math help

What is 9/11 + 9/12?

What is 9/11 + 9/12?

This is how to add

9
11
 +
9
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 9 by 12, and get 108, then we multiply 11 by 12 and get 132.

9/11 times 12

Now for the second term. You multiply 9 by 11, and get 99, then multiply 11 by 12 and get 132.

9/12 times 11

This gives us a new problem that looks like so:

108
132
 +
99
132

Step 2

Since our denominators match, we can add the numerators.

108 + 99 = 207

That gives us an answer of

207
132

Step 3

Can this fraction be reduced?

First, we attempt to divide 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:

207
132
 ÷ 3 =
69
44

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...

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. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. 47 is larger than 44. So we're done reducing.

And we're done! Here's the final answer to 9/11 + 9/12

9
11
 +
9
12
 =
69
44
© 2014 Randy Tayler

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