Here's how you add
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 1 by 7, and get 7, then we multiply 3 by 7 and get 21.
Do the same for the second term. We multiply 1 by 3, and get 3, then multiply 3 by 7 and get 21.
So now our fractions look like this:
Since our denominators match, we can add the numerators.
7 + 3 = 10
Now we have an answer.
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...
Nope! So now we try the next greatest prime number, 3...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
Nope! So now we try the next greatest prime number, 11...
No good. 11 is larger than 10. So we're done reducing.
There you have it! Here's the final answer to 1/3 + 1/7