The multiple extraction method is more effective in terms of yield.
When you extract, the residue will have the same concentration of material as the extract itself. If you extract again, the concentration will be lower, in the extract as well as in the residue.
So with multiple extractions the amount of material left in the residue will be lower, ergo the extraction will be more complete.
Several extractions with smaller volumes of solvent are more effective than a single extraction with a large volume of solvent.
The mass of solute
The formula becomes
(a) Single extraction
∴ 8.6 g extracted and 1.4 g remaining.
We have extracted 86 % of the compound.
(b) Three extractions
∴ 6.7 g extracted and 3.3 g remaining.
∴ 8.9 g extracted and 1.1 g remaining.
∴ 9.6 g extracted and 0.4 g remaining.
We have extracted 96 % of the compound.
Multiple extractions are more efficient than a single extraction with the same volume of solvent.