# Chapter 1: Tools of Algebra 1-2: Algebraic Expressions - PowerPoint PPT Presentation

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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 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

### 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)

### 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 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 Expressions

• Assignment

• Page 15

• Problems 2-36 (even problems)