Page 29 - Maths Class 06

Property 5.
Multiplication Property of 1 : If a is any whole number, then a´ = ´ =1 1 a a.
‘1’ is called the multiplicative identity for whole numbers.

For example, (i) 15 1 15´ = (ii) 1 225´ = 225 (iii) 4532 1´ = 4532
Property 6.

Distributive Law of Multiplication over Addition : If a b, and c are three distinct whole numbers, then
a´( b c+ ) = a b a c´ + ´

and (b c+ ) a´ = b a c a´ + ´ .
For example, (i) Let us consider three whole numbers 11, 13 and 14.
Then, (13 14+ ) 11 27 11 297´ = ´ =

13 11 14 11 143 154´ + ´ = + = 297
Thus, it is clear that,

(13 14+ ) 11 13 11 14 11´ = ´ + ´
(ii) Let us consider three whole numbers 5, 7 and 9.
Then, 5´( 7 9+ ) = 5 16´ = 80

and 5 7 5 9´ + ´ = 35 + 45 = 80
Thus, it is clear that,
5´( 7 9+ ) = 5 7 5 9´ + ´

Property 7.

Distributive Law of Multiplication over Subtraction : If a b, and c are three whole numbers and b c> ,
then, a´( b c- ) = a b a c´ - ´
and (b c- ) a´ = b a c a´ - ´ .
For example, (i) Let us consider three distinct whole numbers 3, 7 and 5.
Then, 3´( 7 5- ) = 3 2´ = 6
3 7 3 5´ - ´ = 21 15- = 6
Hence, it is clear that,

3´( 7 5- ) = 3 7 3 5´ - ´
(ii) Let, us consider three distinct whole numbers 9, 12 and 10.
Then, (12 10- ) 9´ = 2 9´ = 18

12 9 10 9´ - ´ = 108 90- = 18
Thus, it is clear that,

(12 10- ) 9´ = 12 9 10 9´ - ´
IV. Division Properties

Property 1.
Closure Property : If a and b are whole numbers, then a ÷ b may or may not represent a whole number.

Does the closure property hold for division in whole numbers?

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