math help

What is 20/17 + 6/12?

What is 20/17 + 6/12?

This is how to add

20
17
 +
6
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 20 by 12, and get 240, then we multiply 17 by 12 and get 204.

20/17 times 12

Now for the second term. You multiply 6 by 17, and get 102, then multiply 17 by 12 and get 204.

6/12 times 17

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

240
204
 +
102
204

Step 2

Since our denominators match, we can add the numerators.

240 + 102 = 342

That gives us the sum, which is

342
204

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:

342
204
 ÷ 2 =
171
102

Now, try the same number again.

Nope. Try the next prime number, 3...

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

171
102
 ÷ 3 =
57
34

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

No good. 37 is larger than 34. So we're done reducing.

Congratulations! Here's your final answer to 20/17 + 6/12

20
17
 +
6
12
 =
57
34
© 2014 Randy Tayler

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