math help

What is 15/11 + 6/12?

What is 15/11 + 6/12?

This is how you add

15
11
 +
6
12

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 15 by 12, and get 180, then we multiply 11 by 12 and get 132.

15/11 times 12

Do the same for the second term. We multiply 6 by 11, and get 66, then multiply 11 by 12 and get 132.

6/12 times 11

So now our fractions look like this:

180
132
 +
66
132

Step 2

Since our denominators match, we can add the numerators.

180 + 66 = 246

Now we have an answer.

246
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:

246
132
 ÷ 2 =
123
66

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

123
66
 ÷ 3 =
41
22

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. 23 is larger than 22. So we're done reducing.

And we're done! Here's the final answer to 15/11 + 6/12

15
11
 +
6
12
 =
41
22
© 2014 Randy Tayler

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