math help

What is 21/11 + 3/6?

What is 21/11 + 3/6?

This is how to add

21
11
 +
3
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 11 by 6 and get 66.

21/11 times 6

Now for the second term. You multiply 3 by 11, and get 33, then multiply 11 by 6 and get 66.

3/6 times 11

This gives us a new problem that looks like so:

126
66
 +
33
66

Step 2

Since our denominators match, we can add the numerators.

126 + 33 = 159

That gives us an answer of

159
66

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:

159
66
 ÷ 3 =
53
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 21/11 + 3/6

21
11
 +
3
6
 =
53
22
© 2014 Randy Tayler

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