Chapter 2 Notes Lesson 2.1 Lesson 2.2 Lesson 2.3 Lesson 2.4 Lesson 2.5 Lesson 2.6 Lesson 2.7
May 19, 2015
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)