Our brain does not process all arriving information equally. Rather our current brain state influences how we interact with the world. Ongoing neural activity can be measured using electroencephalography (EEG) to track fluctuations (oscillations) in brain states. Specifically, the amplitude of alpha oscillations in the milliseconds preceding stimulus presentation (pre-stimulus alpha) can provide a marker of cortical excitability. Pre-stimulus alpha amplitude has been shown to predict trial-by-trial performance on visual discrimination tasks, and to predict working memory performance, through modulating the quality of simple stimulus encoding. In this study, we investigated whether alpha amplitude is related to event-related potential (ERP) measures of a) the sensory representation of the fraction stimuli, as indexed by N1 amplitude or b) the subsequent cognitive processes involving the extraction of the magnitude representation of fractions as indexed by P3 amplitude. Participants completed a fraction reasoning task while EEG data were collected. Participants were presented with two fractions, separated by a brief delay, and asked to indicate which of the two fractions represented the greater proportion. Fractions were represented either symbolically (standard fraction notation) or non-symbolically (dot clouds). Behavioural and ERP results demonstrated a fractional distance effect in each condition, whereby the closer the numerical distance between two fractions, the longer participants took to make the proportion judgment, and the smaller P3 amplitudes were. Pre-stimulus alpha predicted overall task performance; lower alpha amplitude preceded correct verses incorrect responses. Additionally, individual differences in pre-stimulus alpha influenced post-stimulus behaviour, as indicated by a significant correlation with reaction time. Relationships were observed between pre-stimulus alpha and N1 for the non-symbolic task, but not P3 amplitude, suggesting that pre-stimulus alpha was related to stimulus encoding.