1Cademy - Example: Demonstrating the Multiplication and Division Properties of Inequality with a Negative Number

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Multiplication Property of Inequality

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Example: Demonstrating the Multiplication and Division Properties of Inequality with a Negative Number

Consider the true mathematical statement $10 < 15$ . If we multiply both sides by the negative number $-5$ , we get $10(-5)$ and $15(-5)$ , which evaluate respectively to $-50$ and $-75$ . Because $-50$ is greater than $-75$ , the inequality symbol must reverse its direction, resulting in the true mathematical statement $-50 > -75$ . Similarly, dividing both sides by $-5$ yields $\frac{10}{-5}$ and $\frac{15}{-5}$ , which evaluate to $-2$ and $-3$ . Because $-2$ is greater than $-3$ , the symbol again reverses to give $-2 > -3$ . These numerical examples verify that multiplying or dividing an inequality by a negative number requires reversing the inequality sign to properly maintain a true mathematical statement.

Updated 2026-06-03

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OpenStax Intermediate Algebra

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