math help

What is 21/33 + 8/12?

What is 21/33 + 8/12?

Here's how we add

21
33
 +
8
12

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 12, and get 252, then we multiply 33 by 12 and get 396.

21/33 times 12

Do the same for the second term. We multiply 8 by 33, and get 264, then multiply 33 by 12 and get 396.

8/12 times 33

The problem now has new fractions to add:

252
396
 +
264
396

Step 2

Since our denominators match, we can add the numerators.

252 + 264 = 516

This yields the answer

516
396

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:

516
396
 ÷ 2 =
258
198

So far so good... let's try to divide by that number again.

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

258
198
 ÷ 2 =
129
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:

129
99
 ÷ 3 =
43
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 33. So we're done reducing.

And we're done! Here's the final answer to 21/33 + 8/12

21
33
 +
8
12
 =
43
33
© 2014 Randy Tayler

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