math help

What is 20/17 - 3/12?

What is 20/17 - 3/12?

Here's how to subtract 3/12 from 20/17:

20
17
 −
3
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 20 by 12, and get 240.

Then we multiply 3 by 17, and get 51.

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

So now our fractions look like this:

240
204
 −
51
204

Step 2

Since our denominators match, we can subtract the numerators.

240 − 51 = 189

So the answer is:

189
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...

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:

189
204
 ÷ 3 =
63
68

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...

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...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

No good. 67 is larger than 63. So we're done reducing.

There you have it! The final answer is:
20
17
 −
3
12
 =
63
68

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