 # What is 5/10 + 6/9? 5 10
+
 6 9

## 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 5 by 9, and get 45, then we multiply 10 by 9 and get 90. Do the same for the second term. We multiply 6 by 10, and get 60, then multiply 10 by 9 and get 90. The problem now has new fractions to add:

 45 90
+
 60 90

## Step 2

Since our denominators match, we can add the numerators.

45 + 60 = 105

The sum we get is

 105 90

## 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...

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

 105 90
÷ 3 =
 35 30

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

 35 30
÷ 5 =
 7 6

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 6. So we're done reducing.

There you have it! Here's the final answer to 5/10 + 6/9

 5 10
+
 6 9
=
 7 6