Properties of Whole Numbers
Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

Closure property
Whole numbers are closed under addition and multiplication. Whole numbers are not closed under subtraction and division. If a and b are any two whole numbers, then a+b, axb are also whole numbers.

Commutative property
The sum of two whole numbers is the same, no matter in which order they are added. This is called the commutative property of addition. The product of two whole numbers is the same, no matter in which order they are multiplied. This is called the commutative property of multiplication. Subtraction and division are not commutative in whole numbers. If a and b are any two whole numbers, then a+b = b+a and a×b = b×a.

Additive Identity
A whole number added to '0' remains unchanged. Thus, '0' is called the additive identity in whole numbers. If a is any whole number, then a + 0 = a = 0 + a.

Multiplicative Identity
A whole number multiplied by 1 remains unchanged. Thus, 1 is called the multiplicative identity in whole numbers. If a is any whole number, then a × 1 = a = 1 × a.

Associative property
While adding whole numbers, we can group the numbers in any order. This is called the associative property of addition. While multiplying whole numbers, we can group them in any order. This is called the associative property of multiplication. If a, b and c are any two whole numbers, then (a+b)+c = a+(b+c) and (a×b)×c = a×(b×c).

Distributive property
The product of a whole number with the sum of the two other whole numbers is equal to the sum of the products of the whole number with other two whole numbers. This is called the distributive property of multiplication over addition. If a, b and c are any two whole numbers, then a(b+c) = a×b + a×c.

The product of a whole number with the difference of the two other whole numbers is equal to the difference of the products of the whole number with other two whole numbers. This is called the distributive property of multiplication over subtraction. If a, b and c are any two whole numbers, then a(b–c) = a×b – a×c.

Multiplication by zero
Product of a whole number by zero is equal to zero. If a is any whole number, then a × 0 = 0 = 0 × a.

Division by zero
Division of a whole number by 0 is not defined. If a is any whole number, then a ÷ 0 is not defined.

If a is any whole number, then a ÷ 1 = a.
If a is any non-zero whole number, then a ÷ a = 1.
If a is any non-zero whole number, then 0 ÷ a = 0.

Summary

Closure property
Whole numbers are closed under addition and multiplication. Whole numbers are not closed under subtraction and division. If a and b are any two whole numbers, then a+b, axb are also whole numbers.

Commutative property
The sum of two whole numbers is the same, no matter in which order they are added. This is called the commutative property of addition. The product of two whole numbers is the same, no matter in which order they are multiplied. This is called the commutative property of multiplication. Subtraction and division are not commutative in whole numbers. If a and b are any two whole numbers, then a+b = b+a and a×b = b×a.

Additive Identity
A whole number added to '0' remains unchanged. Thus, '0' is called the additive identity in whole numbers. If a is any whole number, then a + 0 = a = 0 + a.

Multiplicative Identity
A whole number multiplied by 1 remains unchanged. Thus, 1 is called the multiplicative identity in whole numbers. If a is any whole number, then a × 1 = a = 1 × a.

Associative property
While adding whole numbers, we can group the numbers in any order. This is called the associative property of addition. While multiplying whole numbers, we can group them in any order. This is called the associative property of multiplication. If a, b and c are any two whole numbers, then (a+b)+c = a+(b+c) and (a×b)×c = a×(b×c).

Distributive property
The product of a whole number with the sum of the two other whole numbers is equal to the sum of the products of the whole number with other two whole numbers. This is called the distributive property of multiplication over addition. If a, b and c are any two whole numbers, then a(b+c) = a×b + a×c.

The product of a whole number with the difference of the two other whole numbers is equal to the difference of the products of the whole number with other two whole numbers. This is called the distributive property of multiplication over subtraction. If a, b and c are any two whole numbers, then a(b–c) = a×b – a×c.

Multiplication by zero
Product of a whole number by zero is equal to zero. If a is any whole number, then a × 0 = 0 = 0 × a.

Division by zero
Division of a whole number by 0 is not defined. If a is any whole number, then a ÷ 0 is not defined.

If a is any whole number, then a ÷ 1 = a.
If a is any non-zero whole number, then a ÷ a = 1.
If a is any non-zero whole number, then 0 ÷ a = 0.

Videos

References

Like NextGurukul? Also explore our advanced self-learning solution LearnNext
Offered for classes 6-12, LearnNext is a popular self-learning solution for students who strive for excellence
Explore
Animated Video
lessons
All India
Test Series
Interactive Video
Experiments
Best-in class
books

Join India's most happening

Educational community