Properties of Whole Numbers

Properties of Whole Numbers:

  • Addition and multiplication of 2  whole number results in a whole number.
  • Subtraction and division of any 2  whole number may or may not give a whole number.

Properties of Operators:

Closure property

  • Whole numbers are closed under addition and also under multiplication.
  • Whole numbers are not closed under subtraction and division.

Division by zero

Division of any whole number by 0  is undefined.

Commutative property

Addition and multiplication are commutative for whole numbers. i.e., whole numbers can be added or multiplied in any order.

Associative property

Associativity of addition and multiplication

\left( {{\rm{A + B}}} \right){\rm{ + C = A + }}\left( {{\rm{B + C}}} \right)

\left( {{\rm{A}} \times {\rm{B}}} \right) \times {\rm{C = A}} \times \left( {{\rm{B}} \times {\rm{C}}} \right)

Distributive Property

{\rm{A}} \times \left( {{\rm{B + C}}} \right) = {\rm{A}} \times {\rm{B + A}} \times {\rm{C}}

Identities: They are the numbers which when included in addition and multiplication, the value of the operation is unchanged.

Additive Identity

Additive identity gives the same whole number when added to another whole number.

Zero is the additive identity as {\rm{a }} + {\rm{ }}0{\rm{ }} = {\rm{ a}} , ({\rm{a}}  is any whole number).

Multiplicative Identity

Multiplicative identity gives the same whole number when multiplied by another whole number.

{\rm{1}}  is the Multiplicative identity as {\rm{a }} \times {\rm{1 }} = {\rm{ a}} , ({\rm{a}} is any whole number)

Numbers between square numbers

There exists 2{\rm{n}}  non-square numbers between 2  successive square numbers.

Adding odd numbers

Sum of first {\rm{n}}  natural odd numbers are {{\rm{n}}^2}   ,which is a perfect square.

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