Question

ajutor vă rog frumos

Answer 1

$a) \\ \\ ( \frac{1}{10} + \frac{4}{15}) + ( \frac{7}{30} + \frac{1}{12}) = \\ \\ \frac{1}{10} + \frac{4}{15} = \frac{1 \times 3}{10 \times 3} + \frac{4 \times 2}{15 \times 2} = \frac{3}{30} + \frac{8}{30} = \frac{3 + 8}{30} = \frac{11}{30} \\ \\ \frac{7}{30} + \frac{1}{12} = \frac{7 \times 2}{30 \times 2} + \frac{1 \times 5}{12 \times 5} = \frac{14}{60} + \frac{5}{60} = \frac{14 + 5}{60} = \frac{19}{60} \\ \\ \frac{11}{30} + \frac{19}{60} = \frac{11 \times 2}{30 \times 2} + \frac{19}{60} = \frac{22}{60} + \frac{19}{60} = \frac{22 + 19}{60} = \frac{41}{60}$

$b) \\ \\ ( \frac{1}{24} + \frac{3}{36}) + ( \frac{7}{12} + \frac{1}{18}) = \\ \\ \frac{1}{24} + \frac{3}{36} = \frac{1 \times 3}{24 \times 3} + \frac{3 \times 2}{36 \times 2} = \frac{3}{72} + \frac{6}{72} = \frac{3 + 6}{72} = { \frac{9}{72} }^{(9} = \frac{1}{8} \\ \\ \frac{7}{12} + \frac{1}{18} = \frac{7 \times 3}{12 \times 3} + \frac{1 \times 2}{18 \times 2} = \frac{21}{36} + \frac{2}{36} = \frac{21 + 2}{36} = \frac{23}{36} \\ \\ \frac{1}{8} + \frac{23}{36} = \frac{1 \times 9}{8 \times 9} + \frac{23 \times 2}{36 \times 2} = \frac{9}{72} + \frac{46}{72} = \frac{9 + 46}{72} = \frac{55}{72}$

$c) \\ \\ ( \frac{3}{28} + \frac{7}{42}) + ( \frac{5}{14} + \frac{4}{21}) = \\ \\ \frac{3}{28} + \frac{7}{42} = \frac{3 \times 3}{28 \times 3} + \frac{7 \times 2}{42 \times 2} = \frac{9}{84} + \frac{14}{84} = \frac{9 + 14}{84} = \frac{23}{84} \\ \\ \frac{5}{14} + \frac{4}{21} = \frac{5 \times 3}{14 \times 3} + \frac{4 \times 2}{21 \times 2} = \frac{15}{42} + \frac{8}{42} = \frac{15 + 8}{42} = \frac{23}{42} \\ \\ \frac{23}{84} + \frac{23}{42} = \frac{23}{84} + \frac{23 \times 2}{42 \times 2} = \frac{23}{84} + \frac{46}{84} = \frac{23 + 46}{84} = { \frac{69}{84} }^{(3} = \frac{23}{28}$

$d) \\ \\ ( \frac{5}{42} + \frac{3}{56}) + ( \frac{1}{63} + \frac{7}{84}) = \\ \\ \frac{5}{42} + \frac{3}{56} = \frac{5 \times 4}{42 \times 4} + \frac{3 \times 3}{56 \times 3} = \frac{20}{168} + \frac{9}{168} = \frac{20 + 9}{168} = \frac{29}{168} \\ \\ \frac{1}{63} + \frac{7}{84} = \frac{1 \times 4}{63 \times 4} + \frac{7 \times 3}{84 \times 3} = \frac{4}{252} + \frac{21}{252} = \frac{4 + 21}{252} = \frac{25}{252} \\ \\ \frac{29}{168} + \frac{25}{252} = \frac{29 \times 3}{168 \times 3} + \frac{25 \times 2}{252 \times 2} = \frac{87}{504} + \frac{50}{104} = \frac{87 + 50}{104} = \frac{137}{504}$

$e) \\ \\ ( \frac{3}{2} + \frac{5}{24}) + ( \frac{13}{8} + \frac{1}{16}) = \\ \\ \frac{3}{2} + \frac{5}{24} = \frac{3 \times 12}{2 \times 12} + \frac{5}{24} = \frac{36}{24} + \frac{5}{24} = \frac{36 + 5}{24} = \frac{41}{24} \\ \\ \frac{13}{8} + \frac{1}{16} = \frac{13 \times 2}{8 \times 2} + \frac{1}{16} = \frac{26}{16} + \frac{1}{16} = \frac{26 + 1}{16} = \frac{27}{16} \\ \\ \frac{41}{24} + \frac{27}{16} = \frac{41 \times 2}{24 \times 2} + \frac{27 \times 3}{16 \times 3} = \frac{82}{48} + \frac{81}{48} = \frac{82 + 81}{48} = \frac{163}{48} = 3 \frac{19}{48}$

$f) \\ \\ ( \frac{5}{36} + \frac{1}{18}) + ( \frac{5}{24} + \frac{10}{48}) = \\ \\ \frac{5}{36} + \frac{1}{18} = \frac{5}{36} + \frac{1 \times 2}{18 \times 2} = \frac{5}{36} + \frac{2}{36} = \frac{5 + 2}{36} = \frac{7}{36} \\ \\ \frac{5}{24} + \frac{10}{48} = \frac{5 \times 2}{24 \times 2} + \frac{10}{48} = \frac{10}{48} + \frac{10}{48} = \frac{10 + 10}{48} = { \frac{20}{48} }^{(4} = \frac{5}{12} \\ \\ \frac{7}{36} + \frac{5}{12} = \frac{7}{36} + \frac{5 \times 3}{12 \times 3} = \frac{7}{36} + \frac{15}{36} = \frac{7 + 15}{36} = { \frac{22}{36} }^{(2} = \frac{11}{18}$

$g) \\ \\ ( \frac{11}{21} + \frac{3}{7}) + ( \frac{9}{42} + \frac{2}{14}) = \\ \\ \frac{11}{21} + \frac{3}{7} = \frac{11}{21} + \frac{3 \times 3}{7 \times 3} = \frac{11}{21} + \frac{9}{21} = \frac{11 + 9}{21} = \frac{20}{21} \\ \\ \frac{9}{42} + \frac{2}{14} = \frac{9}{42} + \frac{2 \times 3}{14 \times 3} = \frac{9}{42} + \frac{6}{42} = \frac{9 + 6}{42} = { \frac{15}{42} }^{(3} = \frac{5}{14} \\ \\ \frac{20}{21} + \frac{5}{14} = \frac{20 \times 2}{21 \times 2} + \frac{5 \times 3}{14 \times 3} = \frac{40}{42} + \frac{15}{42} = \frac{40 + 15}{42} = \frac{55}{42} = 1 \frac{13}{42}$

$h) \\ \\ ( \frac{7}{18} + \frac{3}{4}) + ( \frac{16}{9} + \frac{1}{6}) = \\ \\ \frac{7}{18} + \frac{3}{4} = \frac{7 \times 2}{18 \times 2} + \frac{3 \times 9}{4 \times 9} = \frac{14}{36} + \frac{27}{36} = \frac{14 + 27}{36} = \frac{41}{36} \\ \\ \frac{16}{9} + \frac{1}{6} = \frac{16 \times 2}{9 \times 2} + \frac{1 \times 3}{6 \times 3} = \frac{32}{18} + \frac{3}{18} = \frac{32 + 3}{18} = \frac{35}{18} \\ \\ \frac{41}{36} + \frac{35}{18} = \frac{41}{36} + \frac{35 \times 2}{18 \times 2} = \frac{41}{36} + \frac{70}{36} = \frac{41 + 70}{36} = { \frac{111}{36} }^{(3} = \frac{37}{12} = 3 \frac{1}{12}$