Fundamental Arithmetic Operations

Fundamental Arithmetic Operations

• Addition: Combining two or more numbers to find the total. The result is called the sum.
• Subtraction: Finding the difference between two numbers. The result is called the difference.
• Multiplication: Repeated addition of the same number. The result is called the product.
• Division: Separating a number into equal parts. The result is called the quotient.

Properties and Rules

• Commutative Property (Addition and Multiplication): Changing the order of numbers doesn't change the result.
  • Example: 2 + 3 = 3 + 2 and 2 × 3 = 3 × 2
• Associative Property (Addition and Multiplication): Grouping numbers differently doesn't change the result.
  • Example: (2 + 3) + 4 = 2 + (3 + 4) and (2 × 3) × 4 = 2 × (3 × 4)
• Distributive Property: Multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
  • Example: 2 × (3 + 4) = (2 × 3) + (2 × 4)
• Identity Property (Addition and Multiplication): Adding zero to a number or multiplying a number by one doesn't change the number.
  • Example: 5 + 0 = 5 and 5 × 1 = 5
• Inverse Property (Addition and Subtraction): Adding a number and its opposite (additive inverse) equals zero.
  • Example: 5 + (-5) = 0
• Zero Property of Multiplication: Multiplying any number by zero results in zero.
• Example: 7 x 0 = 0

Whole Numbers

• Whole numbers consist of zero and all the positive counting numbers (1, 2, 3,...). They are used for counting and measuring.

Integers

• Integers are the set of whole numbers and their opposites (negative numbers). Integers include..., -3, -2, -1, 0, 1, 2, 3,...

Fractions

• Fractions represent parts of a whole. A fraction has a numerator (top number) and a denominator (bottom number). The numerator represents the number of parts being considered, and the denominator represents the total number of equal parts in the whole. Fractions can also represent division.

Decimals

• Decimals represent numbers that have a fractional part to the right of a decimal point. Decimals can be converted to fractions and vice versa.

Order of Operations

• The order of operations (PEMDAS/BODMAS) dictates the sequence for evaluating expressions containing multiple operations:
  • Parentheses (or Brackets)
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Number Systems

• Natural Numbers: Counting numbers (1, 2, 3, etc.)
• Whole Numbers: Natural numbers plus zero (0, 1, 2, 3, etc.)
• Integers: Whole numbers and their opposites (..., -3, -2, -1, 0, 1, 2, 3,...)
• Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers, and q is not zero.
• Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers.
• Real Numbers: The set that includes all rational and irrational numbers.

Number Line

• A number line visually represents numbers along a straight line. Numbers increase from left to right. The number line helps visualize comparisons and relationships between numbers.

Problem Solving

• Understanding the problem.
• Devising a plan.
• Carrying out the plan.
• Looking back.

Estimation

• Using rounded numbers to find an approximate answer/result.
• Often useful in everyday scenarios.

Mental Math

• Using arithmetic strategies and properties to solve problems mentally.
• Often quicker and more efficient for simple calculations.

Application of Arithmetic

• Everyday tasks (shopping, budgeting).
• Measurement (length, weight, volume).
• Geometry (area, perimeter, volume).
• Algebra (equations, formulas).