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Whole Numbers: Properties & Concepts

Whole numbers include natural numbers like 1, 2, 3 and zero. A number's predecessor is the number before it in counting, and its successor is the number after. Whole numbers have properties when added, multiplied and compared on a number line. They are closed under addition and multiplication, meaning these operations always yield a whole number. They associate, have an identity of 0 for addition and 1 for multiplication, and commute for addition and multiplication. The distributive property also applies for whole numbers. However, they are not closed under subtraction or division, and these operations are not commutative with whole numbers.

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182 views2 pages

Whole Numbers: Properties & Concepts

Whole numbers include natural numbers like 1, 2, 3 and zero. A number's predecessor is the number before it in counting, and its successor is the number after. Whole numbers have properties when added, multiplied and compared on a number line. They are closed under addition and multiplication, meaning these operations always yield a whole number. They associate, have an identity of 0 for addition and 1 for multiplication, and commute for addition and multiplication. The distributive property also applies for whole numbers. However, they are not closed under subtraction or division, and these operations are not commutative with whole numbers.

Uploaded by

Madhur Chopra
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Whole Numbers

The numbers used for counting are called natural numbers. The number that comes
immediately before another number in counting is called its predecessor. The number
that comes immediately after another number in counting is called its successor. To find
the successor of any given natural number, just add 1 to the given number. The value of
nothing is represented by the number zero. Example: 3 – 3 = 0.

Natural numbers together with the number zero are called whole numbers. When
comparing two whole numbers, the number that lies to the right on the number line is
greater. When comparing two whole numbers, the smaller number lies to the left on the
number line

Properties of Whole Numbers

1. Closure Property
i) If two whole numbers are added, then the result is again a whole number. Which
implies whole numbers are closed with respect to addition.
ii) If two whole numbers are multiplied, then the result is again a whole number. Which
implies whole numbers are closed with respect to multiplication.

2. Associative Property
If a, b, c are whole numbers, then
i) a + (b + c) = (a + b) + c
i) ii) a × (b × c) = (a × b) × c
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 property is called associative property of multiplication.

3. Identity
i) If a is a whole number, a + 0 = 0 + a = a A whole number added to 0 remains
unchanged. Thus, 0 is called the additive identity in whole numbers.
ii) If a is a whole number, a × 1 = 1 × a = a
A whole number multiplied to 1 remains unchanged. Thus, 1 is called the multiplicative
identity in whole numbers.

4. Commutative Property
If a, b, c are whole numbers, then
i) a + b = b + a ii) a × b = b × a The addition of two whole numbers is the same, no
matter in which order they are added. This is called the commutative property of
addition.
Similarly, 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.

5. Distributive Property of Multiplication over Addition


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

Note

i) Whole numbers are not closed under subtraction and division.

ii) Subtraction and division are not commutative in whole numbers.

iii) No inverse exists for whole numbers.

iii) Associative property does not hold for subtraction and division of whole numbers.

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