math help

What is 20/17 - 10/12?

What is 20/17 - 10/12?

Here's how to subtract 10/12 from 20/17:

20
17
 −
10
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 10 by 17, and get 170.

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

So now our fractions look like this:

240
204
 −
170
204

Step 2

Since our denominators match, we can subtract the numerators.

240 − 170 = 70

So the answer is:

70
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:

70
204
 ÷ 2 =
35
102

Let's try dividing by 2 again...

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

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 35. So we're done reducing.

There you have it! The final answer is:
20
17
 −
10
12
 =
35
102

10/12 + 1/2
10/12 - 1/2
10/12 + 1/3
10/12 - 1/3
10/12 + 2/3
10/12 - 2/3
10/12 + 1/4
10/12 - 1/4
10/12 + 2/4
10/12 - 2/4
10/12 + 3/4
10/12 - 3/4
10/12 + 1/5
10/12 - 1/5
10/12 + 2/5
10/12 - 2/5
10/12 + 3/5
10/12 - 3/5
10/12 + 4/5
10/12 - 4/5
10/12 + 1/6
10/12 - 1/6
10/12 + 2/6
10/12 - 2/6
10/12 + 3/6
10/12 - 3/6
10/12 + 4/6
10/12 - 4/6
10/12 + 5/6
10/12 - 5/6
10/12 + 1/7
10/12 - 1/7
10/12 + 2/7
10/12 - 2/7
10/12 + 3/7
10/12 - 3/7
10/12 + 4/7
10/12 - 4/7
10/12 + 5/7
10/12 - 5/7
10/12 + 6/7
10/12 - 6/7
10/12 + 1/8
10/12 - 1/8
10/12 + 2/8
10/12 - 2/8
10/12 + 3/8
10/12 - 3/8
10/12 + 4/8
10/12 - 4/8
10/12 + 5/8
10/12 - 5/8
10/12 + 6/8
10/12 - 6/8
10/12 + 7/8
10/12 - 7/8
10/12 + 1/9
10/12 - 1/9
10/12 + 2/9
10/12 - 2/9
10/12 + 3/9
10/12 - 3/9
10/12 + 4/9
10/12 - 4/9
10/12 + 5/9
10/12 - 5/9
10/12 + 6/9
10/12 - 6/9
10/12 + 7/9
10/12 - 7/9
10/12 + 8/9
10/12 - 8/9
10/12 + 1/10
10/12 - 1/10
10/12 + 2/10
10/12 - 2/10
10/12 + 3/10
10/12 - 3/10
10/12 + 4/10
10/12 - 4/10
10/12 + 5/10
10/12 - 5/10
10/12 + 6/10
10/12 - 6/10
10/12 + 7/10
10/12 - 7/10
10/12 + 8/10
10/12 - 8/10
10/12 + 9/10
10/12 - 9/10
10/12 + 1/11
10/12 - 1/11
10/12 + 2/11
10/12 - 2/11
10/12 + 3/11
10/12 - 3/11
10/12 + 4/11
10/12 - 4/11
10/12 + 5/11
10/12 - 5/11
10/12 + 6/11
10/12 - 6/11
10/12 + 7/11
10/12 - 7/11
10/12 + 8/11
10/12 - 8/11
10/12 + 9/11
10/12 - 9/11
10/12 + 10/11
10/12 - 10/11
10/12 + 1/12
10/12 - 1/12
10/12 + 2/12
10/12 - 2/12
10/12 + 3/12
10/12 - 3/12
10/12 + 4/12
10/12 - 4/12
10/12 + 5/12
10/12 - 5/12
10/12 + 6/12
10/12 - 6/12
10/12 + 7/12
10/12 - 7/12
10/12 + 8/12
10/12 - 8/12
10/12 + 9/12
10/12 - 9/12
10/12 + 10/12
10/12 - 10/12
10/12 + 11/12
10/12 - 11/12