Tính hợp lí (nếu có thể): f) ( − 2 /3 + 3 /7 ) : 4/ 5 + ( − 1/ 3 + 4 /7 ) : 4 /5 ;
Giải thích
f) \(\left( { - \frac{2}{3} + \frac{3}{7}} \right):\frac{4}{5} + \left( { - \frac{1}{3} + \frac{4}{7}} \right):\frac{4}{5}\)
\( = \left( { - \frac{2}{3} + \frac{3}{7}} \right) \cdot \frac{5}{4} + \left( { - \frac{1}{3} + \frac{4}{7}} \right) \cdot \frac{5}{4}\)
\( = \frac{5}{4} \cdot \left( { - \frac{2}{3} + \frac{3}{7} - \frac{1}{3} + \frac{4}{7}} \right)\)
\( = \frac{5}{4} \cdot \left[ {\left( {\frac{{ - 2}}{3} + \frac{{ - 1}}{3}} \right) + \left( {\frac{3}{7} + \frac{4}{7}} \right)} \right]\)
\( = \frac{5}{4} \cdot \left[ {\frac{{ - 3}}{3} + \frac{7}{7}} \right] = \frac{5}{4} \cdot \left[ { - 1 + 1} \right] = 0\).