GRE Math : How to subtract fractions

Example Questions

Example Question #3 : Operations

Solve for :

Explanation:

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 :

Example Question #4 : Operations

Quantity A:

Quantity B:

Which of the following is true?

The relationship between the quantities cannot be determined.

Quantity B is larger.

Quantity A is larger.

The two quantities are equal.

Quantity A is larger.

Explanation:

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.

Simplify: