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
1. When do you find the difference is the number itself?
Answer: Subtracting zero from a number means no subtraction. The difference is the number itself.
Examples: 11 - 0 = 11
19 - 0 = 19
93 - 0 = 93
2. How do we get the predecessor of a number?
Answer: By subtracting 1 from a number, we get the previous number or predecessor of that number.
Examples: 18 - 1 = 17
29 - 1 = 28
101 - 1 = 100
3. What the difference between two numbers is zero (0)?
Answer: When a number is subtracted from itself the difference is zero.
Examples: 10 - 10 = 0
75 - 75 = 0
98 - 98 = 0
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