math help

What is 10/12 + 9/11?

What is 10/12 + 9/11?

Here's how to add

10
12
 +
9
11

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 10 by 11, and get 110, then we multiply 12 by 11 and get 132.

10/12 times 11

Do the same for the second term. We multiply 9 by 12, and get 108, then multiply 12 by 11 and get 132.

9/11 times 12

The problem now has new fractions to add:

110
132
 +
108
132

Step 2

Since our denominators match, we can add the numerators.

110 + 108 = 218

This yields the answer

218
132

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

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

218
132
 ÷ 2 =
109
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 10/12 + 9/11

10
12
 +
9
11
 =
109
66
© 2014 Randy Tayler

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