Algebraic Expressions

1. SECTION 0-4
Algebraic Expressions
Monday, September 12, 2011

2. ESSENTIAL QUESTION
How do you use the order of operations
to evaluate algebraic expressions?
Monday, September 12, 2011

3. ORDER OF OPERATIONS
Monday, September 12, 2011

4. ORDER OF OPERATIONS
P
E
M
D
A
S
Monday, September 12, 2011

5. ORDER OF OPERATIONS
Parentheses
E
M
D
A
S
Monday, September 12, 2011

6. ORDER OF OPERATIONS
Parentheses
E xponents
M
D
A
S
Monday, September 12, 2011

7. ORDER OF OPERATIONS
Parentheses
E xponents
Multiplication
D
A
S
Monday, September 12, 2011

8. ORDER OF OPERATIONS
Parentheses
E xponents
Multiplication
Division
A
S
Monday, September 12, 2011

9. ORDER OF OPERATIONS
Parentheses
E xponents
Multiplication
Division
} from left to right
A
S
Monday, September 12, 2011

10. ORDER OF OPERATIONS
Parentheses
E xponents
Multiplication
Division
} from left to right
A ddition
S
Monday, September 12, 2011

11. ORDER OF OPERATIONS
Parentheses
E xponents
Multiplication
Division
} from left to right
A ddition
Subtraction
Monday, September 12, 2011

12. ORDER OF OPERATIONS
Parentheses
E xponents
Multiplication
Division
} from left to right
A ddition
Subtraction
} from left to right
Monday, September 12, 2011

13. ORDER OF OPERATIONS
Parentheses
E xponents
Old
way
!
Multiplication
Division
} from left to right
A ddition
Subtraction
} from left to right
Monday, September 12, 2011

14. ORDER OF OPERATIONS
Monday, September 12, 2011

15. ORDER OF OPERATIONS
G
E
M
D
A
S
Monday, September 12, 2011

16. ORDER OF OPERATIONS
Grouping Symbols
E
M
D
A
S
Monday, September 12, 2011

17. ORDER OF OPERATIONS
Grouping Symbols
Parentheses, brackets, division bars, etc.
E
M
D
A
S
Monday, September 12, 2011

18. ORDER OF OPERATIONS
Grouping Symbols
Parentheses, brackets, division bars, etc.
E xponents
Multiplication
Division
} from left to right
A ddition
Subtraction
} from left to right
Monday, September 12, 2011

19. ORDER OF OPERATIONS
Grouping Symbols
Parentheses, brackets, division bars, etc.
E xponents
Multiplication
Division
} from left to right New &
Improved!
A ddition
Subtraction
} from left to right
Monday, September 12, 2011

20. QUESTION
What does it mean to evaluate an expression?
Monday, September 12, 2011

21. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
Monday, September 12, 2011

22. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1
3(4) − 7 + 2(− )
2
Monday, September 12, 2011

23. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1
3(4) − 7 + 2(− )
2
12 − 7 −1
Monday, September 12, 2011

24. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1
3(4) − 7 + 2(− )
2
12 − 7 −1
5 −1
Monday, September 12, 2011

25. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1
3(4) − 7 + 2(− )
2
12 − 7 −1
5 −1
4
Monday, September 12, 2011

26. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1 1
3(4) − 7 + 2(− ) −4 − 8(− )
2 2
12 − 7 −1
5 −1
4
Monday, September 12, 2011

27. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1 1
3(4) − 7 + 2(− ) −4 − 8(− )
2 2
12 − 7 −1 −4 + 4
5 −1
4
Monday, September 12, 2011

28. EXAMPLE 1
1
Evaluate when x = 4 and y = −
2
a. 3x − 7 + 2y b. − x − 8y
1 1
3(4) − 7 + 2(− ) −4 − 8(− )
2 2
12 − 7 −1 −4 + 4
5 −1 0
4
Monday, September 12, 2011

29. EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y
3 − 5x
Monday, September 12, 2011

30. EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y −2(2) + 3
3 − 5x 3 − 5(2)
Monday, September 12, 2011

31. EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y −2(2) + 3 −4 + 3
3 − 5x 3 − 5(2) 3 −10
Monday, September 12, 2011

32. EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y −2(2) + 3 −4 + 3 −1
3 − 5x 3 − 5(2) 3 −10 −7
Monday, September 12, 2011

33. EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y −2(2) + 3 −4 + 3 −1 1
3 − 5x 3 − 5(2) 3 −10 −7 7
Monday, September 12, 2011

34. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
Monday, September 12, 2011

35. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3)
Monday, September 12, 2011

36. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3)
2 8+3
Monday, September 12, 2011

37. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3)
2 8+3
2 11
Monday, September 12, 2011

38. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3)
2 8+3
2 11
2(11)
Monday, September 12, 2011

39. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3)
2 8+3
2 11
2(11)
22
Monday, September 12, 2011

40. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3) 1
−3 − 8
2 8+3 3
2 11
2(11)
22
Monday, September 12, 2011

41. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3) 1
−3 − 8
2 8+3 3
1
2 11 −11
3
2(11)
22
Monday, September 12, 2011

42. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3) 1
−3 − 8
2 8+3 3
1
2 11 −11
3
2(11) 1
(11)
22 3
Monday, September 12, 2011

43. EXAMPLE 3
Evaluate when x = 8 and y = −3.
1
a. 2 x − y b. y − x
3
2 8 − (−3) 1
−3 − 8
2 8+3 3
1
2 11 −11
3
2(11) 1 11
(11)
22 3 3
Monday, September 12, 2011

44. PROBLEM SET
Monday, September 12, 2011

45. PROBLEM SET
p. P10 #1-12 all
“The true sign of intelligence is not knowledge but
imagination.” - Albert Einstein
Monday, September 12, 2011