Properties of Subtraction

Some properties of subtraction of whole numbers are:

Property I:

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 II:

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 III:

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 IV:

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 V:

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.

● Zero Property of Subtraction - When zero is subtracted from the number, the difference is the number itself.

For example,

(i) 8931 – 0 = 8931;

(ii) 5649 – 0 = 5649;

(iii) 245 – 0 = 245

(iv) 197 – 0 = 197

● Properties of Subtraction of a Number from itself: When a number is subtracted from itself the difference is zero.

For example,

(i) 5485 – 5485 = 0

(ii) 345 – 345 = 0

(iii) 279 – 279 = 0

● Predecessor – On subtracting 1 from any number, we get the number just before it. When 1 is subtracted from a number, we get its predecessor.

For example,

(i) 6001 – 1 = 6000

(ii) 6000 – 1 = 5999

(iii) 163 – 1 = 162

(iv) 171 – 1 = 170

Worksheet 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

(xi) 548 - ………….. = 0

(xii) ………….. – 0 = 274

(xiii) 367 - ………….. = 367

(xiv) 765 – 765 = …………..

(xv) 212 – 0 = …………..

(xvi) 167 - ………….. = 0

(xvii) 647 – 647 = …………..

(xviii) 326 – 326 = …………..

(xix) ………….. – 0 = 876

(xx) 429 – 0 = …………..

(xxi) 999 – 999 = …………..

(xxii) 412 - ………….. = 412

(xxiii) 700 - 100 = …………..

(xxiv) 100 - 10 = …………..

(xxv) 9429 - 100 = …………..

(xxvi) 4583 - 1000 = …………..

(xxvii) 9498 - 1000 = …………..

(xxviii) 1000 - 1000 = …………..

Answers:

(i) 568

(ii) 3000

(iii) 7789

(iv) 1

(v) 54172

(vi) 400

(vii) 2101

(viii) 17280

(ix) 30000

(x) 1

(xi) 54

(xii) 274

(xiii) 0

(xiv) 0

(xv) 212

(xvi) 167

(xvii) 0

(xviii) 0

(xix) 876

(xx) 429

(xxi) 0

(xxii) 0

(xxiii) 600

(xxiv) 90

(xxv) 9329

(xxvi) 3583

(xxvii) 8498

(xxviii) 0

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

Answer:

(i) → 3

(ii) → 4

(iii) → 5

(iv) → 1

(v) → 2

III. Write the predecessor of the following numbers:

(i) 259 …………..

(ii) 608 …………..

(iii) 450 …………..

(iv) 374 …………..

(v) 900 …………..

(vi) 529 …………..

(vii) 201 …………..

(viii) 598 …………..

Answers:

III. (i) 258

(ii) 607

(iii) 449

(iv) 373

(v) 899

(vi) 528

(vii) 200

(viii) 597

IV: Fill in the blanks on the basis of subtraction facts:

(i) 43 - 0 = _____

(ii) 18 - 1 = _____

(iii) 77 - 77 = _____

(iv) 54 - 0 = _____

(v) 33 - 1 = _____

(vi) 62 - 0 = _____

(vii) 98 - 1 = _____

(viii) 56 - 56 = _____

(ix) 34 - 0 = _____

Answer:

IV: (i) 43

(ii) 17

(iii) 0

(iv) 54

(v) 32

(vi) 62

(vii) 97

(viii) 0

(ix) 34

Math Only Math is based on the premise that children do not make a distinction between play and work and learn best when learning becomes play and play becomes learning.

However, suggestions for further improvement, from all quarters would be greatly appreciated.

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