Example

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

Consider the true mathematical statement 10<1510 < 15. If we multiply both sides by the positive number 55, we get 10β‹…5<15β‹…510 \cdot 5 < 15 \cdot 5, which simplifies to 50<7550 < 75. This remains a true statement. Similarly, if we divide both sides by the positive number 55, we get 105<155\frac{10}{5} < \frac{15}{5}, which simplifies to 2<32 < 3, also a true statement. These numerical examples verify that when both sides of an inequality are multiplied or divided by a positive number, the direction of the inequality sign stays exactly the same.

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Updated 2026-04-22

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