math help

What is 8/11 + 6/9?

What is 8/11 + 6/9?

This is how to add

8
11
 +
6
9

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 8 by 9, and get 72, then we multiply 11 by 9 and get 99.

8/11 times 9

Do the same for the second term. We multiply 6 by 11, and get 66, then multiply 11 by 9 and get 99.

6/9 times 11

The problem now has new fractions to add:

72
99
 +
66
99

Step 2

Since our denominators match, we can add the numerators.

72 + 66 = 138

This yields the answer

138
99

Step 3

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

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

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

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

138
99
 ÷ 3 =
46
33

Now, try the same number again.

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...

No good. 37 is larger than 33. So we're done reducing.

Congratulations! Here's your final answer to 8/11 + 6/9

8
11
 +
6
9
 =
46
33
© 2014 Randy Tayler

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