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Int Math 2 Section 2-2 1011

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Order of Operations

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Int Math 2 Section 2-2 1011

  1. 1. Section 2-2 Order of Operations
  2. 2. Essential Question ✤ How do you evaluate numerical expressions using the order of operations? ✤ Where you’ll see this: ✤ Part-time jobs, fitness, entertainment, population
  3. 3. Vocabulary 1. Numerical Expression: 2. Value: 3. Simplify: 4. Exponent: 5. Variable Expression: 6. Evaluate:
  4. 4. Vocabulary 1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division) 2. Value: 3. Simplify: 4. Exponent: 5. Variable Expression: 6. Evaluate:
  5. 5. Vocabulary 1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division) 2. Value: Another name for the answer of the numerical expression 3. Simplify: 4. Exponent: 5. Variable Expression: 6. Evaluate:
  6. 6. Vocabulary 1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division) 2. Value: Another name for the answer of the numerical expression 3. Simplify: Finding the value of a numerical expression by applying the order of operations 4. Exponent: 5. Variable Expression: 6. Evaluate:
  7. 7. Vocabulary 1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division) 2. Value: Another name for the answer of the numerical expression 3. Simplify: Finding the value of a numerical expression by applying the order of operations 4. Exponent: Tells how many times we multiply a number by itself 5. Variable Expression: 6. Evaluate:
  8. 8. Vocabulary 1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division) 2. Value: Another name for the answer of the numerical expression 3. Simplify: Finding the value of a numerical expression by applying the order of operations 4. Exponent: Tells how many times we multiply a number by itself 5. Variable Expression: A collection of numbers and variables, combined using the four operations 6. Evaluate:
  9. 9. Vocabulary 1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division) 2. Value: Another name for the answer of the numerical expression 3. Simplify: Finding the value of a numerical expression by applying the order of operations 4. Exponent: Tells how many times we multiply a number by itself 5. Variable Expression: A collection of numbers and variables, combined using the four operations 6. Evaluate: Substitute in for a variable, then simplify
  10. 10. What is the Order of Operations? “Please Excuse My Dear Aunt Sally”
  11. 11. What is the Order of Operations? “Please Excuse My Dear Aunt Sally” P: Parentheses
  12. 12. What is the Order of Operations? “Please Excuse My Dear Aunt Sally” P: Parentheses E: Exponents
  13. 13. What is the Order of Operations? “Please Excuse My Dear Aunt Sally” P: Parentheses E: Exponents M and D: Multiplication and Division as it appears from left to right
  14. 14. What is the Order of Operations? “Please Excuse My Dear Aunt Sally” P: Parentheses E: Exponents M and D: Multiplication and Division as it appears from left to right A and S: Addition and Subtraction as it appears from left to right
  15. 15. What is the Order of Operations? “Golly, Excuse My Dear Aunt Sally” G: Grouping symbols; parentheses, brackets, division bars, etc. E: Exponents M and D: Multiplication and Division as it appears from left to right A and S: Addition and Subtraction as it appears from left to right
  16. 16. Example 1 Simplify each numerical expression. a. 12 + (3i4) b. 16 − (5i 2 )
  17. 17. Example 1 Simplify each numerical expression. a. 12 + (3i4) b. 16 − (5i 2 ) = 12 + 12
  18. 18. Example 1 Simplify each numerical expression. a. 12 + (3i4) b. 16 − (5i 2 ) = 12 + 12 = 24
  19. 19. Example 1 Simplify each numerical expression. a. 12 + (3i4) b. 16 − (5i 2 ) = 12 + 12 = 16 − (5i2) = 24
  20. 20. Example 1 Simplify each numerical expression. a. 12 + (3i4) b. 16 − (5i 2 ) = 12 + 12 = 16 − (5i2) = 24 = 16 − 10
  21. 21. Example 1 Simplify each numerical expression. a. 12 + (3i4) b. 16 − (5i 2 ) = 12 + 12 = 16 − (5i2) = 24 = 16 − 10 =6
  22. 22. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3
  23. 23. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3 =-5i16 + 3
  24. 24. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3 =-5i16 + 3 = −80 + 3
  25. 25. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3 =-5i16 + 3 = −80 + 3 = −77
  26. 26. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3 =-5i16 + 3 =-(2) − 22 3 = −80 + 3 = −77
  27. 27. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3 =-5i16 + 3 =-(2) − 22 3 = −80 + 3 = −4 − 8 = −77
  28. 28. Example 1 Simplify each numerical expression. c. -5i4 − (−3) 2 d. -(10-8) − 2 2 3 =-5i16 + 3 =-(2) − 22 3 = −80 + 3 = −4 − 8 = −77 = −12
  29. 29. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3
  30. 30. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 1 ⎛ 2⎞ = i⎜ ⎟ 2 ⎝ 3⎠
  31. 31. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 1 ⎛ 2⎞ = i⎜ ⎟ 2 ⎝ 3⎠ 1 4 = i 2 9
  32. 32. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 1 ⎛ 2⎞ = i⎜ ⎟ 2 ⎝ 3⎠ 1 4 = i 2 9 4 = 18
  33. 33. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 1 ⎛ 2⎞ = i⎜ ⎟ 2 ⎝ 3⎠ 1 4 = i 2 9 4 2 = = 18 9
  34. 34. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 2 1 ⎛ 2⎞ 1 2 ⎛ 2⎞ = i⎜ ⎟ = i −⎜ ⎟ 2 ⎝ 3⎠ 3 3 ⎝ 3⎠ 1 4 = i 2 9 4 2 = = 18 9
  35. 35. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 2 1 ⎛ 2⎞ 1 2 ⎛ 2⎞ = i⎜ ⎟ = i −⎜ ⎟ 2 ⎝ 3⎠ 3 3 ⎝ 3⎠ 1 4 2 4 = i = − 2 9 9 9 4 2 = = 18 9
  36. 36. Example 2 2 Evaluate each variable expression for k = 3 1 2 1 a. k b. k − k 2 2 3 2 2 1 ⎛ 2⎞ 1 2 ⎛ 2⎞ = i⎜ ⎟ = i −⎜ ⎟ 2 ⎝ 3⎠ 3 3 ⎝ 3⎠ 1 4 2 4 = i = − 2 9 9 9 4 2 2 = = =− 18 9 9
  37. 37. Extra Credit Challenge Demonstrate that using only the number 2 and parentheses, exponents, the order of operations, and the zero power, you can write expressions equal to each of the whole numbers from 1 through 10.
  38. 38. Problem Set
  39. 39. Problem Set p. 58 #1-10 all, 12, 13-30 odd “Do what you love, love what you do, leave the world a better place and don’t pick your nose.” - Jeff Mallett

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