Previous studies on mining association rules focus on discovering associations among items without considering the relationships between items and their purchased quantities. However, exploring associations among items associated with their purchased quantities may discover information useful to improve the quality of business decisions. In this paper, we investigate the issue of mining quantitative association rules in a large database of sales transactions. When purchased quantities are considered, the supports of items associated with their purchased quantities may decrease drastically, and the number of potentially interesting association rules discovered will be few. In order to discover more potentially interesting rules, we present two partition algorithms to partition all the possible quantities into intervals for each item. We also propose an efficient mechanism to discover all the large itemsets from the partitioned data. Experimental results show that by our approach, the total execution time can be reduced significantly. Moreover, the potentially interesting rule discovered from the partitioned data can be considered to be a kind of generalized association rule. The generalized association rule is useful in marketing, business management and decision making, especially when the information from the rules generated from the original data is limited.