Zero Property of Multiplication

The Zero Multiplication Property states that when you multiply any number by zero, the result is always zero. In mathematical terms, for any number \(a\):

Why Is This True?

One way to understand this is by using the distributive property of multiplication over addition. Consider the following:

1. Start with the fact that \(0 = 0 + 0\).
2. Multiply both sides by \(a\): \[ a \times 0 = a \times (0 + 0). \]
3. Use the distributive property: \[ a \times (0 + 0) = a \times 0 + a \times 0. \]
4. So, we have: \[ a \times 0 = a \times 0 + a \times 0. \]
5. Subtract \(a \times 0\) from both sides: \[ a \times 0 - a \times 0 = a \times 0. \] Which simplifies to: \[ 0 = a \times 0 \]

Example

This property is fundamental in arithmetic and algebra, ensuring that any product involving zero is zero regardless of the other factor.

Latex

0 = a \times 0