1. Order of Operations Jan Sands Butterfly Science & Math 2008

2. Why? It is a standard way to simplify mathematical expressions and equations.

3. Purpose Avoids Confusion Gives Consistency For example: Does 8 + 3 4 equal 44 or 20? 8 + 3 4 = 11 4 = 44 8 + 3 4 = 8 + 12 = 20 Which is correct and why?

4. What? Order of Operations is a set of rules that mathematicians have agreed to follow to avoid mass CONFUSION when simplifying mathematical expressions or equations. Without these simple, but important rules, learning mathematics would be maddening.

5. In most languages, the meaning of words depend on their order. Example: Sign the check is not the same as Check the sign

6. Order of Operations Parentheses Exponents Multiplication Division Addition Subtraction

7. Remember… Parenthesis-Please Exponents-Excuse Multiplication-My Division-Dear Addition-Aunt Subtraction-Sally

8. Rules Simplify within Grouping Symbols ( ), { }, [ ], | |, Simplify Exponents Raise to Powers 3 2 is 9 Complete Multiplication and Division from Left to Right Complete Addition and Subtraction from Left to Right

9. The “P” The “P” stands for items in parenthesis. Do all items in the parenthesis first.

10. Fraction Bar A horizontal fraction bar is also a grouping symbol: 4 + 6 10 7 – 2 5 Do the calculations above the fractional bar and below the fractional bar. Simplify the fraction. = = 2

11. The “E” The “E” stands for Exponents. Do anything that has an exponent (power). 5353 3434 2525 4242

12. The “M and D” Represents Multiply and Divide. Do which ever one of these comes first in the problem. Work these two operations from left to right.

13. The “A and S” Represents Add and Subtract. Do which ever one of these comes first. Work these two operations from left to right.

14. The Acronym - PEMDAS Please Excuse My Dear Aunt Sally

15. Practice 1. 5 + (12 – 3) 5 + 9 14 2. 8 – 3 2 + 7 8 - 6 + 7 2 + 7 9

16. Practice 3. 39 ÷ ( 9 + 4 ) 39 ÷ 13 3 4. 10 + 8 ÷ 2 – 6 10 + 4 - 6 14 - 6 8

17. Practice 5. 15 10 3 15 1,000 15,000 6. 36 ÷ (1 + 2) 2 36 ÷ 3 2 36 ÷ 9 4

18. Practice 7. (5 – 1) 3 ÷ 4 4 3 ÷ 4 64 ÷ 4 16 8. 14 + 3(7 -2) – 2 5 14 + 3 5 - 2 5 14 + 15 - 2 5 14 + 15 – 10 29 – 10 19

19. Remember… 1.Work inside grouping symbols. 2.Simplify the exponents. 3.Multiply and divide from left to right. 4.Add and subtract in order from left to right.

20. Check for Understanding 1.3 5 – 4 + 3 = ___ 2.6 + 3 5 – 2 = ___ 3.6 (5 2) + 7 = ___ 4.7 + 4 3 + 8 ÷ 4 = ___ 5.7(6 + 3) + 25 ÷ 5 = ___

21. Check for Understanding - Answers 1.3 5 – 4 + 3 = 14 2.6 + 3 5 – 2 = 19 3.6 (5 2) + 7 = 67 4.7 + 4 3 + 8 ÷ 4 = 21 5.7(6 + 3) + 25 ÷ 5 = 68

22. Remember… Parenthesis-Please Exponents-Excuse Multiplication-My Division-Dear Addition-Aunt Subtraction-Sally

23. Order of Operations A set of rules Organizes numbers Defines procedures Keeps everyone on track PEMDAS

24. Order of Operations