math help

What is 21/11 + 9/12?

What is 21/11 + 9/12?

Here's how we add

21
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 21 by 12, and get 252, then we multiply 11 by 12 and get 132.

21/11 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:

252
132
 +
99
132

Step 2

Since our denominators match, we can add the numerators.

252 + 99 = 351

So what's the answer so far?

351
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:

351
132
 ÷ 3 =
117
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 21/11 + 9/12

21
11
 +
9
12
 =
117
44
© 2014 Randy Tayler

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