Esercizio 8 – Espressione con i numeri razionali

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Esercizio.  (\bigstar\largewhitestar\largewhitestar) Semplificare la seguente espressione

    \[-2+\dfrac{1}{2}-\left(\dfrac{3}{2}\right)^2-\dfrac{1}{12}+\left[\left(\dfrac{2}{3}:\dfrac{4}{15}\right)^3: \dfrac{75}{28}\right]\]

 

Soluzione

Procediamo come segue

    \[\begin{aligned}			-2+\dfrac{1}{2}-\left(\dfrac{3}{2}\right)^2-\dfrac{1}{12}+\left[\left(\dfrac{2}{3}:\dfrac{4}{15}\right)^3: \dfrac{75}{28}\right] & = 		-2+\dfrac{1}{2}-\dfrac{9}{4}-\dfrac{1}{12}+\left[\left(\dfrac{2}{3}\cdot\dfrac{15}{4}\right)^3 \cdot  \dfrac{28}{75}\right]=\\\\ & = -2+\dfrac{1}{2}-\dfrac{9}{4}-\dfrac{1}{12} + \left[\left(\dfrac{\cancel{2}^{\;1}}{\cancel{3}_{\;1}}\cdot\dfrac{\cancel{15}^{\;5}}{\cancel{4}_{\;2}}\right)^3 \cdot  \dfrac{28}{75}\right]=\\\\ & = \dfrac{-24+6-27-1}{12}+ \left[\left(\dfrac{5}{2}\right)^3 \cdot  \dfrac{28}{75}\right]=\\\\ & = -\dfrac{\cancel{46}^{\;23}}{\cancel{12}_{\;6}}+ \left[\dfrac{\cancel{125}^{\;5}}{\cancel{8}_{\;2}}\cdot  \dfrac{\cancel{28}^{\;7}}{\cancel{75}_{\;3}}\right]=\\\\ & = -\dfrac{23}{6}+ \dfrac{35}{6} = \dfrac{12}{6} = 2 \end{aligned}\]


Fonte: Algebra Blu con Statistica – Volume 1