What is 3/11 + 4/9?

 3 11
+
 4 9

Step 1

Can 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 3 by 9, and get 27, then we multiply 11 by 9 and get 99.

Now for the second term. You multiply 4 by 11, and get 44, then multiply 11 by 9 and get 99.

We now have a new problem, that looks like this:

 27 99
+
 44 99

Step 2

Since our denominators match, we can add the numerators.

27 + 44 = 71

 71 99

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide 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...

No good. 73 is larger than 71. So we're done reducing.

There you have it! Here's the final answer to 3/11 + 4/9

 3 11
+
 4 9
=
 71 99