math help

What is 21/33 + 2/6?

What is 21/33 + 2/6?

This is how to add

21
33
 +
2
6

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

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

21/33 times 6

Do the same for the second term. We multiply 2 by 33, and get 66, then multiply 33 by 6 and get 198.

2/6 times 33

The problem now has new fractions to add:

126
198
 +
66
198

Step 2

Since our denominators match, we can add the numerators.

126 + 66 = 192

The sum we get is

192
198

Step 3

The last step is to reduce the fraction if we can.

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:

192
198
 ÷ 2 =
96
99

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:

96
99
 ÷ 3 =
32
33

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. 37 is larger than 32. So we're done reducing.

And we're done! Here's the final answer to 21/33 + 2/6

21
33
 +
2
6
 =
32
33
© 2014 Randy Tayler

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