Properties of multiplication
    (i)    Closure Property : If a and b are whole numbers, then their product a x b = c will always be a whole number. That is whole numbers are closed under multiplication.
        For ex.     7 x 3  = 21x 6 x 8 = 48 x 3 x 0 = 0  

    (ii)    Commutative Property :  In general a x b = b x a  for all whole numbers a and b.
        Consider the following example
            2 x 3 = 3 x 2 = 6
            8 x 9 = 9 x 8 = 72

    (iii)    Associative Property : If a,b and c are whole numbers, then (a x b) x c = a x (b x c)
        That is, whole numbers have the associative property of multiplication.
        For ex.    (3 x 4) x 2 = 3 x  (4 x 2)
            12 x 2 = 3  x 8
            24 = 24

    (iv)    Multiplicative Identity : 1 x a = a x 1 = a. Hence, 1 is called the multiplicative identity for whole numbers.
        For ex.              10 x 1 = 1  x 10  = 10
                     3  x 1  = 1 x 3  = 3
                  672  x 1 = 1  x 672 = 672
                       0 x 1 = 1 x 0 = 0

Properties of division

(i)    Closure Property : If a and b are whole number , then the quotient a ÷ b need not always be a whole number. So, division in whole numbers is not closed.

Commutative Property : If a and b are whole numbers, then a ÷ b is not equal to b ÷  a. So, the commutative property does not hold true for whole numbers.

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Properties and patterns of whole Numbers

Properties of Whole Numbers

1. Closure Property
2. Associative Property
3 Commutative Property
4. Distributive Property

1.Closure Property of Whole Numbers

This property tells us that when whole  number is operated on  "Addition and multiplication” their answer is always in Whole Number.
This property does not be same as on whole numbers in the while doing division and subtraction.
For example: Two whole numbers subtracted then answer will not be whole number, 2 and 4 are whole numbers, but 2 - 4 = -2, is not a whole number. Same in the case of division, 2/4 is not defined

Associative Property of Whole Numbers

This property tells us that "The answer of the sum and the product of whole numbers remain the same, if the numbers are three whole numbers

Example 1:  (1+2)+3 = 1+(2+3) because,
(1+2)+3 = 3+3 = 6
1+(2+3) = 1+5 = 6

Example 2: (1×2) × 3 = 1 × (2×3) because,
(1×2) × 3 = 2 × 3 = 6
1 × (2×3) = 1 × 6 = 6

This  property of whole numbers does not same   for division and subtraction  operations.
For example, 4, 5, and 6 are whole numbers, but 4 - (5 - 6) = 4 - (-1) = 5 and (4 - 5) - 6 = - 1 - 6 = -7. So, 5 ≠ 7.
The same is with the division where 9 ÷ (6 ÷ 3) ≠ (6 ÷ 3) ÷ 9.

Commutative Property of Whole Numbers

“After interchanging the order of the numbers, the sum and the product of two whole numbers always are the same number”.

Example 1: 4+5 = 5+4 because,
4+5 = 9
5+4 = 9
Example 2: 4×2 = 2×4 because,
4×2 = 8
2×4 = 8
the commutative property of whole numbers does not always be the same for on division and subtraction.

Distributive Property of Whole Numbers

The distributive property of multiply and sum is
 A× (b+c) = a×b+a×c.

Example 1:  3× (2+5) = 3×2+3×5 because,
3× (2+5) = 3×7 = 21
3×2+3×5 = 6+15 = 21
the distributive property of multiply and subtract is a× (b−c) =a×b−a×
c.

Example 2:  3× (5−2) = 3×5−3×2 as,
3× (5−2) = 3×3 = 9
3×5-3×2 = 15-6 = 9

 

Patterns in whole numbers

 

 Patterns are defined as the sequence that follows a defined sequence or patterns

Here the numbers are 11, 17, 23, 29, 35, 41, 47, and 53. The

The numbers are increasing by count of 6 every time.

Using Dots Number Patterns

Every whole number is defined in the form of dots and to find the pattern numbers are arranged in the dots representation. These representations are A rectangle, A square, A triangle

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