math help

What is 24/26 + 9/12?

What is 24/26 + 9/12?

Let's add

24
26
 +
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 24 by 12, and get 288, then we multiply 26 by 12 and get 312.

24/26 times 12

Now for the second term. You multiply 9 by 26, and get 234, then multiply 26 by 12 and get 312.

9/12 times 26

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

288
312
 +
234
312

Step 2

Since our denominators match, we can add the numerators.

288 + 234 = 522

That gives us the sum, which is

522
312

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

522
312
 ÷ 2 =
261
156

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 3...

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

261
156
 ÷ 3 =
87
52

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. So next you try the next prime number, which is 53...

No good. 53 is larger than 52. So we're done reducing.

And we're done! Here's the final answer to 24/26 + 9/12

24
26
 +
9
12
 =
87
52
© 2014 Randy Tayler

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