math help

What is 21/33 + 5/6?

What is 21/33 + 5/6?

This is how you add

21
33
 +
5
6

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 21 by 6, and get 126, then we multiply 33 by 6 and get 198.

21/33 times 6

Now for the second term. You multiply 5 by 33, and get 165, then multiply 33 by 6 and get 198.

5/6 times 33

This gives us a new problem that looks like so:

126
198
 +
165
198

Step 2

Since our denominators match, we can add the numerators.

126 + 165 = 291

That gives us an answer of

291
198

Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

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:

291
198
 ÷ 3 =
97
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 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. 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. So next you try the next prime number, which is 61...

No good. So next you try the next prime number, which is 67...

No good. 67 is larger than 66. So we're done reducing.

And we're done! Here's the final answer to 21/33 + 5/6

21
33
 +
5
6
 =
97
66
© 2014 Randy Tayler

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