math help

What is 5/10 + 8/11?

What is 5/10 + 8/11?

This is how to add

5
10
+
8
11

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 11, and get 55, then we multiply 10 by 11 and get 110.

5/10 times 11

Do the same for the second term. We multiply 8 by 10, and get 80, then multiply 10 by 11 and get 110.

8/11 times 10

The problem now has new fractions to add:

55
110
+
80
110

Step 2

Since our denominators match, we can add the numerators.

55 + 80 = 135

This yields the answer

135
110

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...

Nope. Try the next prime number, 5...

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

135
110
÷ 5 =
27
22

Now, try the same number again.

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...

No good. 23 is larger than 22. So we're done reducing.

Congratulations! Here's your final answer to 5/10 + 8/11

5
10
+
8
11
=
27
22
© 2014 Randy Tayler