Right properties of rational numbers if addition , subtraction , multiplicationand division on the A4 size pap

Here are the right properties of rational numbers for addition, subtraction, multiplication, and division:

1. Addition

• Commutative Property: $a + b = b + a$
• Associative Property: $(a + b) + c = a + (b + c)$
• Identity Element: $a + 0 = a$

2. Subtraction

• Non-Commutative Property: $a - b \neq b - a$
• Associative Property: Not applicable.
• Identity Element: $a - 0 = a$

3. Multiplication

• Commutative Property: $a \cdot b = b \cdot a$
• Associative Property: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$
• Identity Element: $a \cdot 1 = a$
• Distributive Property: $a(b + c) = ab + ac$

4. Division

• Non-Commutative Property: $a \div b \neq b \div a$
• Associative Property: Not applicable.
• Identity Element: $a \div 1 = a$ (where $b \neq 0$)
• Division by Zero: Division by zero is undefined.

These properties are fundamental to understanding how rational numbers behave under various operations.