math help

What is 15/11 + 9/12?

What is 15/11 + 9/12?

Here's how you add

15
11
 +
9
12

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 15 by 12, and get 180, then we multiply 11 by 12 and get 132.

15/11 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

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

180
132
 +
99
132

Step 2

Since our denominators match, we can add the numerators.

180 + 99 = 279

That gives us the sum, which is

279
132

Step 3

Now, do we need to simplify this fraction?

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:

279
132
 ÷ 3 =
93
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 15/11 + 9/12

15
11
 +
9
12
 =
93
44
© 2014 Randy Tayler

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