Arumugam and Mathew [Discret. Math. 2012, 312, 1584–1590] introduced the notion of fractional metric dimension of a connected graph. In this paper, a combinatorial technique is devised to compute it. In addition, using this technique the fractional metric dimension of the generalized Jahangir graph J m , k is computed for k ≥ 0 and m = 5 .