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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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