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 countersBlack = +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 =• 4 x -3 =• 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• 12 / -4 = -3 since -3 x -4 = 12• -12 / 4 = -3 since -3 x 4 = -12• -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