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(-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4)=

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(-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4) = (1*-2/(5*2/3))*(-5/6)÷(3/4)
= (-2/10)/(2/3)*(-5/6)÷(3/4) = -1/5*3/2*-5/6÷(3/4)
= -1/5*-5/4*4/3 = (-1*-5*-4)/(5*4*3) = -20/60 = -1/3

Therefore, (-2) ×(1/5)÷(2/3)×(-5/6)÷(3/4) = -1/3.