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Section 2-2
Order of Operations
Essential Question


✤   How do you evaluate numerical expressions using
    the order of operations?



✤   Where you’ll ...
Vocabulary
1. Numerical Expression:



2. Value:

3. Simplify:


4. Exponent:

5. Variable Expression:


6. Evaluate:
Vocabulary
1. Numerical Expression: Two or more numbers combined using the
    four operations (addition, subtraction, mul...
Vocabulary
1. Numerical Expression: Two or more numbers combined using the
    four operations (addition, subtraction, mul...
Vocabulary
1. Numerical Expression: Two or more numbers combined using the
    four operations (addition, subtraction, mul...
Vocabulary
1. Numerical Expression: Two or more numbers combined using the
    four operations (addition, subtraction, mul...
Vocabulary
1. Numerical Expression: Two or more numbers combined using the
    four operations (addition, subtraction, mul...
Vocabulary
1. Numerical Expression: Two or more numbers combined using the
    four operations (addition, subtraction, mul...
What is the Order of Operations?

  “Please Excuse My Dear Aunt Sally”
What is the Order of Operations?

   “Please Excuse My Dear Aunt Sally”

P: Parentheses
What is the Order of Operations?

   “Please Excuse My Dear Aunt Sally”

P: Parentheses
E: Exponents
What is the Order of Operations?

    “Please Excuse My Dear Aunt Sally”

P: Parentheses
E: Exponents

M and D: Multiplica...
What is the Order of Operations?

    “Please Excuse My Dear Aunt Sally”

P: Parentheses
E: Exponents

M and D: Multiplica...
What is the Order of Operations?

    “Golly, Excuse My Dear Aunt Sally”

G: Grouping symbols; parentheses, brackets, divi...
Example 1
           Simplify each numerical expression.

   a. 12 + (3i4)                       b. 16 − (5i 2 )
Example 1
           Simplify each numerical expression.

   a. 12 + (3i4)                       b. 16 − (5i 2 )
    = 12 ...
Example 1
           Simplify each numerical expression.

   a. 12 + (3i4)                       b. 16 − (5i 2 )
    = 12 ...
Example 1
           Simplify each numerical expression.

   a. 12 + (3i4)                       b. 16 − (5i 2 )
    = 12 ...
Example 1
           Simplify each numerical expression.

   a. 12 + (3i4)                       b. 16 − (5i 2 )
    = 12 ...
Example 1
           Simplify each numerical expression.

   a. 12 + (3i4)                       b. 16 − (5i 2 )
    = 12 ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 1
            Simplify each numerical expression.

  c. -5i4 − (−3)
        2
                                    ...
Example 2
                                                2
      Evaluate each variable expression for k =
              ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Example 2
                                                 2
       Evaluate each variable expression for k =
            ...
Extra Credit Challenge

  Demonstrate that using only the number 2 and
      parentheses, exponents, the order of
  operat...
Problem Set
Problem Set



                 p. 58 #1-10 all, 12, 13-30 odd




“Do what you love, love what you do, leave the world a ...
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Int Math 2 Section 2-2 1011

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Order of Operations

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Transcript of "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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