Formula

Division of Zero

The division of zero property states that zero divided by any nonzero real number equals zero. For any real number aa with a0a \neq 0:

0a=0and0÷a=0\frac{0}{a} = 0 \quad \text{and} \quad 0 \div a = 0

Intuitively, if there is nothing to share among any number of people, each person receives nothing. For example, 0÷3=00 \div 3 = 0 because sharing zero cookies among three people gives each person zero cookies. This result can be verified using the related multiplication fact: 0÷3=00 \div 3 = 0 is correct because 03=00 \cdot 3 = 0. The restriction a0a \neq 0 is critical — the case where the divisor is also zero falls under the separate rule that division by zero is undefined.

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Updated 2026-05-03

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