math help

What is 21/33 + 9/12?

What is 21/33 + 9/12?

Here's how you add

21
33
 +
9
12

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 21 by 12, and get 252, then we multiply 33 by 12 and get 396.

21/33 times 12

Now for the second term. You multiply 9 by 33, and get 297, then multiply 33 by 12 and get 396.

9/12 times 33

We now have a new problem, that looks like this:

252
396
 +
297
396

Step 2

Since our denominators match, we can add the numerators.

252 + 297 = 549

Answer:

549
396

Step 3

Now, do we need to simplify this fraction?

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

Nope! So now we try the next greatest prime number, 3...

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

549
396
 ÷ 3 =
183
132

Let's try dividing by that again...

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

183
132
 ÷ 3 =
61
44

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

No good. 47 is larger than 44. So we're done reducing.

There you have it! Here's the final answer to 21/33 + 9/12

21
33
 +
9
12
 =
61
44
© 2014 Randy Tayler

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