math help

What is 21/11 - 4/12?

What is 21/11 - 4/12?

Here's how to subtract 4/12 from 21/11:

21
11
 −
4
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 21 by 12, and get 252.

Then we multiply 4 by 11, and get 44.

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

So now our fractions look like this:

252
132
 −
44
132

Step 2

Since our denominators match, we can subtract the numerators.

252 − 44 = 208

So the answer is:

208
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...

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

208
132
 ÷ 2 =
104
66

Let's try dividing by 2 again...

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

104
66
 ÷ 2 =
52
33

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 33. So we're done reducing.

There you have it! The final answer is:
21
11
 −
4
12
 =
52
33

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