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Chapter 1: Tools of Algebra 1-2: Algebraic ExpressionsPowerPoint Presentation

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

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### Chapter 1: Tools of Algebra1-2: 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
- 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 Expressions

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

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 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 Expressions

- Evaluating an Algebraic Expression with Exponents
- Evaluate -x2 – 2(x + 1) for x = 3

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 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 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 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 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 Expressions

- Some properties for simplifying expressions
- Subtraction
- a – b = a + (-b)

- Division
- The rest (page 13 of your book) are pretty self-explanatory

- Subtraction

1-2: Algebraic Expressions

- Combining Like Terms
- 3k – k
- 5z2 – 10z – 8z2 + z
- –(m + n) + 2(m – 3n)

1-2: Algebraic Expressions

- Combining Like Terms
- 3k – k
- 3k – 1k
- 2k

- 5z2 – 10z – 8z2 + z
- –(m + n) + 2(m – 3n)

- 3k – k

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)

- 3k – k

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

- 3k – k

1-2: Algebraic Expressions

- Assignment
- Page 15
- Problems 2-36 (even problems)

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