math help

What is 5/100 + 5/6?

What is 5/100 + 5/6?

Here's how we add

5
100
 +
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 5 by 6, and get 30, then we multiply 100 by 6 and get 600.

5/100 times 6

Do the same for the second term. We multiply 5 by 100, and get 500, then multiply 100 by 6 and get 600.

5/6 times 100

So now our fractions look like this:

30
600
 +
500
600

Step 2

Since our denominators match, we can add the numerators.

30 + 500 = 530

Now we have an answer.

530
600

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:

530
600
 ÷ 2 =
265
300

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...

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

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

265
300
 ÷ 5 =
53
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 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. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. So next you try the next prime number, which is 53...

No good. So next you try the next prime number, which is 59...

No good. 59 is larger than 53. So we're done reducing.

And we're done! Here's the final answer to 5/100 + 5/6

5
100
 +
5
6
 =
53
60
© 2014 Randy Tayler

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