# Pre-Algebra : Negative Numbers

## Example Questions

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Solve:

Explanation:

### Example Question #1 : Subtract Rational Numbers And Understand The Absolute Value Of Their Difference: Ccss.Math.Content.7.Ns.A.1c

Solve:

Explanation:

The problem indicates that the result is  units more negative than , which is .

### Example Question #2 : Negative Numbers

Evaluate   for .

Explanation:

Substitute 8 for  in the expression and evaluate, paying attention to the order of operations:

### Example Question #2 : Understand Distances Between Numbers On A Number Line: Ccss.Math.Content.7.Ns.A.1b

is equal to which of the following?

Explanation:

This is a straightforward problem. Remember that when adding a negative number, you are actually subtracting:

Be sure to remember that the first number is also negative, meaning we are subtracting a number from a negative number:

### Example Question #221 : Operations And Properties

Evaluate:

Explanation:

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

This is the correct choice.

### Example Question #2 : Negative Numbers

If  and  are integers such that   and , what is the smallest possible value of ?

Explanation:

To make  as small as possible, let  be as small as possible , and subtract the largest value of  possible :

### Example Question #717 : Gre Quantitative Reasoning

Solve for :

Explanation:

To solve this problem, you need to get your variable isolated on one side of the equation:

Taking this step will elminate the  on the side with :

Now divide by  to solve for :

The important step here is to be able to add the negative numbers.  When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

### Example Question #222 : Operations And Properties

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 #3 : 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 #71 : Integers

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:

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