Задание 1

Преобразуйте в десятичную дробь: $$ \frac{9}{25}, \frac{5}{8}, \frac{121}{50} $$.

1. $$ \frac{9}{25} = \frac{9 \cdot 4}{25 \cdot 4} = \frac{36}{100} = 0.36 $$
2. $$ \frac{5}{8} = \frac{5 \cdot 125}{8 \cdot 125} = \frac{625}{1000} = 0.625 $$
3. $$ \frac{121}{50} = \frac{121 \cdot 2}{50 \cdot 2} = \frac{242}{100} = 2.42 $$

Ответ: 0.36; 0.625; 2.42

Задание 2

Приведите к наименьшему общему знаменателю дроби:

1. $$ \frac{1}{9} $$ и $$ \frac{1}{6} $$

   НОЗ(9, 6) = 18

   $$ \frac{1}{9} = \frac{1 \cdot 2}{9 \cdot 2} = \frac{2}{18} $$

   $$ \frac{1}{6} = \frac{1 \cdot 3}{6 \cdot 3} = \frac{3}{18} $$

   Ответ: $$ \frac{2}{18} $$ и $$ \frac{3}{18} $$

2. $$ \frac{7}{12} $$ и $$ \frac{5}{8} $$

   НОЗ(12, 8) = 24

   $$ \frac{7}{12} = \frac{7 \cdot 2}{12 \cdot 2} = \frac{14}{24} $$

   $$ \frac{5}{8} = \frac{5 \cdot 3}{8 \cdot 3} = \frac{15}{24} $$

   Ответ: $$ \frac{14}{24} $$ и $$ \frac{15}{24} $$

3. $$ \frac{4}{39} $$ и $$ \frac{7}{13} $$

   НОЗ(39, 13) = 39

   $$ \frac{4}{39} = \frac{4}{39} $$

   $$ \frac{7}{13} = \frac{7 \cdot 3}{13 \cdot 3} = \frac{21}{39} $$

   Ответ: $$ \frac{4}{39} $$ и $$ \frac{21}{39} $$

4. $$ \frac{3}{8} $$ и $$ \frac{5}{9} $$

   НОЗ(8, 9) = 72

   $$ \frac{3}{8} = \frac{3 \cdot 9}{8 \cdot 9} = \frac{27}{72} $$

   $$ \frac{5}{9} = \frac{5 \cdot 8}{9 \cdot 8} = \frac{40}{72} $$

   Ответ: $$ \frac{27}{72} $$ и $$ \frac{40}{72} $$

5. $$ \frac{14}{15} $$ и $$ \frac{11}{12} $$

   НОЗ(15, 12) = 60

   $$ \frac{14}{15} = \frac{14 \cdot 4}{15 \cdot 4} = \frac{56}{60} $$

   $$ \frac{11}{12} = \frac{11 \cdot 5}{12 \cdot 5} = \frac{55}{60} $$

   Ответ: $$ \frac{56}{60} $$ и $$ \frac{55}{60} $$

6. $$ \frac{3}{4}, \frac{5}{14} $$ и $$ \frac{4}{7} $$

   НОЗ(4, 14, 7) = 28

   $$ \frac{3}{4} = \frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28} $$

   $$ \frac{5}{14} = \frac{5 \cdot 2}{14 \cdot 2} = \frac{10}{28} $$

   $$ \frac{4}{7} = \frac{4 \cdot 4}{7 \cdot 4} = \frac{16}{28} $$

   Ответ: $$ \frac{21}{28}, \frac{10}{28} $$ и $$ \frac{16}{28} $$