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1.2: Algebraic Expressions & Models
Goals:
1.Use the order of operations to simplify expressions2.Substitute the value of a variable to evaluae an expression
Order of
Operations
Parenthesis/Brackets
Exponents
Multiplication/Division
Addition/Subtraction
Parenthesis/Brackets Perform all operations inside
parenthesis/brackets first when solving and equation.
)3(5)624(8 2
)3(5)4(8 2
Order of
Operations
Parenthesis/Brackets
Exponents
Multiplication/Division
Addition/Subtraction
Exponents Next, perform the operations that
involve exponents
)3(5)624(8 2
)3(5)4(8 2
)3(5168
Order of
Operations
Parenthesis/Brackets
Exponents
Multiplication/Division
Addition/Subtraction
Multiplication/Division Thirdly, perform operations either
multiplication or division (in order from left-to-right)
)3(5)624(8 2
)3(5)4(8 2
)3(5168 )15(168
Order of
Operations
Parenthesis/Brackets
Exponents
Multiplication/Division
Addition/Subtraction
Addition/Subtraction The last step you perform is
addition or subtraction (in order from left-to-right).
)3(5)624(8 2
)3(5)4(8 2
)3(5168 )15(168 )15(8
23
Example: Evaluate the following problems by using the order of operations:
82415 2 821615 Exponents: Square 4
first
8)8(15 Division: Take 16 divided by -2
823 Subtraction: Subtract -8 from 15
31 Addition: Add 23 and 8 together
Example: Evaluate the following problems by using the order of operations:
153)327( 2 Work inside the parenthesis first. Square 3
Finish simplifying the parenthesis by dividing 27 by 9
1)15(3 Multiplication: Multiply -3 by 5
112 Addition: Add 3 and -15 together
153)927(
1533
Addition: Add -12 and 1 together
11
Evaluating an Expression
Substitute the values of the variables into the expressionsSubstitute the values of the variables into the expressions
Evaluate the following for when:x = 3, y = 4, and z = -2
xx 94 2 1)
yxz 22 43 2) yzx
xyz2
22
3)
Evaluating an Expression
Substitute the values of the variables into the expressionsSubstitute the values of the variables into the expressions
Evaluate the following for when:x = 3, y = 4, and z = -2
xx 94 2 1)
yxz 22 43 2) yzx
xyz2
22
3)
xx 94 2 )3(9)3(4 2 )3(9)9(4
2736
9
Evaluating an Expression
Substitute the values of the variables into the expressionsSubstitute the values of the variables into the expressions
Evaluate the following for when:x = 3, y = 4, and z = -2
xx 94 2 1)
yxz 22 43 2) yzx
xyz2
22
3)
)4)(3(4)2(3 22
)4)(9(4)4(3 )4(3612
14412
yxz 22 43
132
Evaluating an Expression
Substitute the values of the variables into the expressionsSubstitute the values of the variables into the expressions
Evaluate the following for when:x = 3, y = 4, and z = -2
xx 94 2 1)
yxz 22 43 2) yzx
xyz2
22
3)
yzx
xyz2
22
)4)(3(2
)4)(3()2(2
22
)4)(9(2
)16)(3(4
72
192
3
8
3
8
