 # What is 4/7 + 3/5? 4 7
+
 3 5

## 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 5, and get 20, then we multiply 7 by 5 and get 35. Now for the second term. You multiply 3 by 7, and get 21, then multiply 7 by 5 and get 35. We now have a new problem, that looks like this:

 20 35
+
 21 35

## Step 2

Since our denominators match, we can add the numerators.

20 + 21 = 41

 41 35

## Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

No good. 37 is larger than 35. So we're done reducing.