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):

$$a \times 0 = 0 \quad \text{and} \quad 0 \times a = 0.$$

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

If you multiply 7 by 0, you get:

$$7 \times 0 = 0.$$

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