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.


● When zero is subtracted from the number, the difference is the number itself. For example, 8931 – 0 = 8931, 5649 – 0 = 5649

● When a number is subtracted from itself the difference is zero. For example, 5485 – 5485 = 0

● When 1 is subtracted from a number, we get its predecessor. For example, 6001 – 1 = 6000, 6000 – 1 = 5999


Questions and Answers on Properties of Subtraction:

I. Fill in the blanks:

(i) 568 – 0 = …………….

(ii) 7530 – 4530 = …………….

(iii) 7790 – 1 = …………….

(iv) 65894 – 65893 = …………….

(v) 54172 - ……………. = 0

(vi) 8688 – 8288 = …………….

(vii) 7721 – 5620 = …………….

(viii) 17281 – 1 = …………….

(ix) ……………. – 1 = 29999

(x) 29080 - ……………. = 29079


Answers:

(i) 568

(ii) 3000

(iii) 7789

(iv) 1

(v) 54172

(vi) 400

(vii) 2101

(viii) 17280

(ix) 30000

(x) 1


II. Match the given difference to its solution by coloring the cloud and the shape with same color.

Match the Given Difference

Answer:

(i) → 3

(ii) → 4

(iii) → 5

(iv) → 1

(v) → 2


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