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4. Example 2-1b Objective Evaluate expressions and identify properties

5. Example 2-1b Vocabulary Variable A symbol, usually a letter, used to represent a number x a y

6. Example 2-1b Vocabulary Algebraic expression An expression that contains a variable, a number, and at least one operation symbol 4n x - 3

7. Example 2-1b Vocabulary Numerical expression An expression that contains numbers and at least one operation 3 + 4 7 – 6 6 + 4 - 3

8. Example 2-1b Vocabulary evaluate To find the numerical value of the expression

9. Example 2-1b Vocabulary powers Numbers written using exponents 4 3 8 2

10. Example 2-1b Vocabulary equation A mathematical sentence that contains an equal sign (=) 3 + 4 = 7 X - 4 = 8

11. Example 2-1b Vocabulary Open sentence An equation that contains a variable 2x - 4 = 12

12. Example 2-1b Vocabulary property An open sentence that is true for any numbers

13. Example 2-1b Vocabulary counterexample A statement or example that shows a conjecture is false

14. Example 2-1b Vocabulary Order of operations A set of rules to evaluate expressions

15. Example 2-1b Order of Operations Rules 1.Do all operations within grouping symbols first. ( ) [ ] { } 2.Evaluate all powers before other operations. exponents 3 2 square roots  16 3.Multiply and divide in order from left to right.  x3(4) 4.Add and subtract in order from left to right. + - Please Excuse My Dear Aunt Sally P E MD AS

16. Lesson 2 Contents Example 1Evaluate a Numerical Expression Example 2Evaluate Algebraic Expressions Example 3Evaluate Algebraic Expressions

17. Example 2-1a Evaluate 1/4  Write problem 3 + 9 - 2  ( 8  2 ) Follow the rules of Order of Operations P E MD AS Work inside parenthesis first Bring down 3 + 9 - 2  Divide 8 by 2 3 + 9 - 2  3 + 9 - 2  4

18. Example 2-1a Evaluate 1/4  Follow the rules of Order of Operations P E MD AS 3 + 9 - 2  4 Multiply before adding and subtracting Bring down 3 + 9 - Multiply 2  4 3 + 9 - 3 + 9 - 8

19. Example 2-1a Evaluate 1/4  Follow the rules of Order of Operations P E MD AS Add and subtract from left to right Bring down - 8 Add 3 + 9 3 + 9 - 8 12 12 - 8 Subtract 12 - 8 4 Answer: 4

20. Example 2-1b Evaluate Answer: 2 1/3 

21. Example 2-2a Evaluate the expression 2/3 Write problem 3r + 2s - 4 Replace r with 6 3(6) Replace s with 3 3(6) + 2(3) Bring down - 4 3(6) + 2(3) - 4

22. Example 2-2a Evaluate the expression 2/3 3(6) + 2(3) - 4 Follow the rules of Order of Operations P E MD AS Multiply before adding and subtracting 18 Multiply 3(6) 18 + 18 + 6 Bring down + Multiply 2(3) 18 + 6 - 4 Bring down - 4

23. Example 2-2a Evaluate the expression 2/3 Follow the rules of Order of Operations P E MD AS Add and subtract from left to right 24 Add 18 + 6 Bring down - 4 Subtract 24 - 4 18 + 6 - 4 24 - 4 20 Answer: 20

24. Example 2-2b Answer: 24 Evaluate the expression 2/3

25. Example 2-3a Evaluate the expression 3/3 Write problem Replace q with 5 Replace r with 6 Bring down - 3

26. Example 2-3a Evaluate the expression 3/3 Follow the rules of Order of Operations P E MD AS Remember: The fraction bar is a grouping symbol Work in the numerator first Multiply 6(5) 30. Now work in the denominator Multiply 3(6) 18 Bring down - 3 18 - 3

27. Example 2-3a Evaluate the expression 3/3 Follow the rules of Order of Operations P E MD AS 30. Finish working in the denominator Bring down 30. 15 Now use the fraction bar as division 18 - 3 Subtract 18 - 3 30. Divide 30 by 15 2 Answer: 2

28. Example 2-3b Answer: 2 Evaluate the expression 3/3

29. End of Lesson 2 Assignment Lesson 1:2 Variables, Expressions & Properties 14 - 40 All

30. Example 2-4a Name the property shown by Multiplying by 1 does not change the number. Answer: This is the Multiplicative Identity. 4/4

31. Example 2-4b Name the property shown by the statement Answer: Commutative Property of Multiplication 4/4