math help

What is 21/33 + 10/12?

What is 21/33 + 10/12?

This is how to add

21
33
 +
10
12

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we 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 10 by 33, and get 330, then multiply 33 by 12 and get 396.

10/12 times 33

So now our fractions look like this:

252
396
 +
330
396

Step 2

Since our denominators match, we can add the numerators.

252 + 330 = 582

Now we have an answer.

582
396

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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:

582
396
 ÷ 2 =
291
198

Now, try the same number again.

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

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

291
198
 ÷ 3 =
97
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...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

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

Congratulations! Here's your final answer to 21/33 + 10/12

21
33
 +
10
12
 =
97
66
© 2014 Randy Tayler

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