Let's 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 7 by 9, and get 63, then we multiply 16 by 9 and get 144. Do the same for the second term. We multiply 4 by 16, and get 64, then multiply 16 by 9 and get 144. So now our fractions look like this:


Step 2Since our denominators match, we can add the numerators. 63 + 64 = 127 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! 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... Nope! So now we try the next greatest prime number, 13... Nope! So now we try the next greatest prime number, 17... Nope! So now we try the next greatest prime number, 19... Nope! So now we try the next greatest prime number, 23... Nope! So now we try the next greatest prime number, 29... Nope! So now we try the next greatest prime number, 31... Nope! So now we try the next greatest prime number, 37... Nope! So now we try the next greatest prime number, 41... Nope! So now we try the next greatest prime number, 43... Nope! So now we try the next greatest prime number, 47... Nope! So now we try the next greatest prime number, 53... Nope! So now we try the next greatest prime number, 59... Nope! So now we try the next greatest prime number, 61... Nope! So now we try the next greatest prime number, 67... Nope! So now we try the next greatest prime number, 71... Nope! So now we try the next greatest prime number, 73... Nope! So now we try the next greatest prime number, 79... Nope! So now we try the next greatest prime number, 83... Nope! So now we try the next greatest prime number, 89... Nope! So now we try the next greatest prime number, 97... Nope! So now we try the next greatest prime number, 101... Nope! So now we try the next greatest prime number, 103... Nope! So now we try the next greatest prime number, 107... Nope! So now we try the next greatest prime number, 109... Nope! So now we try the next greatest prime number, 113... Nope! So now we try the next greatest prime number, 127... Nope! So now we try the next greatest prime number, 131... No good. 131 is larger than 127. So we're done reducing. There you have it! Here's the final answer to 7/16 + 4/9
