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# Arithmetic with Positive and Negative Numbers

The absolute value of a number is its distance from zero on the number line. For example, -7 (a negative number) and 7 (a positive number) are the same distance from zero on the number line, and both have an absolute value of 7. Using absolute values simplifies the process of doing arithmetic with positive and negative numbers.

## Part 1: Adding Positive and Negative Numbers

PROCEDURE: Determine if you are adding numbers that have the same or different signs. Then follow the appropriate set of directions below.

 Adding same signs Example-3 + (-5) Adding opposite signs Example -3 + 5 Step 1: Add their absolute values. 3 + 5 = 8 Step 1: Subtract the smaller absolute value from the larger. 5 - 3 = 2 Step 2: Make the sign of the answer the same as the sign of the original numbers. Because -3 and -5 are both negative, the answer will be negative. Answer: -3 + (-5) = â€“8 Step 2: Choose the sign of the number with the greater absolute value. Because 5 has a greater absolute value than 3, and 5 is positive, your answer will also be positive. Answer: -3 + 5 = 2

## Part 2: Subtracting Positive and Negative Numbers

PROCEDURE: To subtract integers, find the opposite of the number you are subtracting. Then add this opposite to the number you are subtracting from. The result is your answer.

SAMPLE PROBLEM: -3 - (-5) =   ?

Step 1: Find the opposite of the number you want to subtract.

The opposite of -5 is 5.

Step 2: Add this opposite to the number you are subtracting from. - 3 - (-5) = -3 + 5 = 2

## Part 3: Multiplying and Dividing Positive and Negative Numbers

PROCEDURE: To multiply or divide two integers, multiply or divide their absolute values. Then apply the following rule to determine if the answer is positive or negative:

â€¢ The product or quotient of two same-sign numbers is positive.

â€¢ The product or quotient of two opposite-sign numbers is negative.

SAMPLE PROBLEM A: -7 Ã— 11 =    ?

Step 1: Multiply the absolute values to find the absolute value of the product.

7 Ã— 11 = 77

Step 2: Apply the rule of signs: Because you are finding the product of oppositesign numbers, the product will be negative.

-7 Ã— 11 = -77

SAMPLE PROBLEM B: -12 Ã· (-4) =    ?

Step 1: Divide the absolute values to find the absolute value of the quotient.

12 Ã· 4 = 3

Step 2: Apply the rule of signs: Because you are finding the quotient of same-sign numbers, the quotient will be positive.

-12 Ã· (-4) = 3