math help

What is 8/11 + 3/9?

What is 8/11 + 3/9?

This is how we add

8
11
+
3
9

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 8 by 9, and get 72, then we multiply 11 by 9 and get 99.

8/11 times 9

Now for the second term. You multiply 3 by 11, and get 33, then multiply 11 by 9 and get 99.

3/9 times 11

We now have a new problem, that looks like this:

72
99
+
33
99

Step 2

Since our denominators match, we can add the numerators.

72 + 33 = 105

That gives us the sum, which is

105
99

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...

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

105
99
÷ 3 =
35
33

Now, try the same number again.

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.

Congratulations! Here's your final answer to 8/11 + 3/9

8
11
+
3
9
=
35
33
© 2014 Randy Tayler