Sensory systems are often tasked to analyse complex signals from the environment, to separate relevant from irrelevant parts. This process of decomposing signals is challenging when component signals interfere with each other. For example, when a mixture of signals does not equal the sum of its parts, this leads to an unpredictable corruption of signal patterns, making the target recognition harder. In olfaction, nonlinear summation is prevalent at various stages of sensory processing, from stimulus transduction in the nasal epithelium to higher areas, including the olfactory bulb (OB) and the piriform cortex. Here, we investigate how the olfactory system deals with binary mixtures of odours, using two-photon imaging with several behavioural paradigms. Unlike previous studies using anaesthetised animals, we found the mixture summation to be substantially more linear when using awake, head-fixed mice performing an odour detection task. This linearisation was also observed in awake, untrained mice, in both engaged and disengaged states, revealing that the bulk of the difference in mixture summation is explained by the brain state. However, in the apical dendrites of M/T cells, mixture representation is dominated by sublinear summation. Altogether, our results demonstrate that the property of mixture representation in the primary olfactory area likely reflects state-dependent differences in sensory processing.