Question

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Answer 1

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★ ★The properties of multiplication of integers are :-

• Closure Property

• Commutative Property

•Multiplication by zero

•Multiplicative identity

•Associative property

•Distributive property

✰✰ Closure Property :-

According to this property, if two integers a and b are multiplied then their resultant a × b is also an integer. Therefore, integers are closed under multiplication.

a × b is an integer, for every integer a and b.

☞ For example :-

– 10 × (– 5) = 50

40 × (– 15) = – 600

✰✰Commutative Property :-

The commutative property of multiplication of integers states that altering the order of operands or the integers does not affect the result of the multiplication.

a × b = b × a, for every integer a and b.

☞ For example :-

5 × (– 6) = – 30 and (– 6) × 5 = – 30

Hence,

5 × (– 6) = (– 6) × 5

✰✰Multiplication by zero:-

On multiplying any integer by zero the result is always zero. In general, if a and b are two integers then,

a × 0 = 0 × a = 0

☞ For example :-

4× 0 = 0

– 7 × 0 = 0

✰✰Multiplicative identity:-

On multiplying any integer by 1 the result obtained is the integer itself. In general, if a and b are two integers then,

a × 1 = 1 × a = a

Therefore 1 is the Multiplicative Identity of Integers.

☞ For example :-

5 x 1 = 5

1 x (- 7) = -7

✰✰ Associative property:-

The result of the product of three or more integers is irrespective of the grouping of these integers. In general, if a, b and c are three integers then,

a × (b × c) = (a × b) × c

☞ For example :-

4( 3 × 2) = ( 4 × 3) 2

✰✰Distributive property:-

According to the distributive property of multiplication of integers, if a, b and c are three integers then,

a× (b + c) = (a × b) + (a × c)

☞ For example :-

12 x (9 + 7) = 12 x 16 = 192

12 x (9 + 7) = 12 x 9 + 12 x 7 = 108 + 84 = 192

Thus, 12 x (9 + 7) = (12 x 9) + (12 x 7)

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