# GRE Math : How to divide negative numbers

## Example Questions

### Example Question #6 : Negative Numbers

Find the value of .

Explanation:

To solve for , divide each side of the equation by -2.

is the same as

which is POSITIVE

### Example Question #136 : Arithmetic

What is ?

45

Explanation:

A negative number divided by a negative number always results in a positive number.  divided by  equals . Since the answer is positive, the answer cannot be  or any other negative number.

### Example Question #137 : Arithmetic

Solve for :

Explanation:

Subtract  from both sides:

, or

Next, subtract  from both sides:

, or

Then, divide both sides by :

Recall that division of a negative by a negative gives you a positive, therefore:

or

### Example Question #1 : How To Divide Negative Numbers

Solve for :

Explanation:

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by  on both sides:

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result.  If the signs are opposites (i.e. one positive, one negative) then you get a negative.

Both of the numbers here are negative, so we will have a positive result:

### Example Question #2 : How To Divide Negative Numbers

Solve for :

Explanation:

To solve, you need to isolate the variable. We first subtract  then divide by :

When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result.  If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.

Therefore: