Page 37 - Start Up Mathematics_6

 Commutative property

Let ‘a’ and ‘b’ be any two whole numbers, then a + b = b + a. Maths Fun
The sum of two whole numbers remains the same irrespective Think of a number.
of the order in which they are added. Multiply it by 5.
For example, 5 + 3 = 8 = 3 + 5 Add 5 to it.

 Existence of additive identity Divide it by 5.
Subtract 1 from it
Let ‘a’ be any whole number, then a + 0 = a = 0 + a.
The result is equal to your
The number ‘0’ is called additive identity for whole numbers. original number.

For example, 6 + 0 = 6 = 0 + 6
 Associative property
Let ‘a’, ‘b’ and ‘c’ be any three whole numbers, then (a + b) + c = a + (b + c)

The sum of the whole numbers remains unchanged even if the grouping is changed.
For example, (7 + 5) + 2 = 14 = 7 + (5 + 2)

Example 5: 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
 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 as it is negative.
Thus, subtraction is not closed under whole numbers.

For example, 6 – 2 = 4, but 2 – 6 is negative, hence not a whole number.
 Let ‘a’ and ‘b’ be two whole numbers, then a – b ≠ b – a.

Subtraction of whole numbers is not commutative.
For example, 5 – 3 ≠ 3 – 5 (since 5 – 3 = 2 and 3 – 5 is negative, hence not a whole number)

 Let ‘a’ be any whole number other than zero, then a – 0 = a.
When zero is subtracted from any whole number we get the same whole number as the answer.
This is known as property of zero.

For example, 4 – 0 = 4
 Let ‘a’, ‘b’ and ‘c’ be three whole numbers, then (a – b) – c ≠ a – (b – c).
Subtraction of whole numbers is not associative.

For example, (9 – 3) – 2 ≠ 9 – (3 – 2),
as LHS = (9 – 3) – 2 = 6 – 2 = 4; RHS = 9 – (3 – 2) = 9 – 1 = 8

 Let ‘a’, ‘b’ and ‘c’ be three whole numbers such that a – b = c, then a = b + c.
For example, 7 – 3 = 4, then 7 = 3 + 4

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