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:<math>S/a=\{s\in M\ \vert\ sa\in S\}</math>
Left quotients may be defined similarly, with operations taking place on the left of a string.{{cn|date=August 2017}}
Hopcroft and Ullman (1979) define the quotient ''L''<sub>1</sub>/''L''<sub>2</sub> of the languages ''L''<sub>1</sub> and ''L''<sub>2</sub> over the same alphabet is defined as ''L''<sub>1</sub>/''L''<sub>2</sub> = { ''s'' | ∃''t''∈''L''<sub>2</sub>. ''st''∈''L''<sub>1</sub> }.<ref>Hopcroft, Ullman (1979), Sect.3.2, p.62</ref>
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