math help

What is 10/11 + 8/10?

What is 10/11 + 8/10?

Here's how we add

10
11
+
8
10

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 10 by 10, and get 100, then we multiply 11 by 10 and get 110.

10/11 times 10

Now for the second term. You multiply 8 by 11, and get 88, then multiply 11 by 10 and get 110.

8/10 times 11

We now have a new problem, that looks like this:

100
110
+
88
110

Step 2

Since our denominators match, we can add the numerators.

100 + 88 = 188

That gives us the sum, which is

188
110

Step 3

Now, do we need to simplify this fraction?

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

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

188
110
÷ 2 =
94
55

Let's try dividing by that again...

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...

No good. 59 is larger than 55. So we're done reducing.

There you have it! Here's the final answer to 10/11 + 8/10

10
11
+
8
10
=
94
55
© 2014 Randy Tayler