1-3

1. 1-3 The Algebraic Order of Operations • Warm-up • NCSCOS / Objectives • Glossary Terms

2. 1.3 The Algebraic Order of Operations Warm-up Evaluate each expression • 187 – 18.7 • 30 + 3.2 + 0.3 • 33 • 40 • 12 168.3 33.5 27 480

3. 1.3 The Algebraic Order of Operations NCSCOS • 1.01, 1.02, • Apply the algebraic order of operations Objectives

4. 1.3 The Algebraic Order of Operations Glossary Terms algebraic order of operations grouping symbols inclusion symbols

5. The Algebraic Order of Operations 1. Perform all operations within grouping symbols from innermost outward. 2. Perform all operations with exponents. 3. Perform all multiplications and divisions in order from left to right. 4. Perform all additions and subtractions in order from left to right. 1.3 The Algebraic Order of Operations Rules and Properties

6. Symbols like parentheses, ( ), brackets [ ], braces { }, and the fraction bar , are all called grouping symbols or inclusion symbols. Operations should always be done within the innermost grouping symbols first, then work outward. 1.3 The Algebraic Order of Operations Rules and Properties

7. Use the algebraic order of operations to find the value of expressions. 1.3 The Algebraic Order of Operations Key Skills 1. operations withingrouping symbols 3(8 – 3) – 42 ÷ 8 + 1 2. operations with exponents 3(5) – 42 ÷ 8 + 1 3. multiplication and division3(5) – 16 ÷ 8 + 1 4. addition and subtraction15 – 2 + 1 = 14

8. 1.3 The Algebraic Order of Operations 1. Perform operations within grouping symbols. 2. Evaluate powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.

9. Order of Operations process: 1. Work inside grouping symbols 2. Multiply or divide 3. Add or subtract (from left to right) PEMDAS – L2R Please Excuse My Dear Aunt Sally L2R Parentheses Exponents Multiply or Divide Add or Subtract Left to Right 1.3 The Algebraic Order of Operations

10. Ex 1: Simplify 4 + 15 ÷ 3 Hint: (PEM/DA/S - L2R) 4 + (15 ÷ 3) 4 + 5 = 9 Ex 1a: Simplify 2 + 5 • 3 Hint: (PEM/DA/S - L2R) 2 + (5 • 3) 2 + 15 = 17 1.3 The Algebraic Order of Operations

11. Ex 2: Simplify 3 • 5 – 8 ÷ 4 + 6 Hint: (PEM/DA/S - L2R) (3 • 5) – (8 ÷ 4) + 6 15 – 2 + 6 13 + 6 = 19 Ex 2b: Simplify 5 + 6 • 4 ÷ 3 – 1 Hint: (PEM/DA/S - L2R) 5 + (6 • 4) ÷ 3 – 1 5 + (24 ÷ 3) – 1 5 + 8 – 1 13 – 1 = 12 1.3 The Algebraic Order of Operations

12. 5x2 + 7y = 5(3)2 + 7(2) = 5(9) + 14 = 45 + 14 = 59 1.3 The Algebraic Order of Operations EX 3: Use the algebraic order of operations to evaluate the following when x = 3 and y = 2: x2 + 5x+ 6 + y = (3)2 + 5(3) + 6 + 2 = (9) + 15 + 6 + 2 = 32

13. 2{2[2(3) + 1] + 1} + 1 = 2{2[6 + 1] + 1} + 1 = 2{2[7] + 1} + 1 = 2{14 + 1} + 1 = 2{15} + 1 = 30 + 1 = 31 1.3 The Algebraic Order of Operations Ex 5: Use the algebraic order of operations to evaluate the following: 2{2[2(5) + 1] + 1} + 1 = 2{2[10 + 1] + 1} + 1 = 2{2[11] + 1} + 1 = 2{22 + 1} + 1 = 2{23} + 1 = 46 + 1 = 47

14. 3{4[5(6) – 3(2)] – 2} + 7 = 3{4[30 – 6] – 2} + 7 = 3{4[24] – 2} + 7 = 3{96 - 2} + 7 = 3{94} + 7 = 282 + 7 = 289 1.3 The Algebraic Order of Operations Ex 5a: Use the algebraic order of operations to evaluate the following: 2{2[2(2) + 2] + 2} + 2 = 2{2[4 + 2] + 2} + 2 = 2{2[6] + 2} + 2 = 2{12 + 2} + 2 = 2{14} + 2 = 28 + 2 = 30

15. 1.3 The Algebraic Order of Operations Lesson Quiz Evaluate in order from left to right. 1.18 ÷ 3 + 7 2. 102 ÷ 4 – 8 3. 10 + 23 – 8 + 7 4. 8  2 – 3 + 24 5. 81 ÷ 9  3 + 15 13 17 32 37 42