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) = –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:
• The product or quotient of two same-sign numbers is positive.
• The product or quotient of two opposite-sign numbers is negative.
SAMPLE PROBLEM A: -7 × 11 = ?
Step 1: Multiply the absolute values to find the absolute value of the product.
7 × 11 = 77
Step 2: Apply the rule of signs: Because you are finding the product of oppositesign
numbers, the product will be negative.
-7 × 11 = -77
SAMPLE PROBLEM B: -12 ÷ (-4) = ?
Step 1: Divide the absolute values to find the absolute value of the quotient.
12 ÷ 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 ÷ (-4) = 3
|
