With each quiet inspired breath, the fraction of alveolar air getting replaced would be:

At the end of a quiet expiration, the volume of air remaining in the lung is functional residual capacity (FRC). The volume of FRC = 2300 mL. This is the existing alveolar air. With next quiet breath, about 500 mL (TV) is inspired. Of this, 150 mL stays in the dead space and 350 mL air will reach alveoli. This 350 mL air (with oxygen) will replace 350 mL alveolar air (containing CO2) to be mixed with dead space air and exhaled out. Out of 2300 mL of existing alveolar air, 350 mL air is getting replaced. 350/2300 = (approx.) 1/7th fraction.