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# Order of operations

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### Order of operations

1. 1. The Order of Operations
2. 2. What You'll Learn Vocabulary 1) order of operations Order of Operations <ul><li>Evaluate numerical expressions by using the order of operations. </li></ul>
3. 3. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 Order of Operations
4. 4. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 Order of Operations
5. 5. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 Order of Operations
6. 6. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 Order of Operations
7. 7. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 Order of Operations
8. 8. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 Order of Operations
9. 9. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 Order of Operations
10. 10. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 = 5 • 5 – 16 Order of Operations
11. 11. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 = 5 • 5 – 16 = 25 – 16 Order of Operations
12. 12. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 = 5 • 5 – 16 = 25 – 16 = 9 Order of Operations
13. 13. Evaluate each expression: Order of Operations P E M D A S lease xcuse y ear unt ally
14. 14. Evaluate each expression: 2(5) + 3(4 + 3) Order of Operations P E M D A S lease xcuse y ear unt ally
15. 15. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) Order of Operations P E M D A S lease xcuse y ear unt ally
16. 16. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 Order of Operations P E M D A S lease xcuse y ear unt ally
17. 17. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. Order of Operations P E M D A S lease xcuse y ear unt ally
18. 18. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] Order of Operations P E M D A S lease xcuse y ear unt ally
19. 19. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] Order of Operations P E M D A S lease xcuse y ear unt ally
20. 20. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] = 2[5 + 25] Order of Operations P E M D A S lease xcuse y ear unt ally
21. 21. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] = 2[5 + 25] = 2[30] Order of Operations P E M D A S lease xcuse y ear unt ally
22. 22. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] = 2[5 + 25] = 2[30] = 60 Order of Operations P E M D A S lease xcuse y ear unt ally
23. 23. Write an expression involving division in which the first step in evaluating the expression is addition . Sample answer: 2 + 4 ÷ 3 Order of Operations
24. 24. Write an expression involving division in which the first step in evaluating the expression is addition . Sample answer: 2 + 4 ÷ 3 Order of Operations How can you “force” the addition to be done before the division?
25. 25. Write an expression involving division in which the first step in evaluating the expression is addition . Sample answer: 2 + 4 ÷ 3 ( ) Order of Operations How can you “force” the addition to be done before the division?
26. 26. Finding error(s) in your calculations is a skill that you must develop. Determine which calculation is incorrect and identify the error . Order of Operations 3[4 + (27 ÷ 3)] 2 = 3(4 + 9 2 ) = 3(4 + 81) = 3(85) = 255 3[4 + (27 ÷ 3)] 2 = 3(4 + 9) 2 = 3(13) 2 = 3(169) = 507
27. 27. Finding error(s) in your calculations is a skill that you must develop. Determine which calculation is incorrect and identify the error . Order of Operations 3[4 + (27 ÷ 3)] 2 = 3(4 + 9 2 ) = 3(4 + 81) = 3(85) = 255 3[4 + (27 ÷ 3)] 2 = 3(4 + 9) 2 = 3(13) 2 = 3(169) = 507 Incorrect quantity raised to the second power. The exponent is outside the grouping symbol.
28. 28. Credits End of Lesson! PowerPoint created by http://robertfant.com Robert Fant
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