math help

What is 10/11 + 10/12?

What is 10/11 + 10/12?

Let's add

10
11
 +
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 10 by 12, and get 120, then we multiply 11 by 12 and get 132.

10/11 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

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

120
132
 +
110
132

Step 2

Since our denominators match, we can add the numerators.

120 + 110 = 230

Answer:

230
132

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:

230
132
 ÷ 2 =
115
66

Now, try the same number again.

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

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...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

No good. 67 is larger than 66. So we're done reducing.

Congratulations! Here's your final answer to 10/11 + 10/12

10
11
 +
10
12
 =
115
66
© 2014 Randy Tayler

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