The properties of multiplying integers are explained using examples.
For any integers ‘a’, ‘b’ and ‘c’, etc.
1. Closure property:
a × b is an integer i.e., product (multiplication) of two integers is always an integer
For example: 2 and 3 are two integers, now 2 × 3 = 6, which is an integer.
2. Commutative property:
a × b = b × a.
For example: 2 × 5 = 5 × 2 and so on.
3. Associative property:
a × (b × c) = (a × b) × c.
For example: 2 × (3 × 4) = (2 × 3) × 4 and so on.
4. Multiplicative Property of Zero:
a × 0 = 0 × a = 0
For example: 5 × 0 = 0 × 5 = 0 and so on.
The result of multiplication of any number with zero (0) is always zero.
i.e., any number × 0 = 0 and 0 × any number = 0
Thus, 7 × 0 = 0, 0 × 7 = 0, (10) × 0 = 0, 0 × (10) = 0
5. Multiplicative identity property:
a × 1 = 1 × a = a
For example: 3 × 1 = 1 × 3 = 3 and so on.
6. Distributive of property multiplication over addition:
(i) a × (b + c) = a × b + a × c,
For example: 2 × (4 + 5) = 2 × 4 + 2 × 5 and so on.
(ii) (b + c) × a = b × a + c × a
For example: (4 + 9) × 3 = 4 × 3 + 9 × 3 and so on.
7. Distributive of property multiplication over subtraction:
(i) a × (b  c) = a × b  a × c
For example: 4 × (7  9) = 4 × 7  4 × 9 and so on.
(ii) (b  c) × a = b × a  c × a
For example: (2  8) × 6 = 2 × 6  8 × 6 and so on.
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