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Ch. 3 Notes Part A
1
Name _____________________________________________________ Hour ______________
3-1 Integers and Number Lines
Real Numbers
Rationals
Irrationals
Integers
Whole Numbers
Natural Numbers
Natural Numbers – ___________________ (N = _____________________)
Whole Numbers – ___________________________ (W = ______________)
Integers – _______________________________ (I =__________________)
Rationals – ______________________________________ (Ex. _________)
Irrationals – ____________________________________ (Ex. __________)
-5
-4
-3
-2
-1
0
Examples:
Graph these numbers on a number line.
1.
-8 and +6
2.
1
1
 3 and 2
4
2
Write the numbers in increasing order.
3.
1
2
1
4
-4, 4 , -5, 2, 2 , 5
Homework:
Section 3-1 # 1-19 all
1
2
3
4
5
Ch. 3 Notes Part A
2
Name _____________________________________________________ Hour ______________
3-1 Opposites and Absolute Value
Opposite – ____________________________________________________
Absolute Value – _______________________________________________
Examples:
Find the opposite of the number.
1.
-7
2.
12
3.
-½
Find the absolute value of the number.
4.
8
Homework:
5.
16   3
6.
72
Section 3-1 # 20-35 all
3-2 Adding and Subtracting Integers using Number Lines
Walking on a number line
Steps:
1.
The first number tells you where to __________________________
2.
The operation tells you which ______________________________
(Addition – __________________, Subtraction – ______________)
3.
The sign on the second number tells you which _________________
(Positive – __________________, Negative – _________________)
4.
The last number tells you how many _________________________
Examples:
1.
3–7
Homework:
2.
Number line worksheet
-5 + (-8)
Ch. 3 Notes Part A
3
Name _____________________________________________________ Hour ______________
3-2 More Adding and Subtracting Integers
Rules:
 _________________________________________________________
_________________________________________________________
Adding Same Sign
 _________________________________________________________
Adding Opposite Signs
 _________________________________________________________
_________________________________________________________
Examples:
Find each sum or difference.
1.
(-7) + (-15)
3.
8 – (-3)
Homework:
2.
5 + (-3)
4.
12 – 20
3-2 # 1-32 all
3-2 Adding and Subtracting Integers
Examples:
Find each sum or difference.
1.
9 – (-3)
Homework:
3-2 # 33-64 all
2.
14 + (-8)
Ch. 3 Notes Part A
4
Name _____________________________________________________ Hour ______________
3-3 Adding and Subtracting Real Numbers
Examples:
Find each sum or difference.
1.
5.7 + (-3.2)
2.

4  7
  
15  15 
Find each sum or difference.
3.
-45 + 76 + 53 – 27 – 53
Homework:
3-3 # 1-27 all
3-3 Evaluating with Integers
Examples:
Evaluate each expression when a = 3, b = -2, and c = -6.
1.
2a – 3b
2.
6a + c
3.
Homework: 3-3 # 28-49 all
-2b + c – a
Ch. 3 Notes Part A
5
Name _____________________________________________________ Hour ______________
3-4 Combining Like Terms
Term – _______________________________________________________
Like Term – ___________________________________________________
___________________________________________________
Coefficient – __________________________________________________
Constant – ____________________________________________________
Examples:
Combine Like Terms
1.
3x – 2x + 7x
3.
2xy – 4x + 7x – 3xy
Homework:
2.
5 hands + 3 hands
4.
5x2 + 3x2 – 12x2
Section 3-4 # 1-24
3-4 More Like Terms
Examples:
Combine Like Terms
1.
4x + 5x – 7
3.
2.
5m2n + 4mn – 11mn – 10m2n + 8
Homework:
Section 3-4 # 25 – 52
2m – 3 – 6m
Ch. 3 Notes Part A
6
Name _____________________________________________________ Hour ______________
3-5 Multiplying Integers
Rules:
Positive times positive = _________________
Negative times negative = ________________
Positive times negative = _________________
Negative times positive = _________________
Examples:
Find each product.
1.
(-15) (2)
3.
2.
(-6.1)(-9)
 7  24 
   
 8  35 
Homework:
Section 3-5 # 1 – 20
3-5 More Multiplying
Examples:
Evaluate each expression when x = -3, y = 7, and z = -2
1.
x + 2y
2.
-6x + -3y
3.
-4(x + z)
4.
7x – 2y + 3z
Ch. 3 Notes Part A
7
Name _____________________________________________________ Hour ______________
Multiply
5.
1
5 of -20
Homework:
6.
2
3 of -66
Section 3-5 # 21 – 44
3-6 Distributive Property
Distributive Property
For all real numbers a, b, and c:
____________________________________
____________________________________
Examples:
Apply the distributive property.
1.
3(x + 8)
3.
1
5 (x – 20)
Homework:
Section 3-6 # 1 – 18
2.
5(x – 7)
4.
3(2x – 8)
Ch. 3 Notes Part A
8
Name _____________________________________________________ Hour ______________
3-6 More Distributive Property
Rules:
_______________________
Examples:
Apply the distributive property.
1.
2x(3 – x)
3.
3x2y(-8x3y2 – 9x2y + 12x – 8y)
Homework:
2.
5x(2x + 8)
4.
1
x
4
(-4x + 8)
Section 3-6 # 19-36 all
3-7 Dividing Integers
Rules:
Positive divided by positive = _________________
Negative divided by negative = ________________
Positive divided by negative = _________________
Negative divided by positive = ________________
Examples:
Find each quotient.
1.
 36
4
3.
 24   42 
    
 36   81 
2.
 3.8 19
Ch. 3 Notes Part A
9
Name _____________________________________________________ Hour ______________
Simplify
4.
3(x – 9) + 6x
Homework:
5.
-2(2x – 18) – 8x
Section 3-7 # 1-30 all
3-8 CRT 1 Review
Fractions
Adding and Subtracting
 Find a ___________________________________________
 Change the _______________________________________
Multiplying
 Change mixed numbers to improper fractions
 ________________________________________________
 Multiply _________________________________________
Dividing
 Change mixed numbers to improper fractions
 _________________________________________________
Decimals
Adding and Subtracting
 _________________________________________________
Multiplying
 Multiply without the decimals
 Count the number of numbers ________________________,
put this many numbers ___________________ in the answer
Dividing
 Move the decimal on the _____________________________
 Move the decimal on the ________ if you moved the outside
 Divide
Ch. 3 Notes Part A
10
Name _____________________________________________________ Hour ______________
Order of Operations
P________________
E________________
M________________/D______________
A________________/S_______________
Examples:
Find each sum or difference.
1.
-2.05 – 30.4
2.
 3  7
    
 16   16 
4.
 10   3 
    
 3   10 
Find each product or quotient.
3.
(-1.2)(4.8)
Evaluate.
7  32   2  4
5.
Homework:
3-8 # 1-30
Name _____________________________________________________ Hour ______________
11
Monday
Tuesday
Warm-ups for 10/5-10/9
Wednesday
Thursday
Friday
Name _____________________________________________________ Hour ______________
12
Monday
Tuesday
Thursday
Warm-ups for 10/12-10/16
Wednesday
Quiz 3.1-3.3
Friday
Name _____________________________________________________ Hour ______________
13
Monday
Tuesday
Thursday
Warm-ups for 10/19-10/23
Wednesday
Friday
Quiz 3.4-3.6
Name _____________________________________________________ Hour ______________
14
Monday
Tuesday
Thursday
Warm-ups for 10/26-10/30
Wednesday
Friday
Ch. 3 Test
Name _____________________________________________________ Hour ______________
Monday
CRT 1A
15
Tuesday
Wednesday
Half Day
Parent Teacher Conferences
Thursday
No School
Friday
Warm-ups for 11/2-11/6
CRT 1B