math help

What is 5/9 + 6/12?

What is 5/9 + 6/12?

Here's how we add

5
9
 +
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 5 by 12, and get 60, then we multiply 9 by 12 and get 108.

5/9 times 12

Do the same for the second term. We multiply 6 by 9, and get 54, then multiply 9 by 12 and get 108.

6/12 times 9

So now our fractions look like this:

60
108
 +
54
108

Step 2

Since our denominators match, we can add the numerators.

60 + 54 = 114

So the answer is:

114
108

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:

114
108
 ÷ 2 =
57
54

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:

57
54
 ÷ 3 =
19
18

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. 19 is larger than 18. So we're done reducing.

And we're done! Here's the final answer to 5/9 + 6/12

5
9
 +
6
12
 =
19
18
© 2014 Randy Tayler

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