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Agenda
• Call Roll
• Introduce
• Class policies & procedures
– Syllabus, textbook form,
• Student Handbook
• Info sheets
• Notes
• Icebreaker
• Assign HW
The Essential 55
by Ron Clark
• Rule 1: When responding to any
adult, you should answer by
saying “Yes ma’am” or “No sir.”
Notes 1.1
Addition and Subtraction
The Real Number System
Reals
Rationals
(fractions, decimals)
Integers
(…, -1, -2, 0, 1, 2, …)
Whole
(0, 1, 2, …)
Natural
(1, 2, …)
Irrationals
(no fractions)
pi, e
Rational vs. Irrational
Rational numbers CAN be
expressed as a fraction.
1

2
9
-2.5
Decimals that
end or repeat
-9.212121…
Irrational numbers CANNOT be
expressed as a fraction.
2

-2.569234567…
The number line
-2.5
-5
-4
-3
-2
1

2
-1

2
0
1
2
3
4
5
Rational or Irrational?
1) 3.12112111211112…
Irrational
2) 8.974974974…
Rational
3) 4.325
Rational
4)
Irrational
17
Rational or Irrational? You Try …
5)  32
Irrational
6)
49
Rational
7) .47646464..
Rational
8)
59
37
Rational
9) 2.573407656631…. Irrational
Addition
Signs are alike, ADD
10) -5 + (-9) = -14
11) 6 + 20 = 26
Subtraction
Signs are different, SUBTRACT
12) 23 + (-11) = 12
13) -12 + 7 = -5
keep the sign of the larger number
You Try …
14) 5 – (- 4)
=5+4=9
15) 8 – (- 9)
= 8 + 9 = 17
16) 23.7 – 5.9
=17.8
17) -12 + (-16) = -28
Adding and Subtracting Fractions
18)
19)
20)
5 1

4 7
3  5
  
8  6
 6   23 
    
 5   10 
Multiplication
If signs are the same, POSITIVE.
1) 5 (10) = 50
2) -6 ( -9) = 54
Multiplication
If signs are different, NEGATIVE
3) 6(-7) = -42
4) -4(5) = -20
Multiplying Fractions
Multiply across
5)
1 3

2 7
6)
1 2

2 5
7)
 6  15
 
 3  24
Commutative Properties
•Addition: a + b = b + a
•Multiplication: a • b = b • a
Associative Properties
•Addition: a + (b + c) = (a + b) + c
•Multiplication: a • (b • c) = (a • b) • c
5.) Use the commutative property of addition to
write an expression equivalent to 3x + 4y
6.) Use the associative property of multiplication.
to write an expression equivalent to 3x(7y • 9z)
Identity Properties
•Addition: a + 0 = a
0 is the additive identity
•Multiplication: a • 1 = a
1 is the multiplicative identity
The identity property allows us to take
an expression and multiply it by 1.
x 8 8x
 =
3 y 8 24 y
This is 1.
These two expressions
are equivalent.
7.) Write an expression equivalent to 6 xy
by simplifying.
2x
6 xy
2x
2  3 x  y

2 x
2 x 3 y
  
2 x 1
 3y
Reciprocal
2
3
3
2
8
1

8
2 3

3 2
=1
 8  1 
     = 1
 1  8 
Division
If signs are alike, POSITIVE.
8)
9)
10  5 = 2
24
 4
6
Division
If signs are different, NEGATIVE
10)
11)
-10  5 = -2
10
1

40
4
Dividing Fractions
Multiply by the reciprocal
12)
1 3

4 5
13)
2  4
 
3  9
14)
 12   7 
   
 5   15 
Zero
7
0
0
7
Homework
• Get syllabus signed
• Get book covered!!!!!
• Get notebook together
• Homework:
7-9/ 15-54 mult. of 3, 55-58 all