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Chapter 1: Tools of Algebra 1-2: Algebraic Expressions

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

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  1. Chapter 1: Tools of Algebra1-2: Algebraic Expressions Essential Question: How is the distributive property useful in simplifying expressions?

  2. 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

  3. 1-2: Algebraic Expressions • Evaluating an Algebraic Expression • Evaluate a – 2b + ab for a = 3 and b = -1

  4. 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)

  5. 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

  6. 1-2: Algebraic Expressions • Evaluating an Algebraic Expression with Exponents • Evaluate -x2 – 2(x + 1) for x = 3

  7. 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)

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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

  13. 1-2: Algebraic Expressions • Combining Like Terms • 3k – k • 5z2 – 10z – 8z2 + z • –(m + n) + 2(m – 3n)

  14. 1-2: Algebraic Expressions • Combining Like Terms • 3k – k • 3k – 1k • 2k • 5z2 – 10z – 8z2 + z • –(m + n) + 2(m – 3n)

  15. 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)

  16. 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

  17. 1-2: Algebraic Expressions • Assignment • Page 15 • Problems 2-36 (even problems)

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