Online conversations have become more prevalent on public discussion platforms (e.g. Reddit). With growing controversial topics, it is desirable to summarize not only diverse arguments, but also their rationale and justification. Early studies on text summarization focus on capturing general salient information in source documents, overlooking the argumentative nature of online conversations. Recent research on conversation summarization although considers the argumentative relationship among sentences, fail to explicate deeper argument structure within sentences for summarization. In this paper, we propose a novel task of argument-aware quantitative summarization to reveal the claim-reason structure of arguments in conversations, with quantities measuring argument strength. We further propose ARQUSUMM, a novel framework to address the task. To reveal the underlying argument structure within sentences, ARQUSUMM leverages LLM few-shot learning grounded in the argumentation theory to identify propositions within sentences and their claim-reason relationships. For quantitative summarization, ARQUSUMM employs argument structure-aware clustering algorithms to aggregate arguments and quantify their support. Experiments show that ARQUSUMM outperforms existing conversation and quantitative summarization models and generate summaries representing argument structures that are more helpful to users, of high textual quality and quantification accuracy. Code and data are included in the Supplementary Material.