Unit 1 Foundations of Algebra

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Unit 1 Foundations of Algebra

• Variables, Expressions and Operations with Real
  Numbers

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Define the following terms

• Factor
• Greatest common factor (GCF)
• Least common multiple (LCM)
• Operator
• Variable
• Constant
• Algebraic expression
• Additive inverse
• Multiplicative inverse
• Coefficient

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What is algebra?

• Mathematical study of structure, relations, and
  quantity
• Writing, understanding and evaluating equations
  expressions (algebra is NOT all about solving
  equations)

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Writing algebraic expressions

• Translating words into mathematical expressions
• (combine, put together, summed, increased)
• - (less than, difference, take away)
• (product, times)
• , / (ratio, per, quotient)
• (equivalent, the same as, equal to)

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Tips when working with real s

• Calculator tip ALWAYS place ( ) around a
  negative number
• Addition
• s w/ same sign add absolute values use the
  sign of those s
• s w/ different signs subtract absolute values
  use the sign of the greater absolute value
• Subtraction
• replace the being subtracted w/ its additive
  inverse use the rules for addition
• algebraic example x y x (-y)
• Multiplication
• s w/ same sign product will be
• s w/ different signs product will be
• any number 0 0
• Division
• same sign rules as multiplication
• 0/any number 0
• any number/0 undefined

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Real s the line

• The number line can be used as a visual guide to
  addition, subtraction, and absolute value
• Ex.
• 3 (-5) ?

Start at 3
Move along the number line -5 places
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Homework

• Workbook Section 1-1 7-15, odd
• Workbook Section 1-2 2-20, even
• Workbook Section 1-3 1-9, odd 13 18-24, even