This is how we add


Step 1Can 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 10 by 7, and get 70, then we multiply 12 by 7 and get 84. Now for the second term. You multiply 2 by 12, and get 24, then multiply 12 by 7 and get 84. We now have a new problem, that looks like this:


Step 2Since our denominators match, we can add the numerators. 70 + 24 = 94 That gives us the sum, which is


Step 3Now, do we need to simplify this fraction? First, we attempt to divide it by 2... Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:
Now, try the same number again. 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... Nope. Try the next prime number, 13... Nope. Try the next prime number, 17... Nope. Try the next prime number, 19... Nope. Try the next prime number, 23... Nope. Try the next prime number, 29... Nope. Try the next prime number, 31... Nope. Try the next prime number, 37... Nope. Try the next prime number, 41... Nope. Try the next prime number, 43... No good. 43 is larger than 42. So we're done reducing. Congratulations! Here's your final answer to 10/12 + 2/7
