Page 41 - Maths Class 05

Associative Property : When three or more numbers are added, the sum is the same

regardless the grouping of the addends. For example : (2 + 3) + 4 = 2 + (3 + 4)

Additive Identity Property : The sum of any number and zero is the number itself.

For example : 5 + 0 = 5 = 0 + 5
Distributive Property : The sum of two numbers times a third number is equal to

the sum of each added times the third number.

For example : 4 × (6 + 3) = 4 × 6 + 4 × 3
2. Properties of Subtraction

There are different properties of subtraction. They are :

« If ‘a’ and ‘b’ are any whole numbers and subtraction is performed on ‘a’ and ‘b’,
when a = b or a > b, then the result is also a whole number.

« Commutative property does not hold true for subtraction. If we will change the
order of numbers we will get different answer.

If a = 475 and b = 379

then, a – b ¹ b – a
i.e., 475 – 379 = 379 – 475 Þ 96 ¹ –96

« As commutative property is not valid in subtraction, similarly associative

property also does not work out in subtraction.

For three natural numbers a, b, and c

(a – b) – c ¹ a – (b – c)
« If any number is subtracted from itself, the result is zero.

If a = 7397426 than a – a = 0

i.e., 7397426 – 7397426 = 0

« If we subtract 0 from any number, the result is the number itself.

If a = 1726502 than a – 0 = a

i.e., 1726502 – 0 = 1726502

3. Properties of Multiplication

« If any number is multiplied by 0 (zero), the product is zero.

125 × 0 = 0 ; 0 × 4967 = 0
« If any number is multiplied by 1, the product is the number itself.

564 × 1 = 564 ; 1 × 8375 = 8375

Mathematics-5 41