Simplify the expression: (−14)+(512)\left(-\dfrac{1}{4}\right) + \left(\dfrac{5}{12}\right)(−41)+(125).
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Given, (−14)+(512)\left(-\dfrac{1}{4}\right) + \left(\dfrac{5}{12}\right)(−41)+(125)
L.C.M. of 4 and 12 = 12.
⇒−14+512⇒−1×34×3+512⇒−312+512⇒−3+512⇒212⇒16.\Rightarrow -\dfrac{1}{4} + \dfrac{5}{12} \\[1em] \Rightarrow -\dfrac{1 \times 3}{4 \times 3} + \dfrac{5}{12} \\[1em] \Rightarrow -\dfrac{3}{12} + \dfrac{5}{12} \\[1em] \Rightarrow \dfrac{-3 + 5}{12} \\[1em] \Rightarrow \dfrac{2}{12} \\[1em] \Rightarrow \dfrac{1}{6}.⇒−41+125⇒−4×31×3+125⇒−123+125⇒12−3+5⇒122⇒61.
Hence, (−14)+(512)=16\left(-\dfrac{1}{4}\right) + \left(\dfrac{5}{12}\right) = \dfrac{1}{6}(−41)+(125)=61.
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