math help

What is 3/20 + 3/6?

What is 3/20 + 3/6?

Here's how we add

3
20
 +
3
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 3 by 6, and get 18, then we multiply 20 by 6 and get 120.

3/20 times 6

Do the same for the second term. We multiply 3 by 20, and get 60, then multiply 20 by 6 and get 120.

3/6 times 20

So now our fractions look like this:

18
120
 +
60
120

Step 2

Since our denominators match, we can add the numerators.

18 + 60 = 78

So the answer is:

78
120

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:

78
120
 ÷ 2 =
39
60

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:

39
60
 ÷ 3 =
13
20

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. 17 is larger than 13. So we're done reducing.

And we're done! Here's the final answer to 3/20 + 3/6

3
20
 +
3
6
 =
13
20
© 2014 Randy Tayler

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