Chapter 1 tools of algebra 1 2 algebraic expressions
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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

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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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