math help

What is 64/17 - 6/12?

What is 64/17 - 6/12?

Here's how to subtract 6/12 from 64/17:

64
17
 −
6
12

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. 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 64 by 12, and get 768.

Then we multiply 6 by 17, and get 102.

Next we give both terms new denominators -- 17 × 12 = 204.

So now our fractions look like this:

768
204
 −
102
204

Step 2

Since our denominators match, we can subtract the numerators.

768 − 102 = 666

So the answer is:

666
204

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:

666
204
 ÷ 2 =
333
102

Let's try dividing by 2 again...

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:

333
102
 ÷ 3 =
111
34

Let's try dividing by 3 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 34. So we're done reducing.

There you have it! The final answer is:
64
17
 −
6
12
 =
111
34

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