math help

What is 21/63 + 3/11?

What is 21/63 + 3/11?

Here's how to add

21
63
+
3
11

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 21 by 11, and get 231, then we multiply 63 by 11 and get 693.

21/63 times 11

Do the same for the second term. We multiply 3 by 63, and get 189, then multiply 63 by 11 and get 693.

3/11 times 63

The problem now has new fractions to add:

231
693
+
189
693

Step 2

Since our denominators match, we can add the numerators.

231 + 189 = 420

This yields the answer

420
693

Step 3

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

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:

420
693
÷ 3 =
140
231

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:

140
231
÷ 7 =
20
33

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. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. 23 is larger than 20. So we're done reducing.

And we're done! Here's the final answer to 21/63 + 3/11

21
63
+
3
11
=
20
33
© 2014 Randy Tayler