Objective - To simplify variable expressions involving parenthesis and exponents.

1
Objective - To simplify variable expressions
involving parenthesis and exponents.
2
Evaluate the expression given a 3.
3
Fact Scientific calculators and computers follow
the order of operations. Four function
calculators do not.
4 - Function Calculator
Scientific Calculator
Computer
3 4 x 2
3 4 2
3 4 x 2

7 x 2 14
3 8 11
3 8 11
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Symbolic Differences in Calculators and Computers
Scientific Calculator
Computer
Expression

/
y
4 x 2
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Key Sequences and Computer Input
Calculator Key Sequence
Computer
Expression
3(8 - 2)
4 3
6 - 2
2
6 8
3 - 1
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Associative Property
Associative -
Re-grouping is ok! You can re-group
numbers together.
Associative Property of Addition
(a b) c a (b c)
(4 2) 9 4 (2 9)
Associative Property of Multiplication
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Write an equivalent expression.
1) (1 5) 9
1 (5 9)
2)
3)
4) (6 2) 3
6 (2 3)
5)
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Addition and multiplication are associative.
Give counterexamples to prove that subtraction
and division are not associative.
Subtraction
Counterexample
Therefore, subtraction is not associative.
Division
Counterexample
Therefore, division is not associative.
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Commutative vs. Associative
Identify each property shown below.
Comm. Prop. Of Add.
1) 5 1 1 5
2)
Assoc. Prop. Of Mult.
3)
Comm. Prop. Of Mult.
4) (6 2) 3 (2 6) 3
Comm. Prop. Of Add.
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Commutative vs. Associative
Commutative
Associative
(2 7) 8 (7 2) 8
(2 7) 8 2 (7 8)
Flip-flop
Re-group
(2 7) 8 8 (2 7)
Flip-flop
( ) does not imply Associative
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Commutative vs. Associative
Identify each property shown below.
Comm. Prop. Of Add.
1) (9 3) 1 (3 9) 1
2)
Assoc. Prop. Of Mult.
3)
Comm. Prop. Of Add.
4)
Comm. Prop. Of Mult.
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Give the property that justifies each step.
Statement
Reasons
16 (27 84)
Given
16 (84 27)
Comm. Prop. of Add.
(16 84) 27
Assoc. Prop. of Add.
(100) 27
Simplify
127
Simplify
13
Use the commutative and associative properties to
simplify each expression.
1)
2) 12 (29 8)
12 (8 29)
(12 8) 29
(20) 29
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