1. Lecture 11 Unit 1 Lecture 1 Signed Numbers  Real Number System  Symbols of equality, inequality, less than, greater than  Unary operations: opposite of; absolute value  Rules of Addition and Subtraction for Signed numbers  Mathematical Statement into Symbols

2. Lecture 12 Objectives To identify Real numbersTo identify Real numbers To learn the rules for addition and subtraction of signed numbersTo learn the rules for addition and subtraction of signed numbers To learn how to go from a mathematical statements to symbols and solveTo learn how to go from a mathematical statements to symbols and solve

3. Lecture 13 Real Numbers Two subsets: Rationals and IrrationalsTwo subsets: Rationals and Irrationals Rationals contain Integers as a subsetRationals contain Integers as a subset Integers contain Whole Numbers as a subsetIntegers contain Whole Numbers as a subset Whole numbers contain Counting Numbers or Natural Numbers as a subset.Whole numbers contain Counting Numbers or Natural Numbers as a subset.

4. Lecture 14Examples } Counting Numbers or Natural Numbers {1, 2, 3,...}Counting Numbers or Natural Numbers {1, 2, 3,...} Whole Numbers {0, 1, 2, 3...}Whole Numbers {0, 1, 2, 3...} Integers {... -3, -2, -1, 0, 1, 2, 3,...}Integers {... -3, -2, -1, 0, 1, 2, 3,...} Rational Numbers { -8, - 1.5, 7/4, 0, 6, etc.}Rational Numbers { -8, - 1.5, 7/4, 0, 6, etc.} Irrational Numbers {Irrational Numbers {

5. Lecture 15

6. 6 Addition of Signed Numbers Like Signs:Like Signs: –Ignore the signs –Add –Take the common sign Unlike Signs:Unlike Signs: –Ignore the signs –Subtract –Look to see what the sign was of the larger unsigned number –Take that sign

7. Lecture 17 Examples Like Signs:Like Signs: + 5 + 3 = + 8 - 5 - 3 = - 8 - 5 - 3 = - 8 Unlike Signs:Unlike Signs: + 5 - 3 = + 2 - 5 + 3 = - 2

8. Lecture 18 Mathematical Statements into Symbols 1. I have $60 and I owe you $90. What is my net worth? + 60 - 90 = - 30 - 30

9. Lecture 19 Mathematical Statements into Symbols 2. I am in debt for $50 and you give me $10. What is my net worth? 2. I am in debt for $50 and you give me $10. What is my net worth? - 50 + 10 = - 40

10. Lecture 110 Mathematical Statements into Symbols 3. I am in debt for $30 and you give me $40. What is my net worth? - 30 + 40 = 10

11. Lecture 111 Mathematical Statements into Symbols 4. I am in debt for $20 and I owe you $50. What is my net worth? - 20 - 50 = -70

12. Lecture 112 – 7 + 5 6 – 10 2 – 11 – 8 – 15 – 6 + 10 Perform the operation:

13. Lecture 113 – 7 + 5 – 2 6 – 10 – 4 2 – 11 – 9 – 8 – 15 – 23 – 6 + 10 4 Perform the operation:

14. Lecture 114 -key, binary key, 7 th row, 5 th column Subtraction Key

15. Lecture 115 (-) key, unary operation 9 th row, 4 th column Opposite Key

16. Lecture 116 To add signed numbers use the opposite (-) key, 9 th row, 4 th column. Use of the calculator to evaluate – 8.6 + 11.4 is keyed in as (-), 8.6, +, 11.4, ENTER 2.8 – 8.6 + 11.4

17. Lecture 117 –) – To add signed numbers use the opposite key (–) and binary subtraction key – Use the calculator to evaluate: – 16.85 – 28.42 is keyed in as (–), 16.85, –, 28.42, ENTER – 16.85 – 28.42 – 45.27