math help

What is 6/11 + 10/12?

What is 6/11 + 10/12?

Here's how we add

6
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 6 by 12, and get 72, then we multiply 11 by 12 and get 132.

6/11 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:

72
132
 +
110
132

Step 2

Since our denominators match, we can add the numerators.

72 + 110 = 182

That gives us the sum, which is

182
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:

182
132
 ÷ 2 =
91
66

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

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

There you have it! Here's the final answer to 6/11 + 10/12

6
11
 +
10
12
 =
91
66
© 2014 Randy Tayler

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