Slide 1 : Properties of Real Numbers
Slide 2 : __ __ ____ _ Properties of Real Numbers Vocabulary 1) real numbers
2) rational numbers
3) irrational numbers Classify real numbers. Use the properties of real numbers to evaluate expressions.
Slide 3 : All of the numbers that you use in everyday life are real numbers. Properties of Real Numbers
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 9 : Real numbers can be classified a either _______ or ________. Properties of Real Numbers
Slide 10 : Real numbers can be classified a either _______ or ________. rational irrational Properties of Real Numbers
Slide 11 : Real numbers can be classified a either _______ or ________. rational irrational zero Properties of Real Numbers
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 17 : Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. Properties of Real Numbers
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 25 : Relationships among the real numbers - (sets and subsets). Properties of Real Numbers
Slide 26 : Q = rationals I = irrationals Relationships among the real numbers - (sets and subsets). Properties of Real Numbers
Slide 27 : Q = rationals I = irrationals Z = integers Relationships among the real numbers - (sets and subsets). Properties of Real Numbers
Slide 28 : Q = rationals I = irrationals Z = integers W = wholes Relationships among the real numbers - (sets and subsets). Properties of Real Numbers
Slide 29 : The square root of any whole number is either whole or irrational. Properties of Real Numbers
Slide 30 : The square root of any whole number is either whole or irrational. Properties of Real Numbers
Slide 31 : The square root of any whole number is either whole or irrational. Properties of Real Numbers
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 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
Slide 41 : Consider these Java Applets to better understand the
Distributive Property Algebra Tiles 1 Algebra Tiles 2 End of Lesson
Slide 42 : Credits