 # What is 5/7 + 10/11? Here's how you add

 5 7
+
 10 11

## Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 5 by 11, and get 55, then we multiply 7 by 11 and get 77. Now for the second term. You multiply 10 by 7, and get 70, then multiply 7 by 11 and get 77. This gives us a new problem that looks like so:

 55 77
+
 70 77

## Step 2

Since our denominators match, we can add the numerators.

55 + 70 = 125

That gives us an answer of

 125 77

## Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

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

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...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

No good. 79 is larger than 77. So we're done reducing.

There you have it! Here's the final answer to 5/7 + 10/11

 5 7
+
 10 11
=
 125 77
© 2014 Randy Tayler