Definition
Zero property of multiplication
The zero property of multiplication says any number multiplied by zero equals zero.
What it means
Multiplication makes equal groups. If there are zero objects in every group, there are no objects altogether. If there are zero groups, there are still no objects altogether. Either way, a zero factor makes the product zero.
Remember it
A zero factor empties the whole product: something times nothing is nothing.
Example
A shelf plan has 9 rows but 0 books in each row. The total is 9 × 0 = 0 books. Reversing the factors also gives 0 × 9 = 0.
Watch for
This rule is about multiplication, not division. Division by zero is not defined, so 9 ÷ 0 is not 0.
Common mix-up
Multiplying by 1 keeps a number unchanged; multiplying by 0 gives 0. Those are different properties.
Exact meaning
For every number a, a × 0 = 0 × a = 0. A product is zero whenever one of its factors is zero.