The frequency of a wave is tripled, while the wave speed is held constant. What happens to the wavelength?

Wherever there are waves,

(the frequency) times (the wavelength) = the wave's speed

This says that the product of multiplying the frequency by the wavelength is always the same number. So if one of them gets multiplied by something, the other one immediately gets divided by the same thing, in order to keep their product from changing.

If the frequency is tripled, the wavelength must be divided by 3.

The wavelength decreases