1Cademy - Simplifying $$-8 \cdot 0$$, $$\frac{0}{-2}$$, and $$\frac{-32}{0}$$

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Simplifying $-8 \cdot 0$ , $\frac{0}{-2}$ , and $\frac{-32}{0}$

Apply the three properties of zero to simplify each expression:

ⓐ $-8 \cdot 0 = 0$ : By the multiplication-by-zero property, the product of any real number and $0$ is $0$ . It does not matter that the factor is negative — multiplying any quantity by zero always yields zero.

ⓑ $\frac{0}{-2} = 0$ : By the division-of-zero property, zero divided by any nonzero number equals zero. Since $-2 \neq 0$ , the quotient is simply $0$ .

ⓒ $\frac{-32}{0}$ is undefined: By the division-by-zero rule, dividing any nonzero number by $0$ has no defined value. No number multiplied by $0$ can produce $-32$ , so the expression cannot be evaluated.

These three parts illustrate the distinct roles zero plays in multiplication and division: as a factor it forces the product to zero, as a dividend it produces a zero quotient, and as a divisor it renders the expression meaningless.

Updated 2026-04-21

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OpenStax Elementary Algebra

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