Some properties of integer subtraction are:

Equipment 1:

If a and b are two integers with a> b or a = b, then a – b is an integer. If a

For example:

9 – 5 = 4

87-36 = 51

130 – 60 = 70

119 – 59 = 60

28 – 0 = 28


Property 2:

The subtraction of integers is not commutative, that is, if a and b are two integers, then a – b is generally 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. For two integers a and b, if a> b then a – b is an integer, but b – a is not possible, and if b> a then b – a is an integer but a – b is not possible .

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

Property 3:

If a is an integer 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.

Likewise 39-0 = 39, but 0-39 is not possible.

Here, too, 42-0 = 42 applies, but 0-42 is not possible.

Property 4:

The subtraction of whole numbers is not associative. That is, if a, b, c are three integers, 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

Hence 20 – (15 – 3) ≠ (20 – 15) – 3.

Likewise 18 – (7 – 5) = 18 – 2 = 16,

and, (18-7) -5 = 11-5 = 6.

Hence 18 – (7 – 5) ≠ (18 – 7) – 5.

Property 5:

If a, b and c are integers with a – b = c, then b + c = a.

Verification:

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

Hence 25 – 8 = 17 or 8 + 17 = 25

Likewise 89 – 74 = 15, because 74 + 15 = 89.

Zero property of subtraction – If 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 subtracting 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
– If we subtract 1 from any number, we get the number just before it. If 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

Questions and answers about the properties of subtraction:

I. Fill in the gaps:

(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

Reply:

(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

II. Assign the indicated difference to their solution by coloring the cloud and the shape with the same color.

Adjust the specified difference

Reply:

(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 ………… ..

Reply:

III. (i) 258

(ii) 607

(iii) 449

(iv) 373

(v) 899

(vi) 528

(vii) 200

(viii) 597

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