Вычисли значения выражений в заданиях 1.33 и 1.34.

Задание 1.33. а) $\frac{4}{7} + \frac{2}{7} = \frac{4+2}{7} = \frac{6}{7}$ б) $\frac{8}{11} + \frac{7}{11} = \frac{8+7}{11} = \frac{15}{11} = 1\frac{4}{11}$ е) $\frac{1}{4} + \frac{3}{16} = \frac{1*4}{4*4} + \frac{3}{16} = \frac{4}{16} + \frac{3}{16} = \frac{4+3}{16} = \frac{7}{16}$ ё) $\frac{1}{20} + \frac{1}{4} + \frac{2}{5} = \frac{1}{20} + \frac{1*5}{4*5} + \frac{2*4}{5*4} = \frac{1}{20} + \frac{5}{20} + \frac{8}{20} = \frac{1+5+8}{20} = \frac{14}{20} = \frac{7}{10}$ и) $4\frac{15}{49} - 2\frac{3}{14} = 4\frac{15*2}{49*2} - 2\frac{3*7}{14*7} = 4\frac{30}{98} - 2\frac{21}{98} = (4-2) + (\frac{30}{98} - \frac{21}{98}) = 2 + \frac{30-21}{98} = 2\frac{9}{98}$ к) $28\frac{3}{4} - 10\frac{2}{7} = 28\frac{3*7}{4*7} - 10\frac{2*4}{7*4} = 28\frac{21}{28} - 10\frac{8}{28} = (28-10) + (\frac{21}{28} - \frac{8}{28}) = 18 + \frac{21-8}{28} = 18\frac{13}{28}$ о) $\frac{8}{15} * \frac{25}{28} = \frac{8*25}{15*28} = \frac{2*5}{3*7} = \frac{10}{21}$ п) $\frac{1}{2} * 1\frac{1}{2} = \frac{1}{2} * \frac{1*2+1}{2} = \frac{1}{2} * \frac{3}{2} = \frac{1*3}{2*2} = \frac{3}{4}$ у) $(1\frac{1}{2})^3 = (\frac{1*2+1}{2})^3 = (\frac{3}{2})^3 = \frac{3^3}{2^3} = \frac{27}{8} = 3\frac{3}{8}$ ф) $\frac{1}{4} : 2 = \frac{1}{4} : \frac{2}{1} = \frac{1}{4} * \frac{1}{2} = \frac{1*1}{4*2} = \frac{1}{8}$ ш) $3\frac{1}{2} : 2\frac{1}{3} = \frac{3*2+1}{2} : \frac{2*3+1}{3} = \frac{7}{2} : \frac{7}{3} = \frac{7}{2} * \frac{3}{7} = \frac{7*3}{2*7} = \frac{3}{2} = 1\frac{1}{2}$ щ) $\frac{7}{48} : 6\frac{6}{7} = \frac{7}{48} : \frac{6*7+6}{7} = \frac{7}{48} : \frac{48}{7} = \frac{7}{48} * \frac{7}{48} = \frac{7*7}{48*48} = \frac{49}{2304}$ Задание 1.34. а) $\frac{13}{17} - \frac{4}{17} = \frac{13-4}{17} = \frac{9}{17}$ б) $\frac{7}{10} + \frac{9}{10} = \frac{7+9}{10} = \frac{16}{10} = \frac{8}{5} = 1\frac{3}{5}$ е) $\frac{2}{3} + \frac{5}{9} = \frac{2*3}{3*3} + \frac{5}{9} = \frac{6}{9} + \frac{5}{9} = \frac{6+5}{9} = \frac{11}{9} = 1\frac{2}{9}$ ё) $\frac{1}{4} + \frac{2}{25} + \frac{3}{100} = \frac{1*25}{4*25} + \frac{2*4}{25*4} + \frac{3}{100} = \frac{25}{100} + \frac{8}{100} + \frac{3}{100} = \frac{25+8+3}{100} = \frac{36}{100} = \frac{9}{25}$ и) $7\frac{4}{25} - 2\frac{3}{4} = 7\frac{4*4}{25*4} - 2\frac{3*25}{4*25} = 7\frac{16}{100} - 2\frac{75}{100} = (7-2) + (\frac{16}{100} - \frac{75}{100}) = 5 + \frac{16-75}{100} = 5 + \frac{-59}{100} = 5 - \frac{59}{100} = 4\frac{100}{100} - \frac{59}{100} = 4\frac{100-59}{100} = 4\frac{41}{100}$ к) $75\frac{8}{15} - 12\frac{7}{30} = 75\frac{8*2}{15*2} - 12\frac{7}{30} = 75\frac{16}{30} - 12\frac{7}{30} = (75-12) + (\frac{16}{30} - \frac{7}{30}) = 63 + \frac{16-7}{30} = 63\frac{9}{30} = 63\frac{3}{10}$ о) $\frac{8}{21} * \frac{7}{10} = \frac{8*7}{21*10} = \frac{8*1}{3*10} = \frac{4*1}{3*5} = \frac{4}{15}$ п) $\frac{1}{3} * 4\frac{1}{5} = \frac{1}{3} * \frac{4*5+1}{5} = \frac{1}{3} * \frac{21}{5} = \frac{1*21}{3*5} = \frac{1*7}{1*5} = \frac{7}{5} = 1\frac{2}{5}$ у) $(4\frac{3}{4})^2 = (\frac{4*4+3}{4})^2 = (\frac{19}{4})^2 = \frac{19^2}{4^2} = \frac{361}{16} = 22\frac{9}{16}$ ф) $\frac{20}{27} : 5 = \frac{20}{27} : \frac{5}{1} = \frac{20}{27} * \frac{1}{5} = \frac{20*1}{27*5} = \frac{4*1}{27*1} = \frac{4}{27}$ ш) $5\frac{1}{2} : 3\frac{2}{3} = \frac{5*2+1}{2} : \frac{3*3+2}{3} = \frac{11}{2} : \frac{11}{3} = \frac{11}{2} * \frac{3}{11} = \frac{11*3}{2*11} = \frac{1*3}{2*1} = \frac{3}{2} = 1\frac{1}{2}$ щ) $4\frac{3}{8} : 5\frac{1}{4} = \frac{4*8+3}{8} : \frac{5*4+1}{4} = \frac{35}{8} : \frac{21}{4} = \frac{35}{8} * \frac{4}{21} = \frac{35*4}{8*21} = \frac{5*1}{2*3} = \frac{5}{6}$