Questions and Answers
Which of the following is NOT a natural number?
What type of number is represented by the expression $\frac{3}{4}$?
Which property states that $a + b = b + a$?
Which of the following is an example of an irrational number?
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If you multiply $2$ by the sum of $3$ and $4$, what does the Distributive Property help you understand?
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Which of the following is a characteristic of complex numbers?
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Study Notes
Types of Numbers
- Natural Numbers: Positive integers, also known as counting numbers (1, 2, 3, ...)
- Whole Numbers: Non-negative integers, including 0 (0, 1, 2, 3, ...)
- Integers: All whole numbers and their negative counterparts (...,-3, -2, -1, 0, 1, 2, 3, ...)
- Rational Numbers: Numbers that can be expressed as a ratio of two integers (e.g. 3/4, 22/7)
- Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers (e.g. π, e)
- Real Numbers: All rational and irrational numbers
- Complex Numbers: Numbers that include an imaginary component (e.g. 3 + 4i)
Number Operations
- Addition: Combining two or more numbers to get a total or a sum (e.g. 2 + 3 = 5)
- Subtraction: Finding the difference between two numbers (e.g. 5 - 3 = 2)
- Multiplication: Repeated addition of a number (e.g. 2 × 3 = 6)
- Division: Splitting a number into equal parts or groups (e.g. 6 ÷ 2 = 3)
Number Properties
- Commutative Property: The order of numbers does not change the result of an operation (e.g. 2 + 3 = 3 + 2)
- Associative Property: The order in which numbers are grouped does not change the result of an operation (e.g. (2 + 3) + 4 = 2 + (3 + 4))
- Distributive Property: A number can be distributed to multiple addends (e.g. 2 × (3 + 4) = 2 × 3 + 2 × 4)
Types of Numbers
- Natural Numbers are positive integers, starting from 1, also referred to as counting numbers.
- Whole Numbers include 0 and all positive integers, making them non-negative integers.
- Integers encompass all whole numbers and their negative counterparts, including 0.
- Rational Numbers can be expressed as a ratio of two integers, such as 3/4 or 22/7.
- Irrational Numbers cannot be expressed as a ratio of two integers, examples include π and e.
- Real Numbers consist of all rational and irrational numbers.
- Complex Numbers have an imaginary component, such as 3 + 4i.
Number Operations
- Addition involves combining two or more numbers to get a total or a sum, for instance, 2 + 3 = 5.
- Subtraction finds the difference between two numbers, such as 5 - 3 = 2.
- Multiplication is repeated addition of a number, for example, 2 × 3 = 6.
- Division splits a number into equal parts or groups, such as 6 ÷ 2 = 3.
Number Properties
- The Commutative Property states that the order of numbers does not change the result of an operation, shown in 2 + 3 = 3 + 2.
- The Associative Property highlights that the order in which numbers are grouped does not change the result of an operation, demonstrated in (2 + 3) + 4 = 2 + (3 + 4).
- The Distributive Property enables a number to be distributed to multiple addends, seen in 2 × (3 + 4) = 2 × 3 + 2 × 4.
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Description
Identify and understand the different types of numbers, from natural and whole numbers to integers, rational, irrational, and real numbers.
