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1.1 – REAL NUMBERS AND NUMBER OPERATIONS Algebra 2

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11 ndash REAL NUMBERS AND NUMBER OPERATIONS

Algebra 2

Objectives

1Know the classifications of numbers

2Know where to find real numbers on the number line

3Know the properties and operations of real numbers

Classification of Real Numbers

hellip -4 -3 -2 -1 0 1 2 3 4hellip

whole numbers

integers

Classification of Real Numbers

rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminatesirrational numbers - numbers that canrsquot be written as a fraction or a decimal that repeats or terminates (π e radic3)

Classification of Real NumbersClassification Examples

counting (natural)

whole

integers

rational

irrational

Using a Number Line

Locate these numbers on a number line

12 12 34 3 72 8

5 3

1 Convert to decimal2 Determine range and mark line3 Plot original values

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Objectives

1Know the classifications of numbers

2Know where to find real numbers on the number line

3Know the properties and operations of real numbers

Classification of Real Numbers

hellip -4 -3 -2 -1 0 1 2 3 4hellip

whole numbers

integers

Classification of Real Numbers

rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminatesirrational numbers - numbers that canrsquot be written as a fraction or a decimal that repeats or terminates (π e radic3)

Classification of Real NumbersClassification Examples

counting (natural)

whole

integers

rational

irrational

Using a Number Line

Locate these numbers on a number line

12 12 34 3 72 8

5 3

1 Convert to decimal2 Determine range and mark line3 Plot original values

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Classification of Real Numbers

hellip -4 -3 -2 -1 0 1 2 3 4hellip

whole numbers

integers

Classification of Real Numbers

rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminatesirrational numbers - numbers that canrsquot be written as a fraction or a decimal that repeats or terminates (π e radic3)

Classification of Real NumbersClassification Examples

counting (natural)

whole

integers

rational

irrational

Using a Number Line

Locate these numbers on a number line

12 12 34 3 72 8

5 3

1 Convert to decimal2 Determine range and mark line3 Plot original values

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Classification of Real Numbers

rational numbers - numbers that can be written as a fraction or a decimal that repeats or terminatesirrational numbers - numbers that canrsquot be written as a fraction or a decimal that repeats or terminates (π e radic3)

Classification of Real NumbersClassification Examples

counting (natural)

whole

integers

rational

irrational

Using a Number Line

Locate these numbers on a number line

12 12 34 3 72 8

5 3

1 Convert to decimal2 Determine range and mark line3 Plot original values

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Classification of Real NumbersClassification Examples

counting (natural)

whole

integers

rational

irrational

Using a Number Line

Locate these numbers on a number line

12 12 34 3 72 8

5 3

1 Convert to decimal2 Determine range and mark line3 Plot original values

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Using a Number Line

Locate these numbers on a number line

12 12 34 3 72 8

5 3

1 Convert to decimal2 Determine range and mark line3 Plot original values

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + ac

opposite of a = -a (additive inverse)inverse of a = 1a (multiplicative inverse)

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Property Addition Multiplication

closure a + b = real number ab = real number

commutative a + b = b + a ab = ba

associative (a + b) + c = a + (b + c)

(ab)c = a(bc)

identity a + 0 = a a x 1 = a

inverse a + -a = 0 a x 1a = 1

distributive a(b + c) = ab + acIdentify the property5 + -5 = 02(3 5) = (2 3)54(3 + 7) = 4 3 + 4 75 + 3 = 3 + 5

(x + 5) + 4 = x + (5 + 4)1x = x23 32 = 12 3 4 = 3 2 4

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

sum ndash answer to an addition problem

difference ndash answer to a subtraction problem

product ndash answer to a multiplication problem

quotient ndash answer to an division problem

Key Vocabulary

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

12 ndash ALGEBRAIC EXPRESSIONS AND MODELS

Algebra 2

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Objectives

1Evaluate algebraic expressions

2Simplify expressions3Apply expressions to real

world examples

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Remember PEMDAS

5 16 2 4 1Parenthesis Exponents Multiplication Division Addition Subtraction

Order of Operations = PEMAMultiplicationdivision and additionsubtraction have equal

priority in an expression In this case we just apply the ldquoleft to rightrdquo rule

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

PEMA

Please Excuse My Aunt Penguins Eat Many Alligators Plaid Eggshells Marinate Aliens Private Earlobes Memorize Anteaters Public Education Manipulates

Adolescents

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Examples

Evaluate these expressions

4 52 (3 5)1) 2)

2 -16

2

2

(4 1) 37 2

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Examples

Evaluate

when x = -4

when x = 3

when x = frac12

3 22x 3x 27

-53

108

28

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

Simplifying Expressions

like terms - terms that have the same variables with the same powers

Simplify these expressions

2x4x2x31x7x 232

2222 yx4xy2yx3xy7yx

8)5(x2)3(x

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow

HOMEWORK DUE TOMORROW

11 pg 7 27 28 33-38 43 45 47 49

12 pg 14 30-32 37-40 48 50

  • 11 ndash Real Numbers and Number Operations
  • Objectives
  • Classification of Real Numbers
  • Classification of Real Numbers (2)
  • Classification of Real Numbers (3)
  • Using a Number Line
  • Slide 7
  • Slide 8
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • Slide 15
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Slide 20
  • Slide 21
  • Slide 22
  • Key Vocabulary
  • 12 ndash Algebraic Expressions and Models
  • Objectives (2)
  • Remember PEMDAS
  • PEMA
  • Examples
  • Examples (2)
  • Simplifying Expressions
  • Homework Due Tomorrow