Here's how you add
Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.
So, we multiply 1 by 10, and get 10, then we multiply 3 by 10 and get 30.
Now for the second term. You multiply 5 by 3, and get 15, then multiply 3 by 10 and get 30.
We now have a new problem, that looks like this:
Since our denominators match, we can add the numerators.
10 + 15 = 25
Now, do we need to simplify this fraction?
First, we attempt to divide it by 2...
Nope. Try the next prime number, 3...
Nope. Try the next prime number, 5...
Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:
Now, try the same number again.
Nope. Try the next prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
Congratulations! Here's your final answer to 1/3 + 5/10