We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 2 by 2, and get 4, then we multiply 3 by 2 and get 6.
Do the same for the second term. We multiply 1 by 3, and get 3, then multiply 3 by 2 and get 6.
So now our fractions look like this:
Since our denominators match, we can add the numerators.
4 + 3 = 7
So the answer is:
Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?
To find out, we try dividing it by 2...
No good. So next you try the next prime number, which is 3...
No good. So next you try the next prime number, which is 5...
No good. So next you try the next prime number, which is 7...
No good. 7 is larger than 6. So we're done reducing.
And we're done! Here's the final answer to 2/3 + 1/2