math help

What is 10/11 + 9/12?

What is 10/11 + 9/12?

Here's how to add

10
11
 +
9
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 10 by 12, and get 120, then we multiply 11 by 12 and get 132.

10/11 times 12

Do the same for the second term. We multiply 9 by 11, and get 99, then multiply 11 by 12 and get 132.

9/12 times 11

The problem now has new fractions to add:

120
132
 +
99
132

Step 2

Since our denominators match, we can add the numerators.

120 + 99 = 219

This yields the answer

219
132

Step 3

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

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

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

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

219
132
 ÷ 3 =
73
44

Let's try dividing by that again...

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...

No good. 47 is larger than 44. So we're done reducing.

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

10
11
 +
9
12
 =
73
44
© 2014 Randy Tayler

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