math help

What is 1/12 - 10/11?

What is 1/12 - 10/11?

Here's how to subtract 10/11 from 1/12:

1
12
10
11

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 1 by 11, and get 11.

Then we multiply 10 by 12, and get 120.

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

So now our fractions look like this:

11
132
120
132

Step 2

Since our denominators match, we can subtract the numerators.

11 − 120 = -109

So the answer is:

-109
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...

Nope! So now we try the next greatest prime number, 97...

Nope! So now we try the next greatest prime number, 101...

Nope! So now we try the next greatest prime number, 103...

Nope! So now we try the next greatest prime number, 107...

Nope! So now we try the next greatest prime number, 109...

Nope! So now we try the next greatest prime number, 113...

No good. 113 is larger than -109. So we're done reducing.

There you have it! The final answer is:
1
12
10
11
=
109
132

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