In mathematics, mastering the basic operations of addition, subtraction, multiplication, and division is crucial. These operations are the building blocks for more complex mathematical concepts. This section delves into each operation with a focus on integers, fractions, and decimals, emphasizing the correct ordering of operations and the use of brackets.

Addition

Addition combines two or more numbers into their total or sum.

• Properties:
  • Commutative: Order doesn't affect the sum, e.g., $3 + 4 = 4 + 3$.
  • Associative: Grouping doesn't affect the sum, e.g., $(2 + 3) + 4 = 2 + (3 + 4)$.

Example: Calculating a Sum

Question: What is the sum of $78$, $45.3$, and $-22$?

Solution:

Subtraction

Subtraction finds the difference between two numbers, essentially reversing addition.

• Symbols and Terms: The - symbol denotes subtraction. The number being subtracted is the subtrahend, from the minuend, to get the difference.
• Properties:
  • Non-Commutative: The order in subtraction matters, e.g., $5 - 2 \neq 2 - 5$.

Example: Finding a Difference

Question: What is the difference between $50$ and $32.75$?

Solution:

Multiplication

Multiplication adds a number to itself a specified number of times, streamlining addition.

• Symbols and Terms: The × or * symbol is for multiplication. The numbers being multiplied are factors, with the result called the product.
• Properties:
  • Commutative: The order of factors doesn't affect the product, e.g., $3 × 4 = 4 × 3$.
  • Associative: Grouping of factors doesn't affect the product, e.g., $(2 × 3) × 4 = 2 × (3 × 4)$.

Example: Multiplying Numbers

Question: Multiply $3.5$ by $2.4$.

Solution:

Division

Division splits a number into equal parts, the inverse of multiplication.

• Symbols and Terms: The ÷ or / symbol represents division. The number being divided is the dividend, by the divisor, to get the quotient.
• Properties:
  • Non-Commutative: Order matters significantly in division.
  • Division by Zero: Undefined.

Example: Dividing Numbers

Question: Divide $56$ by $0.7$.

Solution:

Order of Operations and Bracket Usage

Correct operation ordering and bracket usage are pivotal for solving problems accurately. PEMDAS guides the order: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

• Brackets: Operations within are prioritized; nested ones are solved inside out.

Example: