Действия с обыкновенными дробями

1. $$\frac{1}{5} + \frac{53}{50} = \frac{1*10}{5*10} + \frac{53}{50} = \frac{10}{50} + \frac{53}{50} = \frac{10+53}{50} = \frac{63}{50} = 1\frac{13}{50}$$

   Ответ: $$1\frac{13}{50}$$

2. $$\frac{9}{4} + \frac{8}{5} = \frac{9*5}{4*5} + \frac{8*4}{5*4} = \frac{45}{20} + \frac{32}{20} = \frac{45+32}{20} = \frac{77}{20} = 3\frac{17}{20}$$

   Ответ: $$3\frac{17}{20}$$

3. $$\frac{1}{10} + \frac{6}{15} = \frac{1*3}{10*3} + \frac{6*2}{15*2} = \frac{3}{30} + \frac{12}{30} = \frac{3+12}{30} = \frac{15}{30} = \frac{1}{2}$$

   Ответ: $$\frac{1}{2}$$

4. $$\frac{1}{5} - \frac{47}{10} = \frac{1*2}{5*2} - \frac{47}{10} = \frac{2}{10} - \frac{47}{10} = \frac{2-47}{10} = \frac{-45}{10} = -4\frac{5}{10} = -4\frac{1}{2}$$

   Ответ: $$-4\frac{1}{2}$$

5. $$\frac{1}{2} - \frac{9}{10} = \frac{1*5}{2*5} - \frac{9}{10} = \frac{5}{10} - \frac{9}{10} = \frac{5-9}{10} = \frac{-4}{10} = -\frac{2}{5}$$

   Ответ: $$- \frac{2}{5}$$

6. $$\frac{11}{12} - \frac{5}{18} = \frac{11*3}{12*3} - \frac{5*2}{18*2} = \frac{33}{36} - \frac{10}{36} = \frac{33-10}{36} = \frac{23}{36}$$

   Ответ: $$\frac{23}{36}$$

7. $$\frac{9}{5} \cdot \frac{2}{3} = \frac{9 \cdot 2}{5 \cdot 3} = \frac{18}{15} = \frac{6}{5} = 1\frac{1}{5}$$

   Ответ: $$1\frac{1}{5}$$

8. $$\frac{15}{4} \cdot \frac{6}{5} = \frac{15 \cdot 6}{4 \cdot 5} = \frac{90}{20} = \frac{9}{2} = 4\frac{1}{2}$$

   Ответ: $$4\frac{1}{2}$$

9. $$\frac{2}{3} \cdot \frac{9}{8} = \frac{2 \cdot 9}{3 \cdot 8} = \frac{18}{24} = \frac{3}{4}$$

   Ответ: $$\frac{3}{4}$$