607. Выполните действия:

Решение:

1. а) 2/₃ : 6/₇ 4/₇
   • \( \frac{2}{3} : \frac{6}{7} = \frac{2}{3} \times \frac{7}{6} = \frac{14}{18} = \frac{7}{9} \).
   • \( \frac{7}{9} - \frac{4}{7} = \frac{7 \times 7 - 4 \times 9}{63} = \frac{49 - 36}{63} = \frac{13}{63} \).
2. б) 11/₁2 : 7/₂₄ 21/₂2
   • \( \frac{11}{12} : \frac{7}{24} = \frac{11}{12} \times \frac{24}{7} = \frac{11 \times 2}{7} = \frac{22}{7} \).
   • \( \frac{22}{7} - \frac{21}{22} = \frac{22 \times 22 - 21 \times 7}{154} = \frac{484 - 147}{154} = \frac{337}{154} = 2\frac{29}{154} \).
3. в) 15/₁6 : 8/₃ 4/₄
   • \( \frac{15}{16} : \frac{8}{3} = \frac{15}{16} \times \frac{3}{8} = \frac{45}{128} \).
   • \( \frac{45}{128} - \frac{3}{4} = \frac{45 - 3 \times 32}{128} = \frac{45 - 96}{128} = -\frac{51}{128} \).
4. г) 13/₁₄ : 7/₂₅ 13/₂₅
   • \( \frac{13}{14} : \frac{7}{25} = \frac{13}{14} \times \frac{25}{7} = \frac{325}{98} \).
   • \( \frac{325}{98} - \frac{13}{25} = \frac{325 \times 25 - 13 \times 98}{98 \times 25} = \frac{8125 - 1274}{2450} = \frac{6851}{2450} = 2\frac{1951}{2450} \).
5. д) 3⁳/₄ 4ⁱ/₂ : 6⁳/₄
   • \( 3\frac{3}{4} \times 4\frac{1}{2} = \frac{15}{4} \times \frac{9}{2} = \frac{135}{8} \).
   • \( \frac{135}{8} : 6\frac{3}{4} = \frac{135}{8} : \frac{27}{4} = \frac{135}{8} \times \frac{4}{27} = \frac{135}{2 \times 27} = \frac{5}{2} = 2\frac{1}{2} \).
6. е) (2⁲/₇ + 1ⁱ/₇) 1ⁱ/₆
   • \( 2\frac{2}{7} + 1\frac{1}{7} = 3\frac{3}{7} = \frac{24}{7} \).
   • \( \frac{24}{7} \times 1\frac{1}{6} = \frac{24}{7} \times \frac{7}{6} = \frac{24}{6} = 4 \).
7. ж) (6ⁱ/₂ - 4ⁱ/₄) : 2ⁱ/₂
   • \( 6\frac{1}{2} - 4\frac{1}{4} = \frac{13}{2} - \frac{17}{4} = \frac{26 - 17}{4} = \frac{9}{4} \).
   • \( \frac{9}{4} : 2\frac{1}{2} = \frac{9}{4} : \frac{5}{2} = \frac{9}{4} \times \frac{2}{5} = \frac{9}{10} \).
8. з) (4⁸/₁₅ - 1ⁱ/₃) : 1⁷/₈
   • \( 4\frac{8}{15} - 1\frac{1}{3} = \frac{68}{15} - \frac{4}{3} = \frac{68 - 20}{15} = \frac{48}{15} = \frac{16}{5} \).
   • \( \frac{16}{5} : 1\frac{7}{8} = \frac{16}{5} : \frac{15}{8} = \frac{16}{5} \times \frac{8}{15} = \frac{128}{75} = 1\frac{53}{75} \).
9. и) (2⁲/₃ + 1⁵/₆) : 1ⁱ/₂
   • \( 2\frac{2}{3} + 1\frac{5}{6} = \frac{8}{3} + \frac{11}{6} = \frac{16 + 11}{6} = \frac{27}{6} = \frac{9}{2} \).
   • \( \frac{9}{2} : 1\frac{1}{2} = \frac{9}{2} : \frac{3}{2} = \frac{9}{2} \times \frac{2}{3} = 3 \).
10. к) (3ⁱ/₆ - 2⁷/₁₅) : 1ⁱ/₅
    • \( 3\frac{1}{6} - 2\frac{7}{15} = \frac{19}{6} - \frac{37}{15} = \frac{95 - 74}{30} = \frac{21}{30} = \frac{7}{10} \).
    • \( \frac{7}{10} : 1\frac{1}{5} = \frac{7}{10} : \frac{6}{5} = \frac{7}{10} \times \frac{5}{6} = \frac{7}{12} \).
11. л) (1⁲/₃ + 2⁴/₉) : (4⁴☰/₂₇ - 2⁲/₉)
    • \( 1\frac{2}{3} + 2\frac{4}{9} = \frac{5}{3} + \frac{22}{9} = \frac{15 + 22}{9} = \frac{37}{9} \).
    • \( 4\frac{26}{27} - 2\frac{2}{9} = \frac{134}{27} - \frac{20}{9} = \frac{134 - 60}{27} = \frac{74}{27} \).
    • \( \frac{37}{9} : \frac{74}{27} = \frac{37}{9} \times \frac{27}{74} = \frac{1 \times 3}{1 \times 2} = \frac{3}{2} = 1\frac{1}{2} \).
12. м) (6ⁱ/₂₄ - 2⁲/₃) : (31/2 + 1⁷/₈)
    • \( 6\frac{1}{24} - 2\frac{2}{3} = \frac{145}{24} - \frac{8}{3} = \frac{145 - 64}{24} = \frac{81}{24} = \frac{27}{8} \).
    • \( 3\frac{1}{2} + 1\frac{7}{8} = \frac{7}{2} + \frac{15}{8} = \frac{28 + 15}{8} = \frac{43}{8} \).
    • \( \frac{27}{8} : \frac{43}{8} = \frac{27}{8} \times \frac{8}{43} = \frac{27}{43} \).

Ответ: а) 13/₆3; б) 2⁲⁹/1₅₄; в) -51/1₂₈; г) 21⁹⁵1/₂₄₅₀; д) 21/₂; е) 4; ж) 9/1₀; з) 1⁵3/⁷₅; и) 3; к) 7/1₂; л) 11/₂; м) 2⁷/4⁳.