Let's 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 7 by 10 and get 70. Do the same for the second term. We multiply 4 by 7, and get 28, then multiply 7 by 10 and get 70. The problem now has new fractions to add:


Step 2Since our denominators match, we can add the numerators. 10 + 28 = 38 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... 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... No good. 23 is larger than 19. So we're done reducing. Congratulations! Here's your final answer to 1/7 + 4/10
