# Section I: Distributive Property Section II: Order of Operations.

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Section I: Distributive Property Section II: Order of Operations

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

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

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

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

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

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

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

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

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.

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

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

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

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

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.

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)

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

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

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

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)

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

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

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

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

Simplify 24 – 6  4 ÷ 2 1.72 2.36 3.12 4.0

Simplify 24 – 6  4 ÷ 2 1.72 2.36 3.12 4.0

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

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

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)

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

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