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**Day Problems Write an algebraic expression for each phrase.**

1. The quotient of 4 and c. 2. The sum of 15 and m. Define a variable and write an algebraic expression for each phrase. 3. 9 less than four times a number. 4. The sum of twice a number and 31.

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**1.2 Exponents and Order of Operations**

Simplifying and evaluating expressions and formulas To simplify a numerical expression, you replace it with its simplest name. Ex. The simplest name for 2 • • 3 is 22. Expressions may include exponents. Exponents provide a shorthand way to show a product of equal factors. EX. 24 = 2 • 2 • 2 • 2 - two to the fourth power 2 – base, 4 – exponent Replace 24 with its simplest name, 16.

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Order of Operations Perform operation(s) inside grouping symbols (Parenthesis, brackets, etc.). Simplify powers. Multiply and divide in order from left to right. Add and subtract in order from left to right. PEMDAS (Please Excuse My Dear Aunt Sally)

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**Simplifying a Numerical Expression**

25 – 8 • = 25 – 8 • 2 + 9 = 25 – = 9 + 9 = 18

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**Evaluating an Algebraic Expression**

Evaluate an algebraic expression by substituting a given number for each variable. Then simplify the numerical expression by using the order of operations.

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**Evaluating an Algebraic Expression**

Evaluate 3a – 23 ÷ b for a = 7 and b = 4. 3a – 23 ÷ b = 3 • 7 – 23 ÷ 4 = 3 • 7 – 8 ÷ 4 = 21 – 2 = 19

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**Simplifying and Evaluating Expressions with Grouping Symbols**

Simplifying an Expression with Parentheses. Ex. Simplify 15 (13 – 7) ÷ (8 – 5) 15 (13 – 7) ÷ (8 – 5) = 15 (6) ÷ 3 = 90 ÷ 3 = 30

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**Evaluating Expressions with Exponents**

Evaluate each expression for c = 15 and d = 12. a. (cd)2 b. cd2 = (15 • 12)2 = 15 • 122 = (180)2 = 15 • 144 = 32, = 2160

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**Simplifying an Expression**

2 [(13 – 7)2 ÷ 3] = 2 [(6)2 ÷ 3] = 2 [36 ÷ 3] = 2 [12] = 24

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**More Practice!!!! Classwork – textbook p. 12 – 13 #1 – 31 odd.**

Homework – textbook p. 12 – 13 #2 – 30 even

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