math help

What is 10/12 + 7/11?

What is 10/12 + 7/11?

Here's how you add

10
12
+
7
11

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 10 by 11, and get 110, then we multiply 12 by 11 and get 132.

10/12 times 11

Do the same for the second term. We multiply 7 by 12, and get 84, then multiply 12 by 11 and get 132.

7/11 times 12

So now our fractions look like this:

110
132
+
84
132

Step 2

Since our denominators match, we can add the numerators.

110 + 84 = 194

So the answer is:

194
132

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

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

194
132
÷ 2 =
97
66

Now, try the same number again.

Nope. Try the next prime number, 3...

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...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

No good. 67 is larger than 66. So we're done reducing.

Congratulations! Here's your final answer to 10/12 + 7/11

10
12
+
7
11
=
97
66
© 2014 Randy Tayler