math help

What is 11/12 + 8/9?

What is 11/12 + 8/9?

Here's how you add

11
12
+
8
9

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 11 by 9, and get 99, then we multiply 12 by 9 and get 108.

11/12 times 9

Do the same for the second term. We multiply 8 by 12, and get 96, then multiply 12 by 9 and get 108.

8/9 times 12

So now our fractions look like this:

99
108
+
96
108

Step 2

Since our denominators match, we can add the numerators.

99 + 96 = 195

So the answer is:

195
108

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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:

195
108
÷ 3 =
65
36

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 36. So we're done reducing.

Congratulations! Here's your final answer to 11/12 + 8/9

11
12
+
8
9
=
65
36
© 2014 Randy Tayler