1. Вычислите: a) $$\frac{1,2^2}{3,6}$$; б) $$\left(\frac{2,1}{0,63}\right)^3$$; в) $$\frac{5,85 \cdot 1,43}{1,69 \cdot 1,1}$$; г) $$8,96 : \frac{32}{375} : \frac{560}{93} - 1,5$$.

Решение:

a) $$\frac{1,2^2}{3,6} = \frac{1,2 \cdot 1,2}{3,6} = \frac{1,44}{3,6} = \frac{144}{360} = \frac{2}{5} = 0,4$$

б) $$\left(\frac{2,1}{0,63}\right)^3 = \left(\frac{210}{63}\right)^3 = \left(\frac{10}{3}\right)^3 = \frac{1000}{27} = 37,(037) \approx 37,04$$

в) $$\frac{5,85 \cdot 1,43}{1,69 \cdot 1,1} = \frac{5,85 \cdot 1,43}{1,69 \cdot 1,1} = \frac{585 \cdot 143}{169 \cdot 110} = \frac{585 \cdot 13}{169 \cdot 10} = \frac{45 \cdot 13}{13 \cdot 10} = \frac{45}{10} = 4,5$$

г) $$8,96 : \frac{32}{375} : \frac{560}{93} - 1,5 = 8,96 \cdot \frac{375}{32} \cdot \frac{93}{560} - 1,5 = \frac{896}{100} \cdot \frac{375}{32} \cdot \frac{93}{560} - 1,5 = $$ $$= \frac{28 \cdot 375 \cdot 93}{100 \cdot 560} - 1,5 = \frac{28 \cdot 15 \cdot 93}{4 \cdot 560} - 1,5 = \frac{7 \cdot 15 \cdot 93}{560} - 1,5 = \frac{7 \cdot 3 \cdot 93}{112} - 1,5 = \frac{3 \cdot 93}{16} - 1,5 = \frac{279}{16} - \frac{24}{16} = \frac{255}{16} = 15,9375 \approx 15,94$$

Ответ: a) $$0,4$$, б) $$37,04$$, в) $$4,5$$, г) $$15,94$$