I.  Homework

II.  Review of Number Systems.  We will play the number game where each group of students represents a type number and the group stands up when their number is called.

III.  Double Negative Signs

  -(-7) = 7 and in general -(-x) = x

IV.  Addition Involving Positive and Negative Numbers

We will play a game where some students represent negative numbers, others represent positive numbers and we take away or add negatives or positives to find the answer to the solution.

Algebraic Examples

A)  -3 + 2 :  3 - 2 = 1, since 3 > 2 the answer is -1.

B)  -4 + 10:  10 - 4 = 6, since 10 > 4 the answer is 6.

C)  -3 - 2:  same sign so that 3 + 2 = 5, since they are both negative the answer is 5

D)  -1 - 10 = -11

E)  4 - 6 :  6 - 4 = 2 since 6 > 4 the answer is -2.

V.  Multiplication and Division

Multiplication and Division Rules:  

1)  An even number of negatives gives a positive

2)  An odd number of negatives gives a negative

3)  We can never divide by 0

4)  0/(non zero) = 0

Examples

(-3)(-6) = 18, (-4)(8) = 32, -12/(-4) = 3, 0/10 = 0, 7/0 = undefined

Exercises:

A)  (-3 + 4)/(-2)

B)  (5 - (-3))/2 + (-4)

C)  |3 - 4| - 4

D)  -2(|-4| - |-3|)

E)  -1/2 + 1/3

F) [2/5 - 1/3]/[1/3 - 1/5]

G)  6x/-3

H)  (-5)(5z)

I)  -4(-3x + 2)

J)  -(x - y)

V.  Applications

 Example:

Suppose that you own a casino and want to monitor the average winnings of your patrons.  The four players at your table had the following results:  player 1 won $4, player 2 lost $2, player 3 lost $7 and player 4 broke even. What was the average earnings?

Solution:

To find the average, we add up all the numbers and divide by 4:

(4 + (-2) + (-7) + 0)/4 = (2 + (-7))/4 = -5/4 or $1.25

Exercise:  Suppose your bank balance is $250 and your Visa balance is $750.  What is your net worth?