# Properties of Subtraction

Some properties of subtraction of whole numbers are:

Property 1:

If a and b are two whole numbers such that a > b or a = b, then a – b is a whole number. If a < b, then subtraction a – b is not possible in whole numbers.

For example:

9 - 5 = 4

87 - 36 = 51

130 - 60 = 70

119 - 59 = 60

28 - 0 = 28

Property 2:

The subtraction of whole numbers is not commutative, that is, if a and b are two whole numbers, then in general a – b is not equal to (b – a).

Verification:

We know that 9 – 5 = 4 but 5 – 9 is not possible. Also, 125 – 75 = 50 but 75 – 125 is not possible. Thus, for two whole numbers a and b if a > b, then a – b is a whole number but b – a is not possible and if b > a, then b – a is a whole number but a – b is not possible.

Hence, in general (a – b) is not equal to (b – a)

Property 3:

If a is any whole number other than zero, then a – 0 = a but 0 – a is not defined.

Verification:

We know that 15 – 0 = 15, but 0 – 15 is not possible.

Similarly, 39 – 0 = 39, but 0 – 39 is not possible.

Again, 42 – 0 = 42, but 0 – 42 is not possible.

Property 4:

The subtraction of whole numbers is not associative. That is, if a, b, c are three whole numbers, then in general a – (b – c) is not equal to (a – b) – c.

Verification:

We have,

20 – (15 – 3) = 20 – 12 = 8,

and, (20 – 15) – 3 = 5 – 3 = 2

Therefore, 20 – (15 – 3) ≠ (20 – 15) – 3.

Similarly, 18 – (7 – 5) = 18 – 2 = 16,

and, (18 – 7) – 5 = 11 – 5 = 6.

Therefore, 18 – (7 – 5) ≠ (18 – 7) – 5.

Property 5:

If a, b and c are whole numbers such that a – b = c, then b + c = a.

Verification:

We know that 25 – 8 = 17. Also, 8 + 17 = 25

Therefore, 25 – 8 = 17 or, 8 + 17 = 25

Similarly 89 – 74 = 15 because 74 + 15 = 89.

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