Page 28 - Maths Class 06

4. Property of Zero
If 0 is subtracted from a whole number, then the result is the number itself.
If 0 is subtracted from any whole number, there is no change in the whole number.

For example,

5 – 0 = 5 (A whole number)

NOTE

If any whole number (except 0) is subtracted from zero, then the result is not whole number.
0 – 27 = – 27 (Not a whole number).

III. Multiplication Properties

Property 1.
Closure Property : If a and b are two whole numbers and a b´ = c, then their product c is also a whole
number.
For example, (i) 5 6´ = 30, which is a whole number.

(ii) 4 3´ = 12, which is a whole number.
(iii) 25 5´ = 125, which is a whole number.

Property 2.
Commutative Law of Multiplication : If a and b are any two whole numbers, then a b´ = b a´ .
For example, (i) 5 8´ = 40 and 8 5´ = 40

Thus, 5 8´ = 8 5´
(ii) 12 16´ = 192 and 16 12´ = 192

Thus, 12 16´ = 16 12´
Property 3.

Associative Law of Multiplication : If a b, and c are any three whole numbers,
then (a b´ ) c´ = a´ (b c´ )
For example, (i) (4 5´ ) 6´ = 20 6´ = 120
NOTE
And 4´( 5 6´ ) = 4 30´ = 120
We can use this properties in
Thus, (4 5´ ) 6´ = 4´ (5 6´ ) making multiplication of three or

(ii) (20 21´ ) 25´ = 420 25´ = 10500 more whole numbers simple.
And 20 ´( 21 25´ ) = 20 525´ = 10500
Thus, (20 21´ ) 25´ = 20 ´ (21 25´ )

Property 4.
Multiplication Property of Zero : If a is any whole number, then

a´0 = ´0 a = 0
For example, (i) 3 0´ = 0 (ii) 0 26´ = 0 (iii) 356 0´ = 0

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