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:-
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 :-
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.