math help

What is 9/32 - 11/12?

What is 9/32 - 11/12?

Here's how to subtract 11/12 from 9/32:

9
32
 −
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 9 by 12, and get 108.

Then we multiply 11 by 32, and get 352.

Next we give both terms new denominators -- 32 × 12 = 384.

So now our fractions look like this:

108
384
 −
352
384

Step 2

Since our denominators match, we can subtract the numerators.

108 − 352 = -244

So the answer is:

-244
384

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:

-244
384
 ÷ 2 =
-122
192

Let's try dividing by 2 again...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

-122
192
 ÷ 2 =
-61
96

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...

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 -61. So we're done reducing.

There you have it! The final answer is:
9
32
 −
11
12
 = −
61
96

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11/12 - 9/11
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11/12 - 10/11
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11/12 - 10/12
11/12 + 11/12
11/12 - 11/12