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MAT081 :: Lecture Note :: Week 15
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Overview
Assignment(s):

Signed Numbers

Numbers that are prefixed with a dash are negative numbers and all negative numbers are less than zero. [Note: zero is neither negative nor positive.]

On the number line, negative numbers are to the left of zero.

Negative numbers are the opposite of positive numbers. For example, -5 is the opposite of +5 and vice versa.

The absolute value of a number is its distance from zero on the number line. For example, -5 is five ones to the left of zero; therefore, its absolute value is 5.

Adding Signed Numbers

If both terms have the same sign, then add their respective absolute values and use the common sign as the sign for the sum.

   -5 + -3  
   |-5| + |-3|  =  5 + 3  =  8
   common sign is -
   answer is -8

If the terms have differing signs, subtract the smallest absolute value from the largest absolute value. The sum is given the sign of the largest absolute value.

   -5 + 15
   |15| > |-5|
   15 - 5 = 10
   sign on 15 is +
   answer is 10 (+10)

   -5 + 3
   |-5| > |3|
   5 - 3 = 2
   sign on -5 is -
   answer is -2
Subtracting Signed Numbers

Subtracting signed numbers is performed by converting the problem into an addition problem.

If a and b are numbers, then a - b equals a + (-b). In other words, subtraction equals the first number added to the opposite of the second number.

   general formula:  a - b = a + (-b)
   
    5 -  3 =  5 + (-3) =  2
    5 - -3 =  5 + ( 3) =  8
   -5 -  3 = -5 + (-3) = -8
   -5 - -3 = -5 + ( 3) = -2
Multiplying Signed Numbers

The product of two factors having the same sign is positive. The product of two factors having different signs is negative. In other words, a negative number times a positive number results in a negative number and vice versa. Any number (regardless of sign) times zero is zero.

   "Minus times minus equals plus; the reason for this we won't discuss."
    --anonymous
Dividing Signed Numbers

The quotient of two terms having the same sign is positive. The quotient of two terms having different signs is negative. In other words, a negative number divided by a positive number results in a negative number and vice versa. Any number (regardless of sign) cannot be divided by zero.

Exercise
  1. Graph the numbers 5, -2, -4.7.

       -5   -4   -3   -2  -1     0    1    2    3    4    5
        +----+----+----+----+----+----+----+----+----+----+
          ^            ^                                  ^
        -4.7          -2                                  5
    
    
        -4.7 is less than -2 which is less than 5
        -4.7 < -2 < 5
    

PurpleMath.com:: Introduction to Negative Numbers
UGA.edu::Why is a negative number times a negative number a positive number?

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