Download Objective - To recognize different sets of numbers and to identify a

8/10/2016
Algebra II, Chapter 1
Math is Easier than English
• English Class Sentence
Harding Charter Prep
2016-2017
Dr. Michael T. Lewchuk
For any line, the dependent variable (y) equals
the slope of the line (m) times the independent
variable (x) plus the initial value (b).
• Math Class Sentence
y = mx + b
• Mathematicians are lazy!
Equations and Inequalities
• An algebraic expression is a combination of
numbers, variables and operators
 4x + 7
Section 1.1A
The Real Number System
• An equation is a mathematical sentence formed
by placing an equal sign (=) between two
expressions
 y = 4x + 7
• An inequality is a mathematical sentence formed
by placing an inequality sign (>, ≥, <, ≤) between
two expressions
 y > 4x + 7
Sets of Numbers
Make a Venn Diagram that displays the following sets of numbers:
Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.
Naturals - Natural counting numbers
{ 1, 2, 3… }
Wholes - Natural counting numbers and zero
{ 0, 1, 2, 3… }
Integers - Positive or negative natural numbers or zero
{ … -3, -2, -1, 0, 1, 2, 3… }
Rationals - Any number which can be written as a fraction
using integers
Irrationals - Any decimal number which can’t be written as
a fraction. A non-terminating and non-repeating decimal.
Reals - Rationals & Irrationals
Reals
Rationals
2
3
-2.65
Integers
-3
-19
Wholes
0
Naturals
1, 2, 3...
6
1
4
Irrationals

2
1
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Imaginary Numbers
1
-2.65
Integers
-3
2) 5 7
8
Rational, Real
-19
Wholes
0
6
Naturals
1, 2, 3...
1
4
Irrationals

2
Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) 0
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) -6 Integer, Rational, Real
Reals
Rationals
2
3
Identify all of the sets to which each number belongs.
Whole, Integer, Rational, Real
3) 14 Natural, Whole, Integer,
Rational, Real
4) 6 Irrational, Real
Graphing Real Numbers on a Number Line
Graph the following numbers on a number line.
3
1
1
2
5
3

0.4
2) - 2.03 Rational, Real
-4
3) 2 3
Irrational, Real
-3
3
4) 10 Integer, Rational, Real
-2
-1
0
1 1 0.4
2
1
2
5
3
3
4

List the numbers in the set below that
belong to the set of rational numbers.
1

5,  , .3, .8,
2





(a)
1

5,  , .3, .8,
2

9,  ,

9, 

(b)
1


5,  , .8,  
2


(c)
1

5,  , .3, .8,
2

(d)
1


5,  , .3, .8,  
2


9,

13 

Section 1.1B
Real Numbers and Number
Operations

13 


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Commutative Properties (Change order)
Associative Properties (Change grouping)
Associative Property of Addition
Commutative Property of Addition
a+b=b+a
Example:
3+5=5+3
Commutative Property of Multiplication
a •b  b•a
Example:
4•7  7•4
Identity Properties (stays the same)
Identity Property of Addition
(a + b) + c = a + (b + c)
Example:
(4 + 11) + 6 = 4 + (11 + 6)
Associative Property of Multiplication
(a • b) • c  a • (b • c)
Example:
(2 • 5) • 4  2 • (5 • 4)
Inverse Properties (goes back)
Inverse Property of Addition
x+0=x
x  (  x)  0
Example:
Example:
4+0= 4
77  0
Identity Property of Multiplication
x •1  x
Example:
7 •1  7
Inverse Property of Multiplication
x•
1
1
x
Example:
7•
1
1
7
Distributive Properties (Distributes a term)
Distributive Property of Multiplication
a(b  c)  ab  ac
Example:
4(2  5)  4 • 2  4 • 5
http://www.shelovesmath.com/algebra/beginning-algebra/numbers-properties-and-notation-in-algebra/#properties
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Identify the property shown below.
1) (2 + 10) + 3 = (10 + 2) + 3 Comm. Prop. of Add.
2) 5  (7  4)  (7  4)  5 Comm. Prop. of Mult.
3) (6 + 8) + 9 = 6 + (8 + 9) Assoc. Prop. of Add.
4) (10  4)  3  10  (4  3) Assoc. Prop. of Mult.
5) 5  0  0 Mult. Prop. of Zero
6) 5 + 0 = 5 Identity Prop. of Add.
7) 5  1  5 Identity Prop. of Mult.
http://www.shelovesmath.com/algebra/beginning-algebra/numbers-properties-and-notation-in-algebra/#properties
Identify the property shown below.
1) 7 + ( 3 + 5 ) = ( 7 + 3 ) + 5 Assoc. Prop. of Add.
2) 5  5  0
3) 6  9  9  6
Inverse Prop. of Addition
Comm. Prop. of Mult.
4) 4  (2  7)  (2  7)  4 Comm. Prop. of Mult.
5) 7 + 8 = 8 + 7 Comm. Prop. of Add.
6) 12 + 0 = 12 Identity Prop. of Add.
7) 10  1  10 Identity Prop. of Mult.
Use the distributive property to simplify.
1) 3(x + 7)
6) x(a + m)
3x + 21
ax + mx
2) 2(a - 4)
7) -4(3 - r)
2a - 8
-12 + 4r
3) -7(8 - m)
8) 2(x - 8)
-56 + 7m
2x - 16
4) 3(4 - a)
9) -(2m - 3)
12 - 3a
-2m + 3
5) (3 - k)5
10) (6 - 2y)3
15 - 5k
18 - 6y
Use a property to simplify each expression below.
Identify the property used.
1) 5  19  2
5  2  19
10  19
190
Comm. Prop. of Mult.
2) 7 + ( 43 + 29 )
( 7 + 43 ) + 29
( 50 ) + 29
79
Assoc. Prop. of Add.
Section 1.2
Algebraic Expressions and Models
4