 # What is 3/8 + 2/5? 3 8
+
 2 5

## 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 3 by 5, and get 15, then we multiply 8 by 5 and get 40. Do the same for the second term. We multiply 2 by 8, and get 16, then multiply 8 by 5 and get 40. The problem now has new fractions to add:

 15 40
+
 16 40

## Step 2

Since our denominators match, we can add the numerators.

15 + 16 = 31

 31 40

## Step 3

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

To find out, we try dividing 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...

No good. 37 is larger than 31. So we're done reducing.

There you have it! Here's the final answer to 3/8 + 2/5

 3 8
+
 2 5
=
 31 40