math help

What is 12/13 + 10/12?

What is 12/13 + 10/12?

Here's how you add

12
13
 +
10
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 12 by 12, and get 144, then we multiply 13 by 12 and get 156.

12/13 times 12

Now for the second term. You multiply 10 by 13, and get 130, then multiply 13 by 12 and get 156.

10/12 times 13

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

144
156
 +
130
156

Step 2

Since our denominators match, we can add the numerators.

144 + 130 = 274

That gives us the sum, which is

274
156

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:

274
156
 ÷ 2 =
137
78

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...

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. So next you try the next prime number, which is 59...

No good. So next you try the next prime number, which is 61...

No good. So next you try the next prime number, which is 67...

No good. So next you try the next prime number, which is 71...

No good. So next you try the next prime number, which is 73...

No good. So next you try the next prime number, which is 79...

No good. 79 is larger than 78. So we're done reducing.

And we're done! Here's the final answer to 12/13 + 10/12

12
13
 +
10
12
 =
137
78
© 2014 Randy Tayler

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