# CLASS-7MULTIPLICATIVE PROPERTY OF ZERO

MULTIPLICATIVE PROPERTY OF ZERO -

The multiplicative property of zero states that any number multiplied by zero is zero. This property is fundamental in arithmetic and algebra.Definition

For any number a:-

a x 0 = 0

0 x a = 0

Explanation:-

• When you multiply any number by zero, the result is always zero. This holds true for all types of numbers, including whole numbers, integers, fractions (rational numbers), real numbers, and complex numbers.

Proof:-

To understand why this property holds, consider the distributive property of multiplication over addition:

a x (0 + 0) = a x 0 + a x 0

Since 0 + 0 = 0, we have:-

a x 0 = a x 0 + a x 0

To isolate a x 0, we subtract a x 0 from both sides of the equation:-

a x 0 − a x 0 = a x 0 + a x 0 − a x 0

0 = a x 0

Thus, any number multiplied by zero is zero, proving the multiplicative property of zero.

Examples with Different Types of Numbers :-

1. Whole Number:-

Let, a = 8

So,  a x 0 = 8 x 0 = 0

0 x a = 0 x 8 = 0

2. Integers:-

Let, a = - 5

So, a x 0 = (- 5) x 0 = 0

0 x a = 0 x (- 5) = 0

3. Rational Number:-

Let, a = 4/7

So, a x 0 = (4/7) x 0 = 0

0 x a = 0 x (4/7) = 0

4. Real Number:-

Let, a = π

So, a x 0 =  π x 0 = 0

0 x a = 0 x π = 0

5. Complex Number:-

Let, a = (4 + 5i)

So, a x 0 = (4 + 5i) x 0 = 0

0 x a = 0 x (4 + 5i) = 0

6. Decimal Number:-

Let, a = 0.45

So, a x 0 = 0.45 x 0 = 0

0 x a = 0 x 0.45 = 0

7. Negative Number:-

Let, a = - 9

So, a x 0 = (- 9) x 0 = 0

0 x a = 0 x (- 9) = 0

8. Variable:-

Let, a = Y

So, a x 0 = Y x 0 = 0

0 x a = 0 x Y = 0

In each case, multiplying any number by zero results in zero, demonstrating the multiplicative property of zero.