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What is 72/63 - 2/12?

What is 72/63 - 2/12?

Here's how to subtract 2/12 from 72/63:

72
63
 −
2
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 72 by 12, and get 864.

Then we multiply 2 by 63, and get 126.

Next we give both terms new denominators -- 63 × 12 = 756.

So now our fractions look like this:

864
756
 −
126
756

Step 2

Since our denominators match, we can subtract the numerators.

864 − 126 = 738

So the answer is:

738
756

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:

738
756
 ÷ 2 =
369
378

Let's try dividing by 2 again...

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

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

369
378
 ÷ 3 =
123
126

Let's try dividing by 3 again...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

123
126
 ÷ 3 =
41
42

Let's try dividing by 3 again...

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...

No good. 43 is larger than 41. So we're done reducing.

There you have it! The final answer is:
72
63
 −
2
12
 =
41
42

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