Mathematics: Whole Numbers and Properties

Whole Numbers

• Whole numbers are the set of non-negative integers, including zero and all positive integers.
• They are used in counting and representing quantities.
• Examples: 0, 1, 2, 3, 4, and so on.
• Whole numbers do not include negative numbers or fractions.

Rounding Off

• Rounding off numbers involves approximating a value to a specified degree of accuracy.
• This is done by examining the digit to the right of the desired place value.
• If the digit is 5 or greater, the digit in the desired place value is increased by 1.
• If the digit is less than 5, the digit in the desired place value remains the same.
• Example: Rounding 23.74 to the nearest whole number results in 24.

Properties of Numbers

• Commutative Property: For addition and multiplication, the order of numbers does not affect the result.
  • Example: 2 + 3 = 3 + 2 and 2 × 3 = 3 × 2
• Associative Property: For addition and multiplication, the grouping of numbers does not affect the result.
  • Example: (2 + 3) + 4 = 2 + (3 + 4) and (2 × 3) × 4 = 2 × (3 × 4)
• Distributive Property: Distributes multiplication over addition.
  • Example: 2 × (3 + 4) = (2 × 3) + (2 × 4)
• Identity Property: For addition, the identity element is 0. Adding 0 to any number does not change the number.
  • Example: 5 + 0 = 5
• For multiplication, the identity element is 1. Multiplying any number by 1 does not change the number.
  • Example: 5 × 1 = 5
• Zero Property of Multiplication: Multiplying any number by 0 results in 0.
  • Example: 5 × 0 = 0

Sets, Bodies, etc. (Clarification Needed)

• The terms "sets," "bodies," are not clearly defined mathematical terms in the context of whole numbers. More context is needed to understand their intended use.

Multiples

• A multiple of a number is the product of that number and an integer.
• Examples: Multiples of 3 are 3, 6, 9, 12, and so on. (3 × 1, 3 × 2, 3 × 3, 3 × 4...).

Factors

• Factors of a number are the whole numbers that divide the number evenly (leaving no remainder).
• Examples: Factors of 12 are 1, 2, 3, 4, 6, and 12.

Operations with Numbers

• Addition: Combining numbers.
• Subtraction: Finding the difference between numbers.
• Multiplication: Repeated addition.
• Division: Finding how many times one number fits into another.
• Order of Operations (PEMDAS/BODMAS): A set of rules for evaluating expressions with multiple operations. Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).