This is how we add


Step 1Of 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 10 by 9, and get 90, then we multiply 11 by 9 and get 99. Do the same for the second term. We multiply 8 by 11, and get 88, then multiply 11 by 9 and get 99. The problem now has new fractions to add:


Step 2Since our denominators match, we can add the numerators. 90 + 88 = 178 The sum we get is


Step 3The last step is to reduce the fraction if we can. 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. So next you try the next prime number, which is 11... No good. So next you try the next prime number, which is 13... No good. So next you try the next prime number, which is 17... No good. So next you try the next prime number, which is 19... No good. So next you try the next prime number, which is 23... No good. So next you try the next prime number, which is 29... No good. So next you try the next prime number, which is 31... No good. So next you try the next prime number, which is 37... No good. So next you try the next prime number, which is 41... No good. So next you try the next prime number, which is 43... No good. So next you try the next prime number, which is 47... No good. So next you try the next prime number, which is 53... No good. So next you try the next prime number, which is 59... No good. So next you try the next prime number, which is 61... No good. So next you try the next prime number, which is 67... No good. So next you try the next prime number, which is 71... No good. So next you try the next prime number, which is 73... No good. So next you try the next prime number, which is 79... No good. So next you try the next prime number, which is 83... No good. So next you try the next prime number, which is 89... No good. So next you try the next prime number, which is 97... No good. So next you try the next prime number, which is 101... No good. 101 is larger than 99. So we're done reducing. And we're done! Here's the final answer to 10/11 + 8/9
