A farmer harvested 3 (1)/(2) bags of maize in one season and 2 (3)/(4) bags in another season. How many bags of maize did the farmer harvest altogether?

The farmer harvested $3\frac{1}{2}$ bags in one season and $2\frac{3}{4}$ bags in another season.

To add fractions, they must have a common denominator. The least common multiple of 2 and 4 is 4.
Convert $\frac{7}{2}$ to an equivalent fraction with a denominator of 4:

Now, add the fractions:

Divide 25 by 4:

So, $\frac{25}{4}$ can be written as $6\frac{1}{4}$.

The farmer harvested $6\frac{1}{4}$ bags of maize altogether.

The total number of bags harvested altogether is $6\frac{1}{4} \text{ bags}$.