The purpose of this research was to investigate eighth-grade students' construction of linear equations (of the form ax = b, where a, b are fractional numbers) by using their fractional multiplying schemes and the contribution of these schemes to the construction of inverse reasoning. One pair of eighth grade students participated in a 3-month teaching experiment that consisted of 18 teaching episodes. In the episodes, students engaged in solving tasks that involved quantitative relations between known and unknown quantities. When solving the tasks, the students used a computer tool called JavaBars as well as paper and pencil. The retrospective analysis of the study suggested that the students' construction of fraction multiplying schemes involved coordinating two three-levels-of-units structures and reinterpreting quantities in terms of standard measurement units. The results also suggested that the students' construction of relations between two quantities was based on the operations of their fraction multiplying schemes (distributive partitioning and recursive distributive partitioning operations) as well as their production of a measurement of an unknown quantity.