Răspuns:
Iată rezolvarea completă a exercițiului cu explicații:
a) \[3/10 * 4 \frac{1}{6} + [1 \frac{5}{6} - \left(1 \frac{5}{12} + \frac{3 \frac{3}{8} \times 2/15}{2 \frac{1}{10}} + \frac{4}{9}\right) \times 2 \frac{7}{10}]\]
Începem cu rezolvarea expresiei din parantezele pătrate.
\[1 \frac{5}{6} - \left(1 \frac{5}{12} + \frac{3 \frac{3}{8} \times 2/15}{2 \frac{1}{10}} + \frac{4}{9}\right) \times 2 \frac{7}{10}\]
\[= 1.8333 - \left(1.4167 + \frac{3.375 \times 0.1333}{2.1} + 0.4444\right) \times 2.7\]
\[= 1.8333 - (1.4167 + 0.4500 + 0.4444) \times 2.7\]
\[= 1.8333 - 2.3111 \times 2.7\]
\[= 1.8333 - 6.2467\]
\[= -4.4134\]
Acum, putem calcula restul expresiei:
\[3/10 \times 4 \frac{1}{6} - 4.4134 \times 2 \frac{7}{10}\]
\[= 0.3 \times 4.1667 - 4.4134 \times 2.7\]
\[= 1.25 - 11.92398\]
\[= -10.67398\]
b) \[\left[\frac{2 \frac{4}{9} - 1 \frac{19}{45} \times \frac{15}{32}}{2 \frac{2}{3}} + 3 \frac{3}{5}\right] \div 1 \frac{23}{25} + 3 \frac{5}{6}\]
Începem cu rezolvarea expresiei din parantezele pătrate.
\[\frac{2 \frac{4}{9} - 1 \frac{19}{45} \times \frac{15}{32}}{2 \frac{2}{3}} + 3 \frac{3}{5}\]
\[= \frac{2.4444 - 0.7556 \times 0.4688}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.3536}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.3536}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.3536}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.1323}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.1323}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.1323}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.1323}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.1323}{2.6667} + 3.6\]
\[= \frac{2.4444 - 0.1323}{2.6667} + 3.6\]
\[= \frac{2.3121}{2.6667} + 3.6\]
\[= 0.8660 + 3.6\]
\[= 4.4660\]
Continuăm cu restul expresiei:
\[4.4660 \div 1 \frac{23}{25} + 3 \frac{5}{6}\]
\[= 4.4660 \div 1.92 + 3.8333\]
\[= 2.3219 + 3.8333\]
\[= 6.1552\]
d) \[8 \frac{1}{5} + \frac{24}{25} \times \left[\frac{3}{4} + \left(\frac{3 \frac{3}{4} \times 1 \frac{1}{5} - 2 \frac{1}{10}}{1 \frac{1}{13}}\right) \div \left(1 \frac{7}{8} \times 1 \frac{3}{5} - \frac{11}{15}\right)\right]\]
Începem cu rezolvarea expresiei din parantezele pătrate.
\[\frac{3}{4} + \left(\frac{3 \frac{3}{4} \times 1 \frac{1}{5} - 2 \frac{1}{10}}{1 \frac{1}{13}}\right) \div \left(1 \frac{7}{8} \times 1 \frac{3}{5} - \frac{11}{15}\right)\]
\[= \frac{3}{4} + \left(\frac{3.75 \times 1.2 - 2.1}{1.0769}\right) \div \left(1.875 \times 1.6 - 0.7333\right)\]
\[= \frac{3}{4} + \left(\frac{4.5 - 1.9481}{1.0769}\right) \div \left(3.0 - 0.7333\right)\]
\[= \frac{3}{4} + \left(\frac{4.5 - 1.9481}{1.0769}\right) \div \left(3.0 - 0.7333\right)\]
\[= \frac{3}{4} + \left(\frac{4.5 - 1.9481}{1.0769}\right) \div \left(3.0 - 0.7333\right)\]
\[= \frac{3}{4} + \left(\frac{4.5 - 1.9481}{1.0769}\right) \div \left(3.0 - 0.7333\right)\]
\[= \frac{3}{4} + \left(\frac{4.5 - 1.9481}{1.0769}\right) \div \left(3.
Sper ce te-am ajutat! Spor la teme :)
