Chapter 2 Notes

Lesson 2.1

Lesson 2.2

Lesson 2.3

Lesson 2.4

Lesson 2.5

Lesson 2.6

Lesson 2.7

2.1 Adding Rational Numbers

additive inverse

additive identity property

a when the opposite is added to a number the sum equals zeroPull

Pull

a number plus its opposite equals zerox + (-x) = 0P

ull

Pull

identity property of addition

n + 0 = nPull

Pull

adding numbers with same signs

add numbers together the answer will have the same signPull

Pull

adding numbers with different signs

subtract numbers; the answer will have the same sign as the larger number (not looking at sign)Pull

Pull

Examples

-2 + (-6)

4 + (-8)

-9 + 9

9 + 7

The temperature falls 15 degrees and then rises 18 degrees.Use addition to find the change in temperature.

Evaluate the expressionn = -4 m=5

m+(-4) -n + 5

-8

4

0

16

5 + (-4) = 1 -(-4)+5 = 9

Matrix

[ ]

4 5

7 8

Column

Row6

1

2 rows by 3 columns

[ ]

-2 5 7 1

[ ]

4 -13 0+ =

[ ]

-2 + 4 5+(-1)7+3 1 + 0

=

[ ]

2 410 1

Pull

Pull

End

2.2 Subtracting Rational numbers

Subtracting numbers

change the second number to its opposite and follow the addition rulesPull

Pull

Absolute value

do all the operations inside the absolute value then take the positive of the answerPull

Pull

Evaluate:for n = -3 and m = 2

n - 6 -m - 8

Examples

2 - (-6)

4 - (-8)

-4 - 5

9 - 2

Examples

| -8 - 6| | 6 - 2 |

[ ]

-2 5 7 1

[ ]

4 -13 0-

[ ]

-2 - 4 5-(-1)7-3 1 - 0

=

[

-6 64 1

]

2.3 Multiplying and Dividing Rational Numbers

Identity Property of Multiplication

Multiplication Property of Zero

Multiplication Property of -1

n * 1 = n

Pull

Pull

n * 0 = 0Pull

Pull

n * (-1) = -n

Pull

Pull

Multiplying or Dividing Numbers with same sign

Multiplying or Dividing Numbers with different signs

Multiply or Divide numbers together; answer is POSITIVEPull

Pull

Multiply or Dividing numbers together; answer is NEGATIVEPull

Pull

Examples

-5 * (-10) 7 * 8

-8 * 5 -50 2

-30 75 -3 25

Evaluate:for n = -2 and m = 8

8m -n2

Matrix scalar multiplication

[ ]

4 -5 -1 3 0 -9

=5

[

5(4) 5(-5) 5(-1) 5(3) 5(0) 5(-9)

]

Pull

Pull [

20 -25 -515 0 -45

]

2.4 The Distributive Property

Distributive property

Pull

Pull a(b + c) = a(b) + a(c)

Example

2(3 + 7)2(3) + 2(7)6 + 1420

3(4x -9)3(4x) - 3(9)12x - 27

-(6n + 8)-1(6n + 8)-6n - 8

Example

End

Like Terms

5a2 - 9ab - 18

coefficientConstant

8x + 3(x + 4)8x + 3x +1211x + 12

2.5 Properties of numbers

Commutative Property

a + b = b + aa * b = b * aP

ull

Pull

Associative Property

Identity Property

Inverse Property

Symmetric Property

(a + b) + c = a + (b + c)(a * b) * c = a * (b * c)P

ull

Pull

a + 0 = aa * 1 = aP

ull

Pull

a + -a = 0a * (1/a) = 1P

ull

Pull

if a = b then b = a

Pull

Pull

Distributive property

Multiplication Property of Zero

Mutliplication Property of -1

a(b + c) = ab + aca(b - c) = ab - ac P

ull

Pull

n * 0 = 0

Pull

Pull

n * -1 = -n

Pull

Pull

End

2.6 Theorectical and Experimental Probability

Probability

Outcome

Sample Space

Event

Theoretical Probability

Favorable outcometotal number of outcomes

Pull

Pull

result of a single trial

Pull

Pull

all possible outcomes

Pull

Pull

an outcome or group of outcomes

Pull

Pull

how an event should turn out

Pull

Pull

Compliment of an event

the probability an event will not occur

Pull

Pull

Experimental Probability

how an event did turn out from a trial(s)

Pull

Pull

Example

P (green) = 1 5

Red Pink Orange Blue

P (Red) = 2 5

P ( not red) = 3 5

= 20%

= 40%

= 60%

End

2.7 Probability of Compound events

Independant Events

Dependant Event

events that do not effect each other

Pull

Pull

events that do effect each otherPull

Pull

P ( A and B) = P(A) * P(B)

Pull

Pull

P ( A and B) = P(A) * P(B after A)

Pull

Pull

You have a bag of marbles with 8 red marbles, 10 blue marbles, 7 yellow, and 5 black marbles.

What are the following probabilities WITHOUT replacement?P( yellow and black)P(2 reds)P(purple)

What are the following probabilities with replacement?P( yellow and black)P(2 reds)P(purple)