Lecture 11 Unit 1 Lecture 1 Signed Numbers Real Number System Symbols of equality, inequality, less than, greater than Unary operations: opposite

Lecture 1Lecture 1 11

Unit 1 Lecture 1Unit 1 Lecture 1Signed NumbersSigned Numbers

Real Number SystemSymbols of equality, inequality, less than, greater thanUnary operations: opposite of; absolute valueRules of Addition and Subtraction for Signed numbersMathematical Statement into Symbols


ObjectivesObjectives

• To identify Real numbersTo identify Real numbers

• To learn the rules for addition and To learn the rules for addition and

subtraction of signed numberssubtraction of signed numbers

• To learn how to go from a mathematical To learn how to go from a mathematical

statements to symbols and solvestatements to symbols and solve


Real NumbersReal Numbers

• Two subsets: Rationals and Irrationals Two subsets: Rationals and Irrationals

• Rationals contain Integers as a subsetRationals contain Integers as a subset

• Integers contain Whole Numbers as a Integers contain Whole Numbers as a subsetsubset

• Whole numbers contain Counting Numbers Whole numbers contain Counting Numbers or Natural Numbers as a subset.or Natural Numbers as a subset.


ExamplesExamples

}}, 2, 7, .etc

• Counting Numbers or Natural Numbers Counting Numbers or Natural Numbers {1, 2, 3, . . .}{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, Rational Numbers { -8, - 1.5, 7/4, 0, 6, etc.}etc.}

• Irrational Numbers { Irrational Numbers {



Addition of Signed NumbersAddition of Signed Numbers

• Like Signs:Like Signs:– Ignore the signsIgnore the signs– Add Add – Take the common signTake the common sign

• Unlike Signs:Unlike Signs:– Ignore the signsIgnore the signs– Subtract Subtract – Look to see what the sign was of the Look to see what the sign was of the

larger unsigned numberlarger unsigned number– Take that signTake that sign


ExamplesExamples

• Like Signs:Like Signs:

+ 5 + 3 = + 8+ 5 + 3 = + 8

- 5 - 3 = - 8- 5 - 3 = - 8

• Unlike Signs:Unlike Signs:

+ 5 - 3 = + 2+ 5 - 3 = + 2

- 5 + 3 = - 2- 5 + 3 = - 2


Mathematical Statements into Symbols Mathematical Statements into Symbols

1. I have $60 and I owe you $90. What is 1. I have $60 and I owe you $90. What is

my net worth?my net worth?

+ 60 - 90 = + 60 - 90 = - 30 - 30



2. I am in debt for $50 and you give me 2. I am in debt for $50 and you give me

$10. What is my net worth? $10. What is my net worth?

- 50 + 10 =- 50 + 10 = - 40- 40



3. I am in debt for $30 and you give me 3. I am in debt for $30 and you give me


- 30 + 40 =- 30 + 40 = 1010



4. I am in debt for $20 and I owe you 4. I am in debt for $20 and I owe you


- 20 - 50 =- 20 - 50 = -70-70


–– 7 + 57 + 5

6 6 – 10– 10

2 2 –– 11 11

– – 8 – 158 – 15

– – 6 + 106 + 10

1 5

4 6

Perform the operation:Perform the operation:


–– 7 + 57 + 5 – – 22

6 6 – 10– 10 – – 44

2 2 –– 11 11 – – 99

– – 8 – 158 – 15 – – 2323

– – 6 + 106 + 10 44

1 5

4 6

Perform the operation:Perform the operation:

1 5 3 10 7

4 6 12 12


-key, binary key,

7th row, 5th column

Subtraction KeySubtraction Key


(-) key, unary operation

9th row, 4th column

Opposite KeyOpposite Key


To add signed numbers use the opposite (-) key, 9th row, 4th column.

Use of the calculator to Use of the calculator to evaluate evaluate – 8.6 + 11.4– 8.6 + 11.4

is keyed in as is keyed in as (-)(-),, 8.6 8.6,, + +,, 11.4 11.4, , ENTERENTER

2.82.8

– – 8.6 + 11.48.6 + 11.4


To add signed numbers use the opposite key (–)–) and binary subtraction key ––

Use the calculator to Use the calculator to evaluate: evaluate: – 16.85 – 28.42– 16.85 – 28.42

is keyed in as is keyed in as

((–)–),, 16.85 16.85,, ––,, 28.42 28.42, , ENTERENTER

– – 16.85 – 28.4216.85 – 28.42

– – 45.45.2727

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Lecture 11 Unit 1 Lecture 1 Signed Numbers Real Number System Symbols of equality, inequality, less than, greater than Unary operations: opposite