math help

What is 6/19 + 6/12?

What is 6/19 + 6/12?

Let's add

6
19
 +
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 6 by 12, and get 72, then we multiply 19 by 12 and get 228.

6/19 times 12

Now for the second term. You multiply 6 by 19, and get 114, then multiply 19 by 12 and get 228.

6/12 times 19

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

72
228
 +
114
228

Step 2

Since our denominators match, we can add the numerators.

72 + 114 = 186

Answer:

186
228

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:

186
228
 ÷ 2 =
93
114

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:

93
114
 ÷ 3 =
31
38

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 31. So we're done reducing.

Congratulations! Here's your final answer to 6/19 + 6/12

6
19
 +
6
12
 =
31
38
© 2014 Randy Tayler

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