GRE Math : How to subtract fractions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #2 : Operations

Solve for :

Possible Answers:

Correct answer:

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 #3 : Operations

Quantity A: 

Quantity B: 

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity B is larger.

Quantity A is larger.

The relationship between the quantities cannot be determined.

Correct answer:

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.

Example Question #1 : How To Subtract Fractions

Simplify:

Possible Answers:

Correct answer:

Explanation:

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:

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