# Properties of Multiplication of Integers – Chapter 1

**C****BSE CLASS 7 MATHEMATICS**

**INTEGERS – Chapter 1**

**Properties of Multiplication of Integers:**

**I. Closure under Multiplication:**

For all integers a and b, a x b is an integer.

Consider two integers (-20) and (-5).

Their product = (-20) x (-5) = 100, which is an integer.

This shows that the product of two integers is again an integer. So integers are closed under multiplication.

**II. Commutativity of Multiplication:**

For any two integers a and b, a x b = b x a.

Consider two integers 3 and (-4).

Then 3 x (-4) = -12 and (-4) x 3 = -12, both are equal.

This shows that multiplication is commutative for integers.

**III. Multiplication by zero.**

For any integer a, a x 0 = 0 x a = 0

Examples:

(-3) x 0 = 0

0 x (-4) = 0

This shows that the product of a negative integer and zero is zero.

**IV. Multiplicative Identity:**

For any integer a, a x 1 = 1 x a = a.

Examples:

(-3) x 1 = -3

1 x (-6) = -6

This shows that 1 is the multiplicative identity for integers.

**V. Associativity for Multiplication:**

For any three integers a, b and c,

(a x b) x c = a x (b x c).

Consider-3, -2 and 5.

Look at [(-3) x (-2)] x 5 and (-3) x [(-2) x5]

Case 1.

[(-3) x (-2)] x 5 = 6 x 5 = 30

Case 2.

(-3) x [(-2) x 5] = (-3) x (-10) = 30

So we get the same answer in both the cases.

So we can say that integers are associative for multiplication.

**VI. Distributive property:**

For any integers a, b and c

a x (b + c) = a x b + a x c

Consider the integers -2, 3 and 5.

Look at (-2) x (3 + 5) and (-2) x 3 + (-2) x 5.

Case 1

(-2) x (3+5) = (-2) x 8 = -16

Case2

(-2) x 3 + (-2) x 5 = (-6) + (-10) = -16.

So we get the same answer in both the cases.

So we can say that the distributivity of multiplication over addition is true for integers.