math help

What is 5/12 + 8/9?

What is 5/12 + 8/9?

This is how to add

5
12
+
8
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 5 by 9, and get 45, then we multiply 12 by 9 and get 108.

5/12 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

The problem now has new fractions to add:

45
108
+
96
108

Step 2

Since our denominators match, we can add the numerators.

45 + 96 = 141

This yields the answer

141
108

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:

141
108
÷ 3 =
47
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 5/12 + 8/9

5
12
+
8
9
=
47
36
© 2014 Randy Tayler