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Section I: Distributive Property Section II: Order of Operations

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Objective Use the distributive property to simplify expressions. Section I: The Distributive Property

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The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac and(b + c) a = ba + ca a(b - c) = ab - acand(b - c) a = ba - ca Example #1 5(x + 7) 5 x + 5 7 5x + 35

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Example #2 3(m - 4) 3 m - 3 4 3m - 12 Example #3 -2(y + 3) -2 y + (-2) 3 -2y + (-6) -2y - 6

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Which statement demonstrates the distributive property incorrectly? 1.3(x + y + z) = 3x + 3y + 3z 2.(a + b) c = ac + bc 3.5(2 + 3x) = 10 + 3x 4.6(3k - 4) = 18k - 24

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Which statement demonstrates the distributive property incorrectly? 1.3(x + y + z) = 3x + 3y + 3z 2.(a + b) c = ac + bc 3.5(2 + 3x) = 10 + 3x 4.6(3k - 4) = 18k - 24 Answer Now

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A term is a 1) number, or 2) variable, or 3) a product (quotient of numbers and variables). Example 5 m 2x 2

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The coefficient is the numerical part of the term. Examples 1)4a 4 2) y 2 1 3)

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Like Terms are terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

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Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x 3 y, xy 3 No, the exponents are on different variables.

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The above expression simplifies to: 5a and a are like terms and are like terms

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12a 2) 6.1y - 3.2y 2.9y 3) 4x 2 y + x 2 y 5x 2 y 4) 3m 2 n + 10mn 2 + 7m 2 n - 4mn 2 10m 2 n + 6mn 2 Simplify 1) 5a + 7a

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21a + 6b 6) 4d + 6a 2 - d + 12a 2 18a 2 + 3d 7) y 5) 13a + 8a + 6b

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Objective: Use the order of operations to evaluate expressions Section II: Order of Operations

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Simple question: 7 + 4 3=? Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

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ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

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Once again, evaluate 7 + 4 x 3 and use the order of operations. = 7 + 12(Multiply.) = 19 (Add.)

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Example #1 14 ÷ 7 x 2 - 3 = 2 x 2 - 3 (Divide) = 4 - 3 (Multiply) = 1(Subtract)

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Example #2 3(3 + 7) 2 ÷ 5 = 3(10) 2 ÷ 5(parentheses) = 3(100) ÷ 5(exponents) = 300 ÷ 5(multiplication) = 60(division)

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Example #3 20 - 3 x 6 + 10 2 + (6 + 1) x 4 = 20 - 3 x 6 + 10 2 + (7) x 4(parentheses) = 20 - 3 x 6 + 100 + (7) x 4(exponents) = 20 - 18 + 100 + (7) x 4 (Multiply) = 20 - 18 + 100 + 28 (Multiply) = 2 + 100 + 28 (Subtract ) = 102 + 28 (Add) = 130(Add)

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Which of the following represents 11 2 + 18 - 3 3 · 5 in simplified form? 1.-3,236 2.4 3.107 4.16,996

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Which of the following represents 11 2 + 18 - 3 3 5 in simplified form? 1.-3,236 2.4 3.107 4.16,996

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Simplify 16 - 2(10 - 3) 1.2 2.-7 3.12 4.98

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Simplify 16 - 2(10 - 3) 1.2 2.-7 3.12 4.98

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Simplify 24 – 6 4 ÷ 2 1.72 2.36 3.12 4.0

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Simplify 24 – 6 4 ÷ 2 1.72 2.36 3.12 4.0

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1.substitute the given numbers for each variable. 2.use order of operations to solve. Evaluating a Variable Expression To evaluate a variable expression:

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Example # 4 n + (13 - n) 5 for n = 8 = 8 + (13 - 8) 5 (Substitute.) = 8 + 5 5 (parentheses) = 8 + 1 (Divide) = 9 (Add)

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Example # 5 8y - 3x 2 + 2n for x = 5, y = 2, n =3 = 8 2 - 3 5 2 + 2 3 (Substitute.) = 8 2 - 3 25 + 2 3 (exponents) = 16 - 3 25 + 2 3 (Multiply) = 16 - 75 + 2 3 (Multiply) = 16 - 75 + 6 (Multiply) = -59 + 6 (Subtract) = -53 (Add)

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What is the value of if n = -8, m = 4, and t = 2 ? 1.10 2.-10 3.-6 4.6

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What is the value of if n = -8, m = 4, and t = 2 ? 1.10 2.-10 3.-6 4.6

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