Here's 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 1 by 10, and get 10, then we multiply 3 by 10 and get 30. Do the same for the second term. We multiply 4 by 3, and get 12, then multiply 3 by 10 and get 30. The problem now has new fractions to add:


Step 2Since our denominators match, we can add the numerators. 10 + 12 = 22 This yields the answer


Step 3The last step is to reduce the fraction if we can. To find out, we try dividing it by 2... Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:
Let's try dividing by that again... 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... No good. 13 is larger than 11. So we're done reducing. There you have it! Here's the final answer to 1/3 + 4/10
