math help

What is 9/10 + 11/12?

What is 9/10 + 11/12?

Here's how to add

9
10
 +
11
12

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 9 by 12, and get 108, then we multiply 10 by 12 and get 120.

9/10 times 12

Do the same for the second term. We multiply 11 by 10, and get 110, then multiply 10 by 12 and get 120.

11/12 times 10

The problem now has new fractions to add:

108
120
 +
110
120

Step 2

Since our denominators match, we can add the numerators.

108 + 110 = 218

This yields the answer

218
120

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
120
 ÷ 2 =
109
60

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...

No good. 61 is larger than 60. So we're done reducing.

There you have it! Here's the final answer to 9/10 + 11/12

9
10
 +
11
12
 =
109
60
© 2014 Randy Tayler

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