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Exponents and Order of
Operations
Exponents
• The exponent (little number)
indicates how many times the base
(big number) appears as a factor.
Order of Operations
• Parentheses (grouping symbols)
• Exponents
• Multiplication/Division
• Working from left to right in order they
appear.
• Add/Subtract
• Working from left to right in order they
appear.
Arithmetic Mean
• Fancy way of talking about averages.
• Mean means average
• To average:
• add up all the scores and divide by the
number of scores.
Questions???
A Return to Algebraic
Expressions
• Term: The number/letter
combinations separated by addition
signs in an algebraic expression.
• In my words:
• The “stuff” being added or subtracted
together
Example:
3x + 5y + 7: terms are 3x, 5y, and 7
Components of an
Algebraic Expression
• Constant term: fancy name for a number
• Variable term: terms with letters
• Example: 3xy – 4z + 17
• Variable expression with 3 terms: 3xy, -4z, 17
• 2 variable terms and 1 constant term
Variable Terms
• Consist of two parts
• The variable(letter) part
• The number part
• Example:
− 2xy has a coefficient of 2
− -6j has a coefficient of –6
− W has a coefficient of 1
Algebraic Expressions
• Evaluating Algebraic Expressions:
• Substitute a given value in for the
variable and use order of operations to
simplify
Translating Verbal Expressions
into Variable Expressions
•
Recognize verbal phrases that
translate into mathematical
operations.
Example of evaluating an
expression.
Evaluate 3xy – 2x + 7y when x = 2
and y = 3
3(2)(3) – 2(2) + 7(3)
18 – 4 + 21
14 + 21
35
The value of the expression is 35.
Questions????
Terms
• Like terms
• Terms with the same variable part
• Same means same letter(s) and power(s)
• We simplify variable expressions by
combining like terms.
• To combine like terms, work with the
coefficients of the like terms
Combining Like Terms
• 3x + 5 – 9x
• – 6x + 5
• -5 +3b – 7 – 5b
• -5 – 7 = -12
• 3b – 5b = -2b
• Answer: -2b – 12
Simplifying Numerical
Expressions
• Use order of operations.
• Simplifies to a single number
• Could also be referred to as
evaluating
Simplifying Algebraic
Expressions
• Rewrite using as few symbols as
possible
• Use the distributive property if
necessary to remove parentheses.
• Combine like terms
• More often than not will have
numbers and letters in the final
answer.
Opposite of an expression
• -(4a – 3b + 7c)
• Change everything on the inside to its
opposite
• -4a + 3b – 7c
Distributive Property
• Distributive Property
• This property will be used on a continuous basis
throughout this course.
• a(b + c) = ab + ac
− Examples
2(30 + 5) = 2(30) + 2(5) = 60 + 10 = 70
3(x – 4) = 3(x) – (3)(4) = 3x – 12
• Taking the opposite can be considered distributing -1
• -(4a – 3b + 7c) = -1(4a – 3b + 7c)
Simplifying using the
distributive property
• 5x – 9 + 3(2x + 4)
• 5x – 9 + (3)(2x) + 3(4)
• 5x – 9 + 6x + 12
• 5x + 6x = 11x
• -9 + 12 = 3
• Answer: 11x + 3
Distributing a negative
• -4(y + 2) = (-4)(y) + (-4)(2)
= -4y + (-8)
= -4y – 8
Using the Distributive
Property to Simplify
• 9t – 5r – 2(3r + 6t)
• 9t – 5r – 6r – 12t
• 9t – 12t = -3t
• -5r – 6r = -11r
• Answer: -11r – 3t
Questions???