PROPERTIES OF SUBTRACTION.

 

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.