort.
You're welcome.