Podcast
Questions and Answers
Which of the following types of numbers includes all the negative numbers?
Which of the following types of numbers includes all the negative numbers?
Which of the following is an example of an irrational number?
Which of the following is an example of an irrational number?
What is the property that states a × (b + c) = a × b + a × c?
What is the property that states a × (b + c) = a × b + a × c?
What is the correct order of operations when evaluating expressions?
What is the correct order of operations when evaluating expressions?
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Which of the following types of numbers includes all the real numbers and imaginary numbers?
Which of the following types of numbers includes all the real numbers and imaginary numbers?
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What is the property that states a + b = b + a?
What is the property that states a + b = b + a?
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Study Notes
Number System
Classification of Numbers
- Natural Numbers: 1, 2, 3, ... (counting numbers)
- Whole Numbers: 0, 1, 2, 3, ... (including 0)
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (including negative numbers)
- Rational Numbers: fractions, e.g., 3/4, 22/7, -1/2 (can be expressed as a ratio of integers)
- Irrational Numbers: non-repeating, non-terminating decimals, e.g., π, e, √2 (cannot be expressed as a ratio of integers)
- Real Numbers: includes rational and irrational numbers
- Complex Numbers: numbers with real and imaginary parts, e.g., 3 + 4i, where i = √(-1)
Properties of Operations
- Commutative Property: a + b = b + a, a × b = b × a (addition and multiplication are commutative)
- Associative Property: (a + b) + c = a + (b + c), (a × b) × c = a × (b × c) (addition and multiplication are associative)
- Distributive Property: a × (b + c) = a × b + a × c (multiplication distributes over addition)
Order of Operations
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PEMDAS (or BODMAS): follow the order of operations when evaluating expressions:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Number System
Classification of Numbers
- Natural Numbers are counting numbers starting from 1, such as 1, 2, 3, ...
- Whole Numbers include 0 and all natural numbers, such as 0, 1, 2, 3, ...
- Integers include all whole numbers and their negative counterparts, such as ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational Numbers are fractions that can be expressed as a ratio of integers, such as 3/4, 22/7, -1/2
- Irrational Numbers are non-repeating and non-terminating decimals that cannot be expressed as a ratio of integers, such as π, e, √2
- Real Numbers include both rational and irrational numbers
- Complex Numbers have both real and imaginary parts, such as 3 + 4i, where i = √(-1)
Properties of Operations
- The Commutative Property states that the order of numbers does not change the result of addition and multiplication, such as a + b = b + a, a × b = b × a
- The Associative Property states that the order of operations does not change the result of addition and multiplication, such as (a + b) + c = a + (b + c), (a × b) × c = a × (b × c)
- The Distributive Property states that multiplication can be distributed over addition, such as a × (b + c) = a × b + a × c
Order of Operations
- The PEMDAS (or BODMAS) rule follows a specific order of operations when evaluating expressions
- Evaluate expressions in the following order:
- Parentheses (or Brackets)
- Exponents (or Orders)
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
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Description
Learn about the different types of numbers including natural, whole, integers, rational, irrational, and real numbers. Understand their definitions and characteristics.
