The simplified ratio of $10:15$ is $2:3$.

To simplify a ratio, you need to determine the greatest common divisor (GCD) of the two numbers involved. The GCD is defined as the largest number that can divide both numbers without leaving a remainder. For the ratio $10:15$, we begin by listing the factors of each number. The factors of $10$ are $1, 2, 5, \text{ and } 10$, while the factors of $15$ are $1, 3, 5, \text{ and } 15$. The largest common factor between the two sets is $5$.

Next, we divide both parts of the ratio by their GCD. Specifically, we divide $10$ by $5$, yielding $2$, and we divide $15$ by $5$, yielding $3$. Consequently, the ratio $10:15$ simplifies to $2:3$.

Simplifying ratios is a valuable skill in various areas of mathematics and everyday life. It aids in making comparisons clearer and more comprehensible. For example, whether you are comparing quantities, prices, or any other measurements, a simplified ratio offers a more straightforward perspective. Remember, the essential steps are to identify the GCD and then divide both components of the ratio by this number. This method ensures that the ratio is expressed in its simplest form, making it easier to work with and interpret.