Here's how to add


Step 1We 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 5 by 9, and get 45, then we multiply 10 by 9 and get 90. Do the same for the second term. We multiply 4 by 10, and get 40, then multiply 10 by 9 and get 90. So now our fractions look like this:


Step 2Since our denominators match, we can add the numerators. 45 + 40 = 85 Now we have an answer.


Step 3Last 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. 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... Nope. Try the next prime number, 11... Nope. Try the next prime number, 13... Nope. Try the next prime number, 17... Nope. Try the next prime number, 19... No good. 19 is larger than 17. So we're done reducing. Congratulations! Here's your final answer to 5/10 + 4/9
