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:
 Rational numbers are commutative under addition.
Example:


 Rational numbers are not commutative under subtraction.

Example :
and


 Rational numbers are commutative under multiplication.

Example:


 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:
 Rational numbers are associative under addition.
Example:


 Rational numbers are not associative under subtraction.

Example:


 Rational numbers are associative under multiplication.

Example:


 Rational numbers are not associative under division.

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