In my opinion, it is an essential part of checking to make sure that the math operations you are performing make sense.

For speed and distance problems, it is easy to see that you must divide miles by hours to get miles/hour, or that miles divided by miles/hour gives hours.

For problems involving force, distance, work, energy, power, unit analysis can keep you performing the math operations correctly.

For rate problems (houses painted per hour) versus (hours per house painted) can keep you straight regarding the work done by multiple contributors.

Here is an example of a problem worked with units.

For speed and distance problems, it is easy to see that you must divide miles by hours to get miles/hour, or that miles divided by miles/hour gives hours.

For problems involving force, distance, work, energy, power, unit analysis can keep you performing the math operations correctly.

For rate problems (houses painted per hour) versus (hours per house painted) can keep you straight regarding the work done by multiple contributors.

Here is an example of a problem worked with units.