math help

What is 3/64 - 9/12?

What is 3/64 - 9/12?

Here's how to subtract 9/12 from 3/64:

3
64
 −
9
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 9 by 64, and get 576.

Next we give both terms new denominators -- 64 × 12 = 768.

So now our fractions look like this:

36
768
 −
576
768

Step 2

Since our denominators match, we can subtract the numerators.

36 − 576 = -540

So the answer is:

-540
768

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:

-540
768
 ÷ 2 =
-270
384

Let's try dividing by 2 again...

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

-270
384
 ÷ 2 =
-135
192

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:

-135
192
 ÷ 3 =
-45
64

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...

Nope! So now we try the next greatest prime number, 47...

No good. 47 is larger than -45. So we're done reducing.

There you have it! The final answer is:
3
64
 −
9
12
 = −
45
64

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