math help

What is 21/33 + 6/9?

What is 21/33 + 6/9?

This is how to add

21
33
+
6
9

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 21 by 9, and get 189, then we multiply 33 by 9 and get 297.

21/33 times 9

Now for the second term. You multiply 6 by 33, and get 198, then multiply 33 by 9 and get 297.

6/9 times 33

This gives us a new problem that looks like so:

189
297
+
198
297

Step 2

Since our denominators match, we can add the numerators.

189 + 198 = 387

So what's the answer so far?

387
297

Step 3

Can this fraction be reduced?

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:

387
297
÷ 3 =
129
99

Let's try dividing by that again...

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

129
99
÷ 3 =
43
33

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...

No good. 37 is larger than 33. So we're done reducing.

There you have it! Here's the final answer to 21/33 + 6/9

21
33
+
6
9
=
43
33
© 2014 Randy Tayler