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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
HOMEWORK DUE TOMORROW
11 pg 7 27 28 33-38 43 45 47 49
12 pg 14 30-32 37-40 48 50
Recommended