1. Algebraic Order of Operations Or—More about Aunt Sally

2. Why do we need a rule for this anyway? To avoid confusion and misunderstandings, mathematicians have agreed to certain rules for computation called- - - Algebraic Order of Operations

3. Review of terms Symbols like parentheses ( ), brackets [ ], braces { }, and fraction bars ------ are symbols of inclusion.

4. 1. Perform all operations involving inclusion 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. Algebraic Order of Operations

5. Examples: Use the algebraic order of operations to evaluate the expression. 3 – 12 ÷ 4 3 – 3 = 0Divide first and then subtract.

6. Example: (8 * 7 + 2) + (3 * 2 – 2 * 2) (56 + 2) + (6 – 4) 58 + 2 60

7. And another example 6 2 ÷ 4 * 3 36 ÷ 4 * 3 Evaluate exponent 9 *3Do division 27Do multiplication

8. And still another---- 3 – 1 + 24 ÷ 6 3 – 1 + 4 2 + 4 6

9. And still one more--- Given a = 5, b = 3, and c = 4, evaluate: a + b – c (5) + (3) – (4)Substitute values 8 – 4Addition 4Subtraction

10. And even more --- Given a = 5, b = 3, and c = 4, evaluate: (a 2 - b 2 ) + c 2 (25 – 9) + 16Exponents (16) + 16Parentheses 32Addition

11. Try these--- 1.28 – 2 * 0 2.59 – 4 * 6 – 4 3.28 + 59 97 – 68 4.10 + 2{44 – [3(2 + 7)]} 5.2{2[2(2 + 2)]}