What is 21/63 + 3/5?

Let's add

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 21 by 5, and get 105, then we multiply 63 by 5 and get 315.

Do the same for the second term. We multiply 3 by 63, and get 189, then multiply 63 by 5 and get 315.

So now our fractions look like this:

Step 2

Since our denominators match, we can add the numerators.

105 + 189 = 294

Now we have an answer.

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

No good. So next you try the next prime number, which is 3...

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

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

Are both the numerator and the denominator evenly divisible by 7? Yes! So we reduce it:

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. 17 is larger than 14. So we're done reducing.

And we're done! Here's the final answer to 21/63 + 3/5