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What is 3/11 - 11/12?

What is 3/11 - 11/12?

Here's how to subtract 11/12 from 3/11:

3
11
 −
11
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 3 by 12, and get 36.

Then we multiply 11 by 11, and get 121.

Next we give both terms new denominators -- 11 × 12 = 132.

So now our fractions look like this:

36
132
 −
121
132

Step 2

Since our denominators match, we can subtract the numerators.

36 − 121 = -85

So the answer is:

-85
132

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...

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...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

Nope! So now we try the next greatest prime number, 83...

Nope! So now we try the next greatest prime number, 89...

No good. 89 is larger than -85. So we're done reducing.

There you have it! The final answer is:
3
11
 −
11
12
 = −
85
132

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