math help

What is 8/11 + 10/12?

What is 8/11 + 10/12?

This is how to add

8
11
 +
10
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 8 by 12, and get 96, then we multiply 11 by 12 and get 132.

8/11 times 12

Now for the second term. You multiply 10 by 11, and get 110, then multiply 11 by 12 and get 132.

10/12 times 11

This gives us a new problem that looks like so:

96
132
 +
110
132

Step 2

Since our denominators match, we can add the numerators.

96 + 110 = 206

That gives us an answer of

206
132

Step 3

Can this fraction be reduced?

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

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

206
132
 ÷ 2 =
103
66

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. 67 is larger than 66. So we're done reducing.

And we're done! Here's the final answer to 8/11 + 10/12

8
11
 +
10
12
 =
103
66
© 2014 Randy Tayler

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