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9.1 – Symbols and Sets of Numbers

9.1 – Symbols and Sets of Numbers. Definitions:. Natural Numbers: {1, 2, 3, 4, …}. Whole Numbers: All natural numbers plus zero, {0, 1, 2, 3, …}. Equality Symbols. 9.1 – Symbols and Sets of Numbers. Inequality Symbols. 9.1 – Symbols and Sets of Numbers.

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9.1 – Symbols and Sets of Numbers

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  1. 9.1 – Symbols and Sets of Numbers Definitions: • Natural Numbers: {1, 2, 3, 4, …} • Whole Numbers: All natural numbers plus zero, {0, 1, 2, 3, …} Equality Symbols

  2. 9.1 – Symbols and Sets of Numbers Inequality Symbols

  3. 9.1 – Symbols and Sets of Numbers Equality and Inequality Symbols are used to create mathematical statements.

  4. 9.1 – Symbols and Sets of Numbers Order Property for Real Numbers For any two real numbers, a and b, a is less than b if a is to the left of b on the number line. -92 -25 -11 0 1 12 43 67

  5. 9.1 – Symbols and Sets of Numbers True or False

  6. 9.1 – Symbols and Sets of Numbers Translating Sentences into Mathematical Statements

  7. 9.1 – Symbols and Sets of Numbers Identifying Common Sets of Numbers Definitions: Integers: All positive numbers, negative numbers and zero without fractions and decimals. {…, -3, -2, -1, 0, 1, 2, 3, 4, …}

  8. 9.1 – Symbols and Sets of Numbers Identifying Common Sets of Numbers Definitions: Rational Numbers: Any number that can be expressed as a quotient of two integers. Irrational Numbers: Any number that can not be expressed as a quotient of two integers.

  9. 9.1 – Symbols and Sets of Numbers Real Numbers Irrational Rational Non-integer rational #s Integers Negative numbers Whole numbers Natural numbers Zero

  10. 9.1 – Symbols and Sets of Numbers Given the following set of numbers, identify which elements belong in each classification: All elements

  11. 9.2 – Properties of Real Numbers Commutative Properties Addition: Multiplication:

  12. 9.2 – Properties of Real Numbers Associative Properties Addition: Multiplication:

  13. 9.2 – Properties of Real Numbers Distributive Property of Multiplication

  14. 9.2 – Properties of Real Numbers Identity Properties: Addition: 0 is the identity element for addition Multiplication: 1 is the identity element for multiplication

  15. 9.2 – Properties of Real Numbers Additive Inverse Property: The numbers a and –a are additive inverses or opposites of each other if their sum is zero. Multiplicative Inverse Property: The numbers are reciprocals or multiplicative inverses of each other if their product is one.

  16. 9.2 – Properties of Real Numbers Name the appropriate property for the given statements: Distributive Commutative prop. of addition Associative property of multiplication Commutative prop. of addition Multiplicative inverse Commutative and associative prop. of multiplication

  17. 9.3 – Solving Linear Equations Suggestions for Solving Linear Equations: 1. If fractions exist, multiply by the LCD to clear all fractions. 2. If parentheses exist, used the distributive property to remove them. 3. Simplify each side of the equation by combining like-terms. 4. Get the variable of interest to one side of the equation and all terms to the other side. 5. Use the appropriate properties to get the variable’s coefficient to be 1. 6. Check the solution by substituting it into the original equation.

  18. 9.3 – Solving Linear Equations Example 1: Check:

  19. 9.3 – Solving Linear Equations Example 2: Check:

  20. 9.3 – Solving Linear Equations Check: Example 3: LCD = 6

  21. 9.3 – Solving Linear Equations Example 4:

  22. 9.3 – Solving Linear Equations Example 4: Check:

  23. 9.3 – Solving Linear Equations Example 5: Identity Equation – It has an infinite number of solutions.

  24. 9.3 – Solving Linear Equations Example 6: LCD = 6 No Solution

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