Esercizio 4 – Espressione con i numeri razionali

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

    \[\dfrac{\dfrac{3}{7}\cdot \left(	-\dfrac{4}{5}+\dfrac{1}{2}\right)}{\dfrac{1}{14}-\left(\dfrac{2}{7}-\dfrac{1}{4}\right)} \cdot \left(\dfrac{5}{9}-1\right)\]

 

Soluzione

Procediamo come segue

    \[\begin{aligned} 	\dfrac{\dfrac{3}{7}\cdot \left(	-\dfrac{4}{5}+\dfrac{1}{2}\right)}{\dfrac{1}{14}-\left(\dfrac{2}{7}-\dfrac{1}{4}\right)} \cdot \left(\dfrac{5}{9}-1\right) & = \dfrac{\dfrac{3}{7}\cdot \left(	\dfrac{-8+5}{10} \right)}{\dfrac{1}{14}-\left(\dfrac{8 - 7}{28}\right)} \cdot \left(\dfrac{5-9}{9}\right) = \dfrac{\dfrac{3}{7}\cdot \left(	\dfrac{-8+5}{10} \right)}{\dfrac{1}{14}-\left(\dfrac{8 - 7}{28}\right)} \cdot \left(\dfrac{5-9}{9}\right) = \\\\ 	& = \dfrac{\dfrac{3}{7}\cdot \left(	- \dfrac{3}{10} \right)}{\dfrac{1}{14}-\dfrac{1}{28}} \cdot \left(\dfrac{-4}{9}\right) = \dfrac{- \dfrac{9}{70} }{\dfrac{2-1}{28}} \cdot \left(-\dfrac{4}{9}\right) =  \dfrac{- \dfrac{9}{70} }{\dfrac{1}{28}} \cdot \left(-\dfrac{4}{9}\right) = \\\\ 	& = - \dfrac{\cancel{9}}{\cancel{70}_{\; \cancel{10}_{\;5}}} \cdot \cancel{28}^{\; 4} \cdot \left(-\dfrac{\cancel{4}^{\;2}}{\cancel{9}}\right) = \dfrac{8}{5} \end{aligned}\]


Fonte: Algebra Blu con Statistica – Volume 1