 # What is 4/7 + 1/3? Let's add

 4 7
+
 1 3

## 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 4 by 3, and get 12, then we multiply 7 by 3 and get 21. Now for the second term. You multiply 1 by 7, and get 7, then multiply 7 by 3 and get 21. We now have a new problem, that looks like this:

 12 21
+
 7 21

## Step 2

Since our denominators match, we can add the numerators.

12 + 7 = 19

That gives us the sum, which is

 19 21

## 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...

No good. 23 is larger than 19. So we're done reducing.

There you have it! Here's the final answer to 4/7 + 1/3

 4 7
+
 1 3
=
 19 21
© 2014 Randy Tayler