Integers Whole Numbers = { 0,1,2,3,….} Natural Numbers or Positive Integers = {1,2,3,4,…} Negative Integers = { -1,-2,-3,-4,….} Integers ={ …-3,-2,-1,0,1,2,3,…} Zero is neither positive nor negative.

Additive Inverse For every integer n the negative of n is called the additive inverse of n. N + -N = 0 Negative of a Negative -(-N) = N Think of - as “the opposite of”

Integer Representation Colored counters Black = + Red = - Game keeping score. Mail Time Representation Number Line Representaion

Absolute Value The Absolute Value of a number is the distance on the number line away from 0. 5 and -5 are both 5 units away from 0. | 5 | = 5 |-5| = 5

Homework Pg 291 #1,2,457,8,29

Ordering Integers The larger integer is the integer further to the right on the number line. In the case of a thermometer, the higher number (more degrees, more heat)

Addition of Integers Represent sum of integers using colored counter diagrams. Mail Time Stories ( pg 297) Number Line

Subtraction of Integers Using colored Counters. 7- 4 BBBBBBB -8 - -3 RRRRRRRR

Subtraction of Integers Using colored Counters. 7 – (-3) Since we have to take away -3 (3 red counters), we have to represent 7 using 3 red counters. BBBBBBB BBB RRR

Subtraction of Integers Using colored Counters. 8 – 9 Since we have to take away 9 ( black counters), we have to represent 8 using 9 black counters. BBBBBBBB B R

Draw Diagrams for each of the following: 7 – 4 -3 - -2 8 - -5 7 – 10 -7 - 3

Subtraction of Integers Subtracting an integer is the same as adding its opposite. A – B = A + (-B)

Rewrite each of the following as adding the opposite 8 – 6 8 – -6 -6 – 5 -8 - - 3 - 8 - -10 8 – 12 5 - -6 + 8 – 6 – 3 - -2 + 5

Homework Pg 310 # 1,2,34,5,11 43

Multiplication of Integers 4 x 3 = 3 + 3 + 3 + 3 =12 4 x (-3) = -3 + -3 + -3 + -3 = -12 Doesn’t work for -4 x -3

Pattern of Products 4 x 3 = 4 x 2 = 4 x 1 = 4 x 0 = 4 x -1 = 4x -2 = Positive times a Negative = Negative

3 x -3 = 2 x -3 = 1 x -3 = 0 x -3 = -1 x -3 = -2 x -3 = -3 x -3 = Negative times a Negative = Negative

Rules for Multiplication of Integers MULTIPLY THE NUMBERS: Positive x Positive = Positive Positive X Negative = Negative Negative x Positive = Negative Negative X Negative = Positive

Mail Time Stories Pg 317

Division of Integers 12 / 4 = 3 since 3 x 4 = 12

Rules for Dividing Integers Divide THE NUMBERS: Positive ÷ Positive = Positive Positive ÷ Negative = Negative Negative ÷ Positive = Negative Negative ÷ Negative = Positive

Homework Pg 320 # 1 all, 2all, 10