math help

What is 6/7 + 10/12?

What is 6/7 + 10/12?

Here's how to add

6
7
 +
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 6 by 12, and get 72, then we multiply 7 by 12 and get 84.

6/7 times 12

Now for the second term. You multiply 10 by 7, and get 70, then multiply 7 by 12 and get 84.

10/12 times 7

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

72
84
 +
70
84

Step 2

Since our denominators match, we can add the numerators.

72 + 70 = 142

Answer:

142
84

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:

142
84
 ÷ 2 =
71
42

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. 43 is larger than 42. So we're done reducing.

And we're done! Here's the final answer to 6/7 + 10/12

6
7
 +
10
12
 =
71
42
© 2014 Randy Tayler

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