The question asks about what happens to the scale of a map when the denominator of the representative fraction (RF) increases.

The representative fraction (RF) is a method to express the scale of a map, usually in the format \(\frac{1}{D}\), where \(D\) is the denominator. It shows the ratio between the map distance and the ground distance. For instance, if a map has an RF of \(\frac{1}{50,000}\), it means 1 unit on the map equals 50,000 units on the ground.

Now, let's analyze the effect of increasing the denominator, \(D\):

1. An increase in the denominator means that the value of \(\frac{1}{D}\) becomes smaller. For example, if the RF changes from \(\frac{1}{50,000}\) to \(\frac{1}{100,000}\), the scale decreases because each unit on the map now represents a larger ground area.
2. This indicates a decrease in the scale, which means the map is showing a larger area with less detail.

Therefore, with an increase in the denominator of the representative fraction, the scale of the map will decrease.

Hence, the correct answer is: decrease.