Sensory pathways process behaviorally relevant signals in various contexts and therefore have to adapt to differing background conditions. Depending on changes in signal statistics, this adjustment might be a combination of two fundamental computational operations: subtractive adaptation shifting a neuron's threshold and divisive gain control scaling its sensitivity. The cricket auditory system has to deal with highly stereotyped conspecific songs at low carrier frequencies, and likely much more variable predator signals at high frequencies. We proposed that due to the differences between the two signal classes, the operation that is implemented by adaptation depends on the carrier frequency. We aimed to identify the biophysical basis underlying the basic computational operations of subtraction and division. We performed in vivo intracellular and extracellular recordings in a first-order auditory interneuron (AN2) that is active in both mate recognition and predator avoidance. We demonstrated subtractive shifts at the carrier frequency of conspecific songs and division at the predator-like carrier frequency. Combined application of current injection and acoustic stimuli for each cell allowed us to demonstrate the subtractive effect of cell-intrinsic adaptation currents. Pharmacological manipulation enabled us to demonstrate that presynaptic inhibition is most likely the source of divisive gain control. We showed that adjustment to the sensory context can depend on the class of signals that are relevant to the animal. We further revealed that presynaptic inhibition is a simple mechanism for divisive operations. Unlike other proposed mechanisms, it is widely available in the sensory periphery of both vertebrates and invertebrates.