. Addition (+):
- Addition is a basic arithmetic operation that combines two or more numbers to find their total sum.
- It is commutative, meaning the order of the numbers does not affect the result: .
- It is associative, meaning the grouping of numbers does not affect the result: .
2. Subtraction (-):
- Subtraction is the operation of finding the difference between two numbers.
- It is not commutative: is not necessarily equal to .
- It is also not associative: is not necessarily equal to .
3. Multiplication (×):
- Multiplication is the operation of repeated addition and finding the total product of two or more numbers.
- It is commutative: .
- It is associative: .
- Multiplication by zero results in zero: 0 .
4. Division (÷):
- Division is the operation of splitting a quantity into equal parts or finding how many times one number is contained within another.
- Division by zero is undefined: 0 is undefined.
- Division is not commutative: is not necessarily equal to .
6. Order of Operations (PEMDAS/BODMAS):
- Parentheses/Brackets: Perform operations inside parentheses or brackets first.
- Exponents/Orders: Evaluate expressions with exponents or orders next.
- Multiplication and Division: Perform multiplication and division operations from left to right.
- Addition and Subtraction: Perform addition and subtraction operations from left to right.
7. Properties of Operations:
- Commutative Property: Changing the order of the numbers does not change the result (e.g., addition and multiplication).
- Associative Property: Changing the grouping of numbers does not change the result (e.g., addition and multiplication).
- Distributive Property: Multiplying a number by a sum or difference is the same as multiplying the number by each term separately and then adding or subtracting the results.
Understanding these basic mathematical operations and their properties is essential for solving mathematical problems and performing computations accurately and efficiently.
