1.50. Вычислите: А) 2⅓ + 3⁵/₆ Б) 7⁵/₁₂ + 1⁹/₁₈ В) 13¹³/₁₀ - 6¹¹/₂₀ Г) 2²/₃ - 1³/₄ Д) 4¹/₂ : 2²/₃ Е) 3⁷/₁₁ : 2¹⁴/₃₃ Ж) 6⁷:15 3) 3¹/₄ + 2⁷/₈ И) 17⁴/₁₅ - 8¹¹/₃₀ К) 2¹/₄ - 3²/₃ Л) (3¹/₂)² М) 3¹/₂ : 2¹/₄ Н) 3¹/₁₃ : 2/26 О) 8⁷/₇ П) 7·12³/₁₄ Р) 56²¹/₃₂ : 14 С) 23⁷/₉ : 1¹/₆ Т) 72²/₃₃ : 12/33

Решение:

А) 2⅓ + 3⁵/₆

\( 2\frac{1}{3} + 3\frac{5}{6} = 2\frac{2}{6} + 3\frac{5}{6} = (2+3) + (\frac{2}{6} + \frac{5}{6}) = 5 + \frac{7}{6} = 5 + 1\frac{1}{6} = 6\frac{1}{6} \)

Б) 7⁵/₁₂ + 1⁹/₁₈

\( 7\frac{5}{12} + 1\frac{9}{18} = 7\frac{5}{12} + 1\frac{1}{2} = 7\frac{5}{12} + 1\frac{6}{12} = (7+1) + (\frac{5}{12} + \frac{6}{12}) = 8 + \frac{11}{12} = 8\frac{11}{12} \)

В) 13¹³/₁₀ - 6¹¹/₂₀

\( 13\frac{13}{10} - 6\frac{11}{20} = 13\frac{26}{20} - 6\frac{11}{20} = (13-6) + (\frac{26}{20} - \frac{11}{20}) = 7 + \frac{15}{20} = 7 + \frac{3}{4} = 7\frac{3}{4} \)

Г) 2²/₃ - 1³/₄

\( 2\frac{2}{3} - 1\frac{3}{4} = 2\frac{8}{12} - 1\frac{9}{12} = 1\frac{20}{12} - 1\frac{9}{12} = \frac{11}{12} \)

Д) 4¹/₂ : 2²/₃

\( 4\frac{1}{2} : 2\frac{2}{3} = \frac{9}{2} : \frac{8}{3} = \frac{9}{2} \times \frac{3}{8} = \frac{27}{16} = 1\frac{11}{16} \)

Е) 3⁷/₁₁ : 2¹⁴/₃₃

\( 3\frac{7}{11} : 2\frac{14}{33} = \frac{40}{11} : \frac{80}{33} = \frac{40}{11} \times \frac{33}{80} = \frac{40 \times 33}{11 \times 80} = \frac{1 \times 3}{1 \times 2} = \frac{3}{2} = 1\frac{1}{2} \)

Ж) 6⁷:15

\( 6 \times 7 : 15 = 42 : 15 = \frac{42}{15} = \frac{14}{5} = 2\frac{4}{5} \)

3) 3¹/₄ + 2⁷/₈

\( 3\frac{1}{4} + 2\frac{7}{8} = 3\frac{2}{8} + 2\frac{7}{8} = (3+2) + (\frac{2}{8} + \frac{7}{8}) = 5 + \frac{9}{8} = 5 + 1\frac{1}{8} = 6\frac{1}{8} \)

И) 17⁴/₁₅ - 8¹¹/₃₀

\( 17\frac{4}{15} - 8\frac{11}{30} = 17\frac{8}{30} - 8\frac{11}{30} = 16\frac{38}{30} - 8\frac{11}{30} = (16-8) + (\frac{38}{30} - \frac{11}{30}) = 8 + \frac{27}{30} = 8 + \frac{9}{10} = 8\frac{9}{10} \)

К) 2¹/₄ - 3²/₃

\( 2\frac{1}{4} - 3\frac{2}{3} = 2\frac{3}{12} - 3\frac{8}{12} = \frac{27}{12} - \frac{44}{12} = -\frac{17}{12} = -1\frac{5}{12} \)

Л) (3¹/₂)²

\( (3\frac{1}{2})^2 = (\frac{7}{2})^2 = \frac{49}{4} = 12\frac{1}{4} \)

М) 3¹/₂ : 2¹/₄

\( 3\frac{1}{2} : 2\frac{1}{4} = \frac{7}{2} : \frac{9}{4} = \frac{7}{2} \times \frac{4}{9} = \frac{28}{18} = \frac{14}{9} = 1\frac{5}{9} \)

Н) 3¹/₁₃ : 2/26

\( 3\frac{1}{13} : \frac{2}{26} = \frac{40}{13} : \frac{1}{13} = \frac{40}{13} \times 13 = 40 \)

О) 8⁷/₇

\( 8 \times \frac{7}{7} = 8 \times 1 = 8 \)

П) 7·12³/₁₄

\( 7 \times 12\frac{3}{14} = 7 \times \frac{171}{14} = \frac{7 \times 171}{14} = \frac{171}{2} = 85\frac{1}{2} \)

Р) 56²¹/₃₂ : 14

\( 56\frac{21}{32} : 14 = \frac{56 \times 32 + 21}{32} : 14 = \frac{1792 + 21}{32} : 14 = \frac{1813}{32} : 14 = \frac{1813}{32} \times \frac{1}{14} = \frac{1813}{448} \)

С) 23⁷/₉ : 1¹/₆

\( 23\frac{7}{9} : 1\frac{1}{6} = \frac{214}{9} : \frac{7}{6} = \frac{214}{9} \times \frac{6}{7} = \frac{214 \times 6}{9 \times 7} = \frac{214 \times 2}{3 \times 7} = \frac{428}{21} = 20\frac{8}{21} \)

Т) 72²/₃₃ : 12/33

\( 72\frac{2}{33} : \frac{12}{33} = \frac{72 \times 33 + 2}{33} : \frac{12}{33} = \frac{2376 + 2}{33} : \frac{12}{33} = \frac{2378}{33} : \frac{12}{33} = \frac{2378}{33} \times \frac{33}{12} = \frac{2378}{12} = \frac{1189}{6} = 198\frac{1}{6} \)

Ответ: А) 6¹/₆, Б) 8¹¹/₁₂, В) 7¾, Г) ¹¹/₁₂, Д) 1¹¹/₁₆, Е) 1½, Ж) 2⁴/₅, 3) 6¹/₈, И) 8⁹/₁₀, К) -1⁵/₁₂, Л) 12¼, М) 1⁵/₉, Н) 40, О) 8, П) 85½, Р) ¹⁸¹³/₄₄₈, С) 20⁸/₂₁, Т) 198¹/₆