This document defines key terms and concepts for evaluating numerical expressions using order of operations. It begins by defining numerical expression, value, simplify, exponent, variable expression, and evaluate. It then explains the mnemonic "Please Excuse My Dear Aunt Sally" for the standard order of operations: Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right). Examples are provided to demonstrate simplifying expressions and evaluating variable expressions. The document concludes with an extra credit challenge and assigning practice problems.

1. Section 2-2
Order of Operations

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. Vocabulary
1. Numerical Expression:
2. Value:
3. Simplify:
4. Exponent:
5. Variable Expression:
6. Evaluate:

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

11. What is the Order of Operations?
“Please Excuse My Dear Aunt Sally”
P: Parentheses

12. What is the Order of Operations?
“Please Excuse My Dear Aunt Sally”
P: Parentheses
E: Exponents

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

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

18. Example 1
Simplify each numerical expression.
a. 12 + (3i4) b. 16 − (5i 2 )
= 12 + 12
= 24

19. Example 1
Simplify each numerical expression.
a. 12 + (3i4) b. 16 − (5i 2 )
= 12 + 12 = 16 − (5i2)
= 24

20. Example 1
Simplify each numerical expression.
a. 12 + (3i4) b. 16 − (5i 2 )
= 12 + 12 = 16 − (5i2)
= 24 = 16 − 10

21. Example 1
Simplify each numerical expression.
a. 12 + (3i4) b. 16 − (5i 2 )
= 12 + 12 = 16 − (5i2)
= 24 = 16 − 10
=6

22. Example 1
Simplify each numerical expression.
c. -5i4 − (−3)
2
d. -(10-8) − 2
2 3

23. Example 1
Simplify each numerical expression.
c. -5i4 − (−3)
2
d. -(10-8) − 2
2 3
=-5i16 + 3

24. Example 1
Simplify each numerical expression.
c. -5i4 − (−3)
2
d. -(10-8) − 2
2 3
=-5i16 + 3
= −80 + 3

25. Example 1
Simplify each numerical expression.
c. -5i4 − (−3)
2
d. -(10-8) − 2
2 3
=-5i16 + 3
= −80 + 3
= −77

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. 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. 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. Example 2
2
Evaluate each variable expression for k =
3
1 2 1
a. k b. k − k 2
2 3

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. 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. 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. 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. 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. 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. 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. 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. Problem Set

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