math help

What is 78/10 + 6/11?

What is 78/10 + 6/11?

Here's how to add

78
10
+
6
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 78 by 11, and get 858, then we multiply 10 by 11 and get 110.

78/10 times 11

Now for the second term. You multiply 6 by 10, and get 60, then multiply 10 by 11 and get 110.

6/11 times 10

This gives us a new problem that looks like so:

858
110
+
60
110

Step 2

Since our denominators match, we can add the numerators.

858 + 60 = 918

That gives us an answer of

918
110

Step 3

Can this fraction be reduced?

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

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

918
110
÷ 2 =
459
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 78/10 + 6/11

78
10
+
6
11
=
459
55
© 2014 Randy Tayler