math help

What is 12/13 + 5/6?

What is 12/13 + 5/6?

Let's add

12
13
 +
5
6

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 12 by 6, and get 72, then we multiply 13 by 6 and get 78.

12/13 times 6

Do the same for the second term. We multiply 5 by 13, and get 65, then multiply 13 by 6 and get 78.

5/6 times 13

So now our fractions look like this:

72
78
 +
65
78

Step 2

Since our denominators match, we can add the numerators.

72 + 65 = 137

Now we have an answer.

137
78

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...

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 78. So we're done reducing.

There you have it! Here's the final answer to 12/13 + 5/6

12
13
 +
5
6
 =
137
78
© 2014 Randy Tayler

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