Properties Of Subtraction:
1. Closure Property.
2. Commutative Property (or) Order property.
3. Associative Property.
4. Zero Property (or) Identity property .
5. Subtracting a number from itself.
6. Subtraction of 1.
1.
Closure Property:
When a whole number is subtracted from another whole
number, the difference is not always a whole number.
i.e; a – b = c , a whole number ; (a > b).
a – b =
-c , not a whole number ;( a < b).
Example:
25 – 10 = 15
, a whole number. ( a > b ).
5 – 15 = - 10
, not a whole number. ( a < b ).
2.
Commutative Property (or) Order Property:
In subtraction, the order in which the numbers are
subtracted is important. i.e: Minuend, a > Subtrahend,
b. ( a>b)
i.e; ( a – b ) ≠ ( b – a ) ; a, b are whole
numbers.
65
– 35 = 30;
35
– 65 = -30.
3.
Associative Property:
The subtraction of whole numbers is not associative.
i.e; if a, b, c are whole numbers, then in general:
a
– ( b – c ) ≠ ( a – b ) – c .
Example:
let a = 40 ; b = 20 ; c = 10.
a – ( b – c ) = 40 – ( 20 – 10 ) = 40 – 10 = 30.
(a – b ) – c = ( 40 – 20 ) – 10 = 20 – 10 = 10.
Therefore, a –
( b – c ) ≠ ( a – b ) – c.
4.
Zero Property (or) Identity property:
In this property 0 is subtracted from a number.
When 0 is subtracted from a number gives the number
itself.
i.e; a – 0 = a.
Here, Minuend
= Number = 30,
Subtrahend
= 0,
Difference
= Number itself = 30
Example: 30 – 0 = 30; 100 – 0 = 100;
(- 5) - 0 = -5 ; ( -25) - 0 = -25.
5.
Subtracting a number from itself:
If the number is subtracted from itself, the
difference is Zero.
i.e; a – a = 0.
Here, Minuend = Number = 58,
Subtrahend = Number itself = 58,
Difference = Zero = 0.
Example: 58 – 58 = 0; 72 – 72 = 0.
6.
Subtraction of 1:
When 1 is subtracted from a number, we get its Predecessor.
Example: 500 – 1 = 499; 499 – 1 = 498; 498 – 1 =
497.
