Ответ: Решения представлены ниже.
Краткое пояснение: Выполняем действия с дробями, следуя правилам сложения, вычитания, умножения и деления.
Задание №2
- \[\frac{1}{3} + \frac{5}{8} = \frac{8}{24} + \frac{15}{24} = \frac{8+15}{24} = \frac{23}{24}\]
- \[\frac{7}{8} - \frac{3}{8} = \frac{7-3}{8} = \frac{4}{8} = \frac{1}{2}\]
- \[\frac{11}{16} - \frac{5}{8} = \frac{11}{16} - \frac{10}{16} = \frac{11-10}{16} = \frac{1}{16}\]
- \[\frac{4}{5} + \frac{3}{36} = \frac{4}{5} + \frac{1}{12} = \frac{48}{60} + \frac{5}{60} = \frac{48+5}{60} = \frac{53}{60}\]
- \[\frac{8}{16} - \frac{4}{16} = \frac{8-4}{16} = \frac{4}{16} = \frac{1}{4}\]
- \[\frac{7}{16} + \frac{6}{12} = \frac{7}{16} + \frac{1}{2} = \frac{7}{16} + \frac{8}{16} = \frac{7+8}{16} = \frac{15}{16}\]
- \[\frac{11}{48} - \frac{6}{36} = \frac{11}{48} - \frac{1}{6} = \frac{11}{48} - \frac{8}{48} = \frac{11-8}{48} = \frac{3}{48} = \frac{1}{16}\]
- \[\frac{7}{8} + \frac{11}{16} = \frac{14}{16} + \frac{11}{16} = \frac{14+11}{16} = \frac{25}{16} = 1\frac{9}{16}\]
- \[\frac{5}{8} + \frac{12}{6} = \frac{5}{8} + 2 = \frac{5}{8} + \frac{16}{8} = \frac{5+16}{8} = \frac{21}{8} = 2\frac{5}{8}\]
Задание №5
- \[\frac{2}{5} \cdot \frac{5}{8} = \frac{2 \cdot 5}{5 \cdot 8} = \frac{10}{40} = \frac{1}{4}\]
- \[1 \frac{1}{2} \cdot \frac{5}{3.4} = \frac{3}{2} \cdot \frac{5}{3.4} = \frac{3 \cdot 5}{2 \cdot 3.4} = \frac{15}{6.8} = \frac{150}{68} = \frac{75}{34} = 2\frac{7}{34}\]
- \[\frac{1}{6} - \frac{6}{7} = \frac{7}{42} - \frac{36}{42} = \frac{7-36}{42} = \frac{-29}{42} = -\frac{29}{42}\]
- \[\frac{3}{5} - \frac{5}{8} = \frac{24}{40} - \frac{25}{40} = \frac{24-25}{40} = \frac{-1}{40} = -\frac{1}{40}\]
- \[\frac{1}{9} \cdot \frac{9}{10} = \frac{1 \cdot 9}{9 \cdot 10} = \frac{9}{90} = \frac{1}{10}\]
- \[\frac{6}{11} \cdot \frac{5}{18} = \frac{6 \cdot 5}{11 \cdot 18} = \frac{30}{198} = \frac{5}{33}\]
- \[2 \frac{1}{5} - \frac{5}{3} = \frac{11}{5} - \frac{5}{3} = \frac{33}{15} - \frac{25}{15} = \frac{33-25}{15} = \frac{8}{15}\]
- \[1 \frac{1}{6} - \frac{2}{7} = \frac{7}{6} - \frac{2}{7} = \frac{49}{42} - \frac{12}{42} = \frac{49-12}{42} = \frac{37}{42}\]
- \[\frac{2}{3} \cdot \frac{3}{13} = \frac{2 \cdot 3}{3 \cdot 13} = \frac{6}{39} = \frac{2}{13}\]
- \[1 \frac{1}{10} - \frac{10}{8} = \frac{11}{10} - \frac{10}{8} = \frac{44}{40} - \frac{50}{40} = \frac{44-50}{40} = \frac{-6}{40} = -\frac{3}{20}\]
- \[\frac{3}{15} - \frac{15}{19} = \frac{1}{5} - \frac{15}{19} = \frac{19}{95} - \frac{75}{95} = \frac{19-75}{95} = \frac{-56}{95} = -\frac{56}{95}\]
- \[\frac{5}{2} \cdot \frac{5}{2} = \frac{5 \cdot 5}{2 \cdot 2} = \frac{25}{4}\]
- \[\frac{21}{7} - \frac{2}{7} = \frac{21-2}{7} = \frac{19}{7}\]
- \[8 \cdot \frac{25}{15} = \frac{8}{1} \cdot \frac{25}{15} = \frac{8 \cdot 25}{1 \cdot 15} = \frac{200}{15} = \frac{40}{3}\]
- \[\frac{12}{35} \cdot \frac{14}{15} = \frac{12 \cdot 14}{35 \cdot 15} = \frac{168}{525} = \frac{56}{175}\]
- \[\frac{8}{25} - \frac{5}{32} = \frac{256}{800} - \frac{125}{800} = \frac{256-125}{800} = \frac{131}{800}\]
- \[\frac{12}{35} - \frac{14}{15} = \frac{36}{105} - \frac{98}{105} = \frac{36-98}{105} = \frac{-62}{105}\]
- \[\frac{2}{9} \cdot \frac{3}{8} = \frac{2 \cdot 3}{9 \cdot 8} = \frac{6}{72} = \frac{1}{12}\]
- \[\frac{5}{6} - \frac{12}{35} = \frac{175}{210} - \frac{72}{210} = \frac{175-72}{210} = \frac{103}{210}\]
- \[\frac{7}{8} - \frac{8}{40} = \frac{35}{40} - \frac{8}{40} = \frac{35-8}{40} = \frac{27}{40}\]
- \[\frac{27}{32} \cdot \frac{4}{5} = \frac{27 \cdot 4}{32 \cdot 5} = \frac{108}{160} = \frac{27}{40}\]
- \[\frac{45}{49} \cdot \frac{7}{10} = \frac{45 \cdot 7}{49 \cdot 10} = \frac{315}{490} = \frac{9}{14}\]
- \[\frac{12}{15} - \frac{35}{36} = \frac{144}{180} - \frac{175}{180} = \frac{144-175}{180} = \frac{-31}{180}\]
- \[4 \cdot \frac{1}{6} = \frac{4 \cdot 1}{6} = \frac{4}{6} = \frac{2}{3}\]
- \[7 \cdot \frac{2}{7} = \frac{7 \cdot 2}{7} = \frac{14}{7} = 2\]
- \[9 \cdot \frac{5}{18} = \frac{9 \cdot 5}{18} = \frac{45}{18} = \frac{5}{2}\]
- \[8 \cdot \frac{3}{16} = \frac{8 \cdot 3}{16} = \frac{24}{16} = \frac{3}{2}\]
- \[12 \cdot \frac{7}{18} = \frac{12 \cdot 7}{18} = \frac{84}{18} = \frac{14}{3}\]
- \[4 \cdot \frac{3}{14} = \frac{4 \cdot 3}{14} = \frac{12}{14} = \frac{6}{7}\]
- \[21 \cdot \frac{5}{9} = \frac{21 \cdot 5}{9} = \frac{105}{9} = \frac{35}{3}\]
- \[44 \cdot \frac{4}{33} = \frac{44 \cdot 4}{33} = \frac{176}{33} = \frac{16}{3}\]
- \[15 \cdot \frac{3}{10} = \frac{15 \cdot 3}{10} = \frac{45}{10} = \frac{9}{2}\]
- \[43 \cdot \frac{10}{43} = \frac{43 \cdot 10}{43} = 10\]
Ответ: Решения представлены выше.
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