math help

What is 21/33 + 3/6?

What is 21/33 + 3/6?

Here's how to add

21
33
 +
3
6

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

21/33 times 6

Now for the second term. You multiply 3 by 33, and get 99, then multiply 33 by 6 and get 198.

3/6 times 33

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

126
198
 +
99
198

Step 2

Since our denominators match, we can add the numerators.

126 + 99 = 225

That gives us the sum, which is

225
198

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:

225
198
 ÷ 3 =
75
66

Let's try dividing by that again...

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

75
66
 ÷ 3 =
25
22

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...

No good. 23 is larger than 22. So we're done reducing.

There you have it! Here's the final answer to 21/33 + 3/6

21
33
 +
3
6
 =
25
22
© 2014 Randy Tayler

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