Page 27 - Maths Class 06

For example : (i) (4 5+ ) 6+ = 9 + 6 = 15
Again, 4 +( 5 6+ ) = 4 11 15+ =
So that, (4 5+ ) 6+ = 4 + (5 6+ )

(ii) (15 16+ ) 17+ = 15 + (16 + 17 )
(iii) (115 226+ ) 338+ = 115 + (226 + 338 )

II. Subtraction Properties
Operations of addition and subtraction are inverse of each other.

1. Closure Property
The closure property does not hold good for subtraction of whole numbers. If a and b are whole numbers,
then a – b is a whole number, when a > b or a = b. If a < b, then a – b is not a whole number.

For example,

5 – 3 = 2 (A whole number)

8 – 8 = 0 (A whole number)

2 – 3 = -1 (Not a whole number)

2. Commu ta tive Prop erty
If a and b are two whole numbers, then in general, a – b is not equal to b – a i.e., a – b ¹ b –a. Hence, the
commutative property is not true for subtraction of whole number.

For example, 5 3- ¹ 3 5- ; 16 - 12 ¹ 12 - 16

NOTE

We may restate the Commutative property as: If a and b are whole numbers and a ¹ b, then either a – b is a whole
number or b – a is a whole number. Both are whole numbers only, if a = b.

3. Associative Property
If a, b, c are three whole numbers and c is not equal to 0, then a – (b – c) is not equal to (a – b) – c.

Thus, the associative property for subtraction also does not hold for whole numbers.
Study the following carefully:
(5 – 2) – 1 5 – (2 – 1)

3 – 1 = 2 5 – 1 = 4

different
Thus, (5 – 2) – 1 ¹ 5 – (2 – 1)

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