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Real numbers

• Commutativity
• Whole numbers are commutative under addition and multiplication. However, they are not commutative under subtraction and division.
• Integers are commutative under addition and multiplication. However, they are not commutative under subtraction and division.
• Rational numbers:
1. Rational numbers are commutative under addition.

Example: 1. Rational numbers are not commutative under subtraction.

Example : and  1. Rational numbers are commutative under multiplication.

Example: 1. Rational numbers are not commutative under division.

2 ÷ 5 ≠ 5 ÷ 2

• Associativity
• Whole numbers are associative under addition and multiplication. However, they are not associative under subtraction and division.
• Integers are associative under addition and multiplication. However, they are not associative under subtraction and division.
• Rational numbers:
1. Rational numbers are associative under addition.

Example: 1. Rational numbers are not associative under subtraction.

Example:   1. Rational numbers are associative under multiplication.

Example: 1. Rational numbers are not associative under division.

Example: • 0 is the additive identity of whole numbers, integers,…

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