Here is the classic counterexample: Items: (weight= P0, value= P1), (weight= P2, value= P3), (weight= P4, value= P5). Capacity = . Ratios: , , . Greedy takes item (ratio P11), then item (ratio P13). Total weight: , total value: . Item does not fit (need P17 more, only P18 left).
But items + : weight = , value = . Much better! Greedy got , optimal is . That's why / knapsack needs DP. This example shows greedy's local choice blocks a better global solution.