The order of operations is a set of rules for performing mathematical operations in the proper sequence. It states that operations inside parentheses should be performed first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. The document provides examples of applying the order of operations to evaluate expressions step-by-step. It also includes practice problems and resources for further learning.

1. Order of Operations

2. Definition The order in which mathematicians perform math problems. Parenthesis – working inward outward Exponents Multiply or Divide – Left to Right Add or Subtract – Left to Right

3. Mnemonic P lease Parenthesis E xcuse Exponents M y D ear Multiply or Divide – Left to Right A unt S ally Add or Subtract – Left to Right

4. Example 1: 2 x 3 - (4-2) + 3 2 Multiplication Parenthesis Subtraction Addition Exponents

5. 2 x 3 - (4-2) + 3 2 2 x 3 - 2 + 3 2 Parenthesis Exponents 6 - 2 + 9 Multiply 2 x 3 - 2 + 9 Add or Subtract – Left to Right 4 + 9 13

6. Example 2: 4 X 6 – (3 + 4) + 2 2 Multiplication Parenthesis Subtraction Addition Exponents

7. 4 X 6 – (3 + 4) + 2 2 4 x 6 - 7 + 2 2 Parenthesis Exponents 24 – 7 + 4 Multiply 4 X 6 – 7 + 4 Add or Subtract – Left to Right 17 + 4 21

8. Practice Problems 3 + 5 x 7 (1 + 3) x (8 - 4) 6 - 6 + (7 - 0) - 7 4 - 3 + (5 - 1) - 3 3 + 9 x 8 – 6 2 24 / 6 x 2 x 2 / 4 2+3 x (4+(6 x 3-8)) x2 Answer Answer Answer Answer Answer Answer Answer

9. Resources Math Goodies http://www.mathgoodies.com/lessons/vol7/order_operations.html Amby.com http://amby.com/educate/ord-op/ The World of Math Online http://www.math.com/school/subject2/lessons/S2U1L2GL.html Fun Brain http://www.funbrain.com/algebra/index.html Dositey – Mystery Game http://www.dositey.com/math/m/mystery2SMA.htm Aplus Math – Flash Cards http://www.aplusmath.com/cgi-bin/Flashcards/Order_Of_Operations AAA Math.com http://www.aaamath.com/pro73c-order-of-operations.html

10. 3 + 5 x 7 3 + 35 38 Back

11. (1 + 3) x (8 - 4) 4 x (8 – 4) 4 x 4 16 Back

12. 6 - 6 + (7 - 0) – 7 6 – 6 + 7 - 7 0 + 7 – 7 7 – 7 0 Back

13. 4 - 3 + (5 - 1) – 3 4 – 3 + 4 -3 1 + 4 – 3 5 – 3 2 Back

14. 3 + 9 x 8 – 6 2 3 + 9 X 8 – 36 3 + 72 – 36 75 – 36 39 Back

15. 24 / 6 x 2 x 2 / 4 4 x 2 x 2 8 x 2 16 Back

16. 2+3 x (4+(6 x 3-8)) x2 2 + 3 x (4 + (18 – 8)) x 2 2 + 3 x (4 + 10) x 2 2 + 3 x 14 x 2 2 + 42 x 2 2 + 84 86 Back