Question

ajutor vă rog frumos

Answer 1

$a)[( \frac{24}{35} + \frac{7}{5}) + 1 \frac{3}{7}] + 2 \frac{4}{5} = \\ \\ \frac{24}{35} + \frac{7}{5} = \frac{24}{35} + \frac{7 \times 7}{5 \times 7} = \frac{24}{35} + \frac{49}{35} = \frac{24 + 49}{35} = \frac{73}{35} \\ \\ 1 \frac{3}{7} = \frac{1 \times 7 + 3}{7} = \frac{10}{7} \\ \\ \frac{73}{35} + \frac{10}{7} = \frac{73}{35} + \frac{10 \times 5}{7 \times 5} = \frac{73}{35} + \frac{50}{35} = \frac{73 + 50}{35} = \frac{123}{35} \\ \\ 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5} \\ \\ \frac{123}{35} + \frac{14}{5} = \frac{123}{35} + \frac{14 \times 7}{5 \times 7} = \frac{123}{35} + \frac{98}{35} = \frac{123 + 98}{35} = \frac{221}{35} = 6 \frac{11}{35}$

$b)[(1 \frac{7}{12} + \frac{25}{18}) + 3 \frac{5}{6}] + 1 \frac{4}{24} = \\ \\ 1 \frac{7}{12} = \frac{1 \times 12 + 7}{12} = \frac{19}{12} \\ \\ \frac{19}{12} + \frac{25}{18} = \frac{19 \times 3}{12 \times 3} + \frac{25 \times 2}{18 \times 2} = \frac{57}{36} + \frac{50}{36} = \frac{57 + 50}{36} = \frac{107}{36} \\ \\ 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{23}{6} \\ \\ \frac{107}{36} + \frac{23}{6} = \frac{107}{36} + \frac{23 \times 6}{6 \times 6} = \frac{107}{36} + \frac{138}{36} = \frac{107 + 138}{36} = \frac{245}{36} \\ \\ 1 \frac{4}{24} = \frac{1 \times 24 + 4}{24} = \frac{28}{24} \\ \\ \frac{245}{36} + \frac{28}{24} = \frac{245 \times 2}{36 \times 2} + \frac{28 \times 3}{24 \times 3} = \frac{490}{72} + \frac{84}{72} = \frac{490 + 84}{72} = { \frac{572}{72} }^{(2} = \frac{287}{36} = 7 \frac{35}{36}$

$c)[(2 \frac{5}{21} + (3 \frac{3}{7} + \frac{17}{21})] + 4 \frac{1}{3} = \\ \\ 3 \frac{3}{7} = \frac{3 \times 7 + 3}{7} = \frac{24}{7} \\ \\ \frac{24}{7} + \frac{17}{21} = \frac{24 \times 3}{7 \times 3} + \frac{17}{21} = \frac{72}{21} + \frac{17}{21} = \frac{72 + 17}{21} = \frac{89}{21} \\ \\ 2 \frac{5}{21} = \frac{2 \times 21 + 5}{21} = \frac{47}{21} \\ \\ \frac{47}{21} + \frac{89}{21} = \frac{47 + 89}{21} = \frac{136}{21} \\ \\ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{13}{3} \\ \\ \frac{136}{21} + \frac{13}{3} = \frac{136}{21} + \frac{13 \times 7}{3 \times 7} = \frac{136}{21} + \frac{91}{21} = \frac{136 + 91}{21} = \frac{227}{21} = 10 \frac{17}{21}$

$d)[(1 \frac{7}{9} + \frac{3}{4}) + 1 \frac{15}{12}] + 1 \frac{3}{4} = \\ \\ 1 \frac{7}{9} = \frac{1 \times 9 + 7}{9} = \frac{16}{9} \\ \\ \frac{16}{9} + \frac{3}{4} = \frac{16 \times 4}{9 \times 4} + \frac{3 \times 9}{4 \times 9} = \frac{64}{36} + \frac{27}{36} = \frac{64 + 27}{36} = \frac{91}{36} \\ \\ 1 \frac{15}{12} = \frac{1 \times 12 + 15}{12} = \frac{27}{12} \\ \\ \frac{91}{36} + \frac{27}{12} = \frac{91}{36} + \frac{27 \times 3}{12 \times 3} = \frac{91}{36} + \frac{81}{36} = \frac{91 + 81}{36} = { \frac{172}{36} }^{(4} = \frac{43}{9} \\ \\ 1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4} \\ \\ \frac{43}{9} + \frac{7}{4} = \frac{43 \times 4}{9 \times 4} + \frac{7 \times 9}{4 \times 9} = \frac{172}{36} + \frac{63}{36} = \frac{172 + 63}{36} = \frac{235}{36} = 6 \frac{19}{36}$