What is 31/12 + 6/9?

This is how you add

Step 1

Of 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 31 by 9, and get 279, then we multiply 12 by 9 and get 108.

Do the same for the second term. We multiply 6 by 12, and get 72, then multiply 12 by 9 and get 108.

The problem now has new fractions to add:

Step 2

Since our denominators match, we can add the numerators.

279 + 72 = 351

This yields the answer

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

Nope. Try the next prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

Now, try the same number again.

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

Now, try the same number again.

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

Now, try the same number again.

Nope. Try the next prime number, 5...

No good. 5 is larger than 4. So we're done reducing.

Congratulations! Here's your final answer to 31/12 + 6/9