Page 34 - ICSE Math 6

• Associative property

The sum of whole numbers remains the same even if their grouping is changed, i.e., if ‘a’, ‘b’
and ‘c’ are any three whole numbers then (a + b) + c = a + (b + c). This property is known as the
associative property of addition of whole numbers. For example, (7 + 5) + 2 = 12 + 2 = 14 and
7 + (5 + 2) = 7 + 7 = 14
• Existence of additive identity

When 0 is added to a whole number we get the same number, i.e., if ‘a’ is a whole number then
a + 0 = a = 0 + a. Thus, 0 is the additive identity of whole numbers.
For example, 6 + 0 = 6 = 0 + 6
• Additive inverse
If a + b = 0, then we say that b is the additive inverse of a and a is the additive inverse of b.

Since for any given whole number ‘a’ there is no whole number ‘b’ such that a + b = 0, the additive
inverse for whole numbers does not exist.
For example, 7 is a whole number and 7 + (–7) = 0, but –7 is not a whole number.
Example 3: Find the sum by suitable rearrangement.
(a) 837 + 208 + 363 (b) 1,962 + 453 + 1,038 + 747

Solution: (a) 837 + 208 + 363 = (837 + 363) + 208
= 1,200 + 208 = 1,408
(b) 1,962 + 453 + 1,038 + 747 = (1,962 + 1,038) + (453 + 747)
= 3,000 + 1,200 = 4,200

II. Subtraction
• Closure property

Let ‘a’ and ‘b’ be two whole numbers such that a ≥ b, then (a – b) is a whole number, but
(b – a) is not a whole number.
Thus, whole numbers are not closed under subtraction.
For example, 6 – 2 = 4, but 2 – 6 is not a whole number.
• Commutative property
Let ‘a’ and ‘b’ be two whole numbers, then a – b ≠ b – a.
Thus, whole numbers are not commutative under subtraction.

For example, 5 – 3 ≠ 3 – 5 (since 5 – 3 = 2 and 3 – 5 is not a whole number)
• Associative property
Let ‘a’, ‘b’ and ‘c’ be three whole numbers, then (a – b) – c ≠ a – (b – c).
Thus, whole numbers are not associative under subtraction.
For example, (9 – 3) – 2 ≠ 9 – (3 – 2),
as LHS = (9 – 3) – 2 = 6 – 2 = 4; RHS = 9 – (3 – 2) = 9 – 1 = 8
• Property of zero Maths Info

When zero is subtracted from any whole number we get the same
whole number as the answer. This is known as the property of zero Under subtraction, the identity
under subtraction. and inverse of whole numbers
do not exist.
For example, 4 – 0 = 4

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