math help

What is 21/33 + 1/6?

What is 21/33 + 1/6?

Here's how you add

21
33
 +
1
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 1 by 33, and get 33, then multiply 33 by 6 and get 198.

1/6 times 33

This gives us a new problem that looks like so:

126
198
 +
33
198

Step 2

Since our denominators match, we can add the numerators.

126 + 33 = 159

So what's the answer so far?

159
198

Step 3

Can this fraction be reduced?

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

Nope. Try the next prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

159
198
 ÷ 3 =
53
66

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

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

Congratulations! Here's your final answer to 21/33 + 1/6

21
33
 +
1
6
 =
53
66
© 2014 Randy Tayler

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