Let the capacity of the bucket be x litres. Then,
Capacity of 1 large bottle = \(\frac{x}4\)
Capacity of 1 small bottle = \(\frac{x}7\)
Fluid left in large bottle = \(\frac{x}4\) - \(\frac{x}7\) = \(\frac{3x}{28}\)
∴ Required fraction = \(\frac{\frac{3x}{28}}{\frac{x}4} = \) \(\frac{3x}{28}\) x \(\frac4x\) = \(\frac37.\)