89. Написать числа, которые вдвое меньше каждой из следующих дробей: a) \(\frac{4}{15}, \frac{2}{3}, \frac{6}{17}, \frac{8}{21}, \frac{12}{13}, \frac{10}{19}\) b) \(\frac{1}{2}, \frac{1}{3}, \frac{1}{5}, \frac{1}{4}, \frac{3}{4}, \frac{1}{8}, \frac{1}{7}, \frac{5}{9}, \frac{8}{15}, \frac{7}{17}, \frac{13}{21}, \frac{16}{23}, \frac{14}{25}, \frac{18}{357}\)

Пошаговое решение:

а) Умножаем знаменатель каждой дроби на 2:

• \(\frac{4}{15 \cdot 2} = \frac{4}{30} = \frac{2}{15}\)
• \(\frac{2}{3 \cdot 2} = \frac{2}{6} = \frac{1}{3}\)
• \(\frac{6}{17 \cdot 2} = \frac{6}{34} = \frac{3}{17}\)
• \(\frac{8}{21 \cdot 2} = \frac{8}{42} = \frac{4}{21}\)
• \(\frac{12}{13 \cdot 2} = \frac{12}{26} = \frac{6}{13}\)
• \(\frac{10}{19 \cdot 2} = \frac{10}{38} = \frac{5}{19}\)

б) Умножаем знаменатель каждой дроби на 2:

• \(\frac{1}{2 \cdot 2} = \frac{1}{4}\)
• \(\frac{1}{3 \cdot 2} = \frac{1}{6}\)
• \(\frac{1}{5 \cdot 2} = \frac{1}{10}\)
• \(\frac{1}{4 \cdot 2} = \frac{1}{8}\)
• \(\frac{3}{4 \cdot 2} = \frac{3}{8}\)
• \(\frac{1}{8 \cdot 2} = \frac{1}{16}\)
• \(\frac{1}{7 \cdot 2} = \frac{1}{14}\)
• \(\frac{5}{9 \cdot 2} = \frac{5}{18}\)
• \(\frac{8}{15 \cdot 2} = \frac{8}{30} = \frac{4}{15}\)
• \(\frac{7}{17 \cdot 2} = \frac{7}{34}\)
• \(\frac{13}{21 \cdot 2} = \frac{13}{42}\)
• \(\frac{16}{23 \cdot 2} = \frac{16}{46} = \frac{8}{23}\)
• \(\frac{14}{25 \cdot 2} = \frac{14}{50} = \frac{7}{25}\)
• \(\frac{18}{357 \cdot 2} = \frac{18}{714} = \frac{9}{357}\)

Ответ:

а) \(\frac{2}{15}, \frac{1}{3}, \frac{3}{17}, \frac{4}{21}, \frac{6}{13}, \frac{5}{19}\)

б) \(\frac{1}{4}, \frac{1}{6}, \frac{1}{10}, \frac{1}{8}, \frac{3}{8}, \frac{1}{16}, \frac{1}{14}, \frac{5}{18}, \frac{4}{15}, \frac{7}{34}, \frac{13}{42}, \frac{8}{23}, \frac{7}{25}, \frac{9}{357}\)