This is how we add
Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.
Now you multiply 1 by 5, and get 5, then we multiply 2 by 5 and get 10.
Do the same for the second term. We multiply 2 by 2, and get 4, then multiply 2 by 5 and get 10.
The problem now has new fractions to add:
Since our denominators match, we can add the numerators.
5 + 4 = 9
This yields the answer
The last step is to reduce the fraction if we can.
To find out, we try dividing it by 2...
Nope. Try the next prime number, 3...
Nope. Try the next prime number, 5...
Nope. Try the next prime number, 7...
Nope. Try the next prime number, 11...
No good. 11 is larger than 9. So we're done reducing.
Congratulations! Here's your final answer to 1/2 + 2/5