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Chapter 1: Tools of Algebra 1-2: Algebraic Expressions. Essential Question: How is the distributive property useful in simplifying expressions?. 1-2: Algebraic Expressions. Definitions A symbol (usually a letter) that represents one or more numbers is called a variable

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chapter 1 tools of algebra 1 2 algebraic expressions

Chapter 1: Tools of Algebra1-2: Algebraic Expressions

Essential Question: How is the distributive property useful in simplifying expressions?

1 2 algebraic expressions
1-2: Algebraic Expressions
  • Definitions
    • A symbol (usually a letter) that represents one or more numbers is called a variable
    • An expression that contains one or more variables is called an algebraic expression or variable expression
    • You evaluate an expression by substituting numbers for the variable in an expression
1 2 algebraic expressions1
1-2: Algebraic Expressions
  • Evaluating an Algebraic Expression
    • Evaluate a – 2b + ab for a = 3 and b = -1
1 2 algebraic expressions2
1-2: Algebraic Expressions
  • Evaluating an Algebraic Expression
    • Evaluate a – 2b + ab for a = 3 and b = -1
    • Substitute the letters in the equation for their numerical value
      • a – 2b + ab
      • (3) – 2(-1) + (3)(-1)
1 2 algebraic expressions3
1-2: Algebraic Expressions
  • Evaluating an Algebraic Expression
    • Evaluate a – 2b + ab for a = 3 and b = -1
    • Substitute the letters in the equation for their numerical value
      • a – 2b + ab
      • (3) – 2(-1) + (3)(-1)
    • Use PEMDAS
      • 3 + 2 – 3
      • 5 – 3
      • 2
1 2 algebraic expressions4
1-2: Algebraic Expressions
  • Evaluating an Algebraic Expression with Exponents
    • Evaluate -x2 – 2(x + 1) for x = 3
1 2 algebraic expressions5
1-2: Algebraic Expressions
  • Evaluating an Algebraic Expression with Exponents
    • Evaluate -x2 – 2(x + 1) for x = 3
    • Solved no differently. First substitute
      • -x2 – 2(x + 1)
      • -(3)2 – 2((3) + 1)
1 2 algebraic expressions6
1-2: Algebraic Expressions
  • Evaluating an Algebraic Expression with Exponents
    • Evaluate -x2 – 2(x + 1) for x = 3
    • Solved no differently. First substitute
      • -x2 – 2(x + 1)
      • -(3)2 – 2((3) + 1)
    • Then use PEMDAS
      • -(3)2 – 2(4)
      • -9 – 2(4)
      • -9 – 8
      • -17
1 2 algebraic expressions7
1-2: Algebraic Expressions
  • Evaluating using word problems
    • The expression -0.3y + 61 models the percent of eligible voters who voted in presidential elections from 1960 to 2000. In the expression, y represents the number of years since 1960. Find the approximate percentage of eligible voters who voted in 1988.
1 2 algebraic expressions8
1-2: Algebraic Expressions
  • Evaluating using word problems
    • The expression -0.3y + 61 models the percent of eligible voters who voted in presidential elections from 1960 to 2000. In the expression, y represents the number of years since 1960. Find the approximate percentage of eligible voters who voted in 1988.
    • Since we’re looking for the year 1988, and ‘y’ represents the number of years since 1960, we’ll use 1988-1960 = 28 for y in the equation
      • -0.3(28) + 61
      • -8.4 + 61 = 52.6
      • So about 52.6% of eligible voters voted in 1988.
1 2 algebraic expressions9
1-2: Algebraic Expressions
  • Some more definitions
    • A number, variable, or the product of numbers and variables is called a term
    • If there is a number involved in the term, it is called a coefficient
    • Terms that share the same variable parts can be combined
    • Some examples:
      • 3r2 & -r2
      • -2xy3 & 3xy3
    • When like terms are combined (added/subtracted), only the coefficient is changed.
1 2 algebraic expressions10
1-2: Algebraic Expressions
  • Some properties for simplifying expressions
    • Subtraction
      • a – b = a + (-b)
    • Division
    • The rest (page 13 of your book) are pretty self-explanatory
1 2 algebraic expressions11
1-2: Algebraic Expressions
  • Combining Like Terms
    • 3k – k
    • 5z2 – 10z – 8z2 + z
    • –(m + n) + 2(m – 3n)
1 2 algebraic expressions12
1-2: Algebraic Expressions
  • Combining Like Terms
    • 3k – k
      • 3k – 1k
      • 2k
    • 5z2 – 10z – 8z2 + z
    • –(m + n) + 2(m – 3n)
1 2 algebraic expressions13
1-2: Algebraic Expressions
  • Combining Like Terms
    • 3k – k
      • 3k – 1k
      • 2k
    • 5z2 – 10z – 8z2 + z
      • 5z2– 8z2– 10z + 1z (just reordered for clarity)
      • -3z2 – 9z
    • –(m + n) + 2(m – 3n)
1 2 algebraic expressions14
1-2: Algebraic Expressions
  • Combining Like Terms
    • 3k – k
      • 3k – 1k
      • 2k
    • 5z2 – 10z – 8z2 + z
      • 5z2– 8z2– 10z + 1z (just reordered for clarity)
      • -3z2 – 9z
    • –(m + n) + 2(m – 3n)
      • -1(m + n) + 2(m – 3n) (distribute)
      • -1m – 1n + 2m – 6n
      • 1m – 7n
1 2 algebraic expressions15
1-2: Algebraic Expressions
  • Assignment
    • Page 15
    • Problems 2-36 (even problems)
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