Properties of Real Numbers
You'll Learn To: Properties of Real Numbers  Vocabulary 1) real numbers 2) rational numbers 3) irrational numbers <ul><li>...
All of the numbers that you use in everyday life are  real numbers . Properties of Real Numbers
All of the numbers that you use in everyday life are  real numbers . Each real number corresponds to exactly one point on ...
All of the numbers that you use in everyday life are  real numbers . Each real number corresponds to exactly one point on ...
All of the numbers that you use in everyday life are  real numbers . Each real number corresponds to exactly one point on ...
All of the numbers that you use in everyday life are  real numbers . Each real number corresponds to exactly one point on ...
All of the numbers that you use in everyday life are  real numbers . Each real number corresponds to exactly one point on ...
Real numbers can be classified a either _______ or ________. Properties of Real Numbers
Real numbers can be classified a either _______ or ________. rational irrational Properties of Real Numbers
Real numbers can be classified a either _______ or ________. rational irrational zero Properties of Real Numbers  Ratio na...
Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational numbe...
Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational numbe...
Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational numbe...
Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational numbe...
Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational numbe...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irr...
Relationships among the real numbers  - ( sets   and  subsets ). Properties of Real Numbers
Q = rationals I =  irrationals Relationships among the real numbers  - ( sets   and  subsets ). Properties of Real Numbers...
Q = rationals I =  irrationals Z = integers Relationships among the real numbers  - ( sets   and  subsets ). Properties of...
Q = rationals I =  irrationals Z = integers W = wholes Relationships among the real numbers  - ( sets   and  subsets ). Pr...
The square root of  any  whole number is either whole or irrational. Properties of Real Numbers
The square root of  any  whole number is either whole or irrational. Properties of Real Numbers  For example,  is a whole ...
The square root of  any  whole number is either whole or irrational. Properties of Real Numbers  x 0 1 3 2 4 5 6 7 9 8 10 ...
The square root of  any  whole number is either whole or irrational. Common Misconception: Do not  assume  that a number i...
The square root of  any  whole number is either whole or irrational. Common Misconception: Do not  assume  that a number i...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
The real number system is an example of a mathematical structure called a  field . Some of the properties of a field are s...
Consider these Java Applets to better understand the Distributive Property Algebra Tiles 1 Algebra Tiles 2 End  of  Lesson
Credits  PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant
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Properties of Real Numbers

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Students review some of the properties of Real Numbers.

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Properties of Real Numbers

  1. 1. Properties of Real Numbers
  2. 2. You'll Learn To: Properties of Real Numbers Vocabulary 1) real numbers 2) rational numbers 3) irrational numbers <ul><li>Classify real numbers. </li></ul><ul><li>Use the properties of real numbers to evaluate expressions. </li></ul>
  3. 3. All of the numbers that you use in everyday life are real numbers . Properties of Real Numbers
  4. 4. All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and Properties of Real Numbers
  5. 5. All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and Properties of Real Numbers x
  6. 6. All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and Properties of Real Numbers x 0 1 2 3 4 5 -5 -4 -2 -1 -3
  7. 7. All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and every point on the number line represents one real number. Properties of Real Numbers x 0 1 2 3 4 5 -5 -4 -2 -1 -3
  8. 8. All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and every point on the number line represents one real number. Properties of Real Numbers x 0 1 2 3 4 5 -5 -4 -2 -1 -3
  9. 9. Real numbers can be classified a either _______ or ________. Properties of Real Numbers
  10. 10. Real numbers can be classified a either _______ or ________. rational irrational Properties of Real Numbers
  11. 11. Real numbers can be classified a either _______ or ________. rational irrational zero Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
  12. 12. Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
  13. 13. Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
  14. 14. Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
  15. 15. Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
  16. 16. Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
  17. 17. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. Properties of Real Numbers
  18. 18. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. Properties of Real Numbers
  19. 19. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Properties of Real Numbers
  20. 20. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: Properties of Real Numbers
  21. 21. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Properties of Real Numbers
  22. 22. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? Properties of Real Numbers
  23. 23. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? Properties of Real Numbers
  24. 24. Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? They’re all PRIME numbers! Properties of Real Numbers
  25. 25. Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers
  26. 26. Q = rationals I = irrationals Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers Q I
  27. 27. Q = rationals I = irrationals Z = integers Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers Q I Z
  28. 28. Q = rationals I = irrationals Z = integers W = wholes Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers Q I Z W
  29. 29. The square root of any whole number is either whole or irrational. Properties of Real Numbers
  30. 30. The square root of any whole number is either whole or irrational. Properties of Real Numbers For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
  31. 31. The square root of any whole number is either whole or irrational. Properties of Real Numbers x 0 1 3 2 4 5 6 7 9 8 10 For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
  32. 32. The square root of any whole number is either whole or irrational. Common Misconception: Do not assume that a number is irrational just because it is expressed using the square root symbol. Find its value first! Properties of Real Numbers x 0 1 3 2 4 5 6 7 9 8 10 For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
  33. 33. The square root of any whole number is either whole or irrational. Common Misconception: Do not assume that a number is irrational just because it is expressed using the square root symbol. Find its value first! Study Tip: KNOW and recognize (at least) these numbers, Properties of Real Numbers x 0 1 3 2 4 5 6 7 9 8 10 For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
  34. 34. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Properties of Real Numbers
  35. 35. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Associative Identity Inverse Distributive Properties of Real Numbers Commutative Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
  36. 36. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
  37. 37. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
  38. 38. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
  39. 39. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
  40. 40. The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
  41. 41. Consider these Java Applets to better understand the Distributive Property Algebra Tiles 1 Algebra Tiles 2 End of Lesson
  42. 42. Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant

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