The simplified ratio of $40$ to $60$ is $2:3$.

To simplify a ratio, you first need to determine the greatest common divisor (GCD) of the two numbers. The GCD is the largest number that divides both numbers evenly, without leaving a remainder. In the case of $40$ and $60$, the GCD is $20$.

To simplify the ratio, divide both numbers by their GCD. Thus, $40$ divided by $20$ equals $2$, and $60$ divided by $20$ equals $3$. Therefore, the ratio $40:60$ can be simplified to $2:3$.

Ratios serve as a means to compare quantities and are commonly used in various real-life situations, such as in recipes, maps, and scales. Simplifying ratios makes them more comprehensible and easier to work with.

Keep in mind that the process involves identifying the GCD and then dividing both components of the ratio by this number. Practicing this method with different sets of numbers will enhance your comfort and proficiency in simplifying ratios.