First, consider each quantity separately.

Quantity A

These two fractions do not have a common factor. Their common denominator is . Thus, we multiply the fractions as follows to give them a common denominator:

This is the same as:

Quantity B

The common denominator of these two values is . Therefore, you multiply the fractions as follows to give them a common denominator:

This is the same as:

Since Quantity A is larger than and Quantity B is a positive fraction less than , we know that Quantity A is larger without even using a calculator.

Just like adding fractions, when you subtract fractions, you need to find a common denominator. For and , the least common denominator is . In order to do your subtraction, you need to multiply appropriately to give your fractions this denominator:

Which is the same as...

Now, you can subtract the numerators and retain the denominator:

Begin by isolating the factors:

Now, the common denominator of these two fractions is . Therefore, multiply by :

Now, you can subtract the left values:

Now, multiply both sides by :