What is 21/63 - 5/11?

Here's how to subtract 5/11 from 21/63:

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 11, and get 231.

Then we multiply 5 by 63, and get 315.

Next we give both terms new denominators -- 63 × 11 = 693.

So now our fractions look like this:

Step 2

Since our denominators match, we can subtract the numerators.

231 − 315 = -84

So the answer is:

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...

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

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...

Are both the numerator and the denominator evenly divisible by 7? Yes! So we reduce it:

Let's try dividing by 7 again...

No good. 7 is larger than -4. So we're done reducing.