13 Сравни.

Решение:

Сначала преобразуем смешанные числа в неправильные дроби:

• \( 1\frac{8}{15} = \frac{1\cdot15+8}{15} = \frac{23}{15} \)
• \( 2\frac{3}{4} = \frac{2\cdot4+3}{4} = \frac{11}{4} \)
• \( 5\frac{7}{22} = \frac{5\cdot22+7}{22} = \frac{117}{22} \)
• \( 3\frac{9}{23} = \frac{3\cdot23+9}{23} = \frac{78}{23} \)
• \( 4\frac{5}{9} = \frac{4\cdot9+5}{9} = \frac{41}{9} \)
• \( \frac{7}{14} = \frac{1}{2} \)
• \( 1\frac{4}{11} = \frac{1\cdot11+4}{11} = \frac{15}{11} \)
• \( \frac{15}{11} \)
• \( \frac{17}{3} = 5\frac{2}{3} \)
• \( 4\frac{2}{3} = \frac{4\cdot3+2}{3} = \frac{14}{3} \)
• \( \frac{16}{7} = 2\frac{2}{7} \)
• \( 2\frac{7}{7} \)
• \( \frac{29}{10} = 2\frac{9}{10} \)
• \( \frac{9}{10} \)

Теперь выполним умножение:

• \( \frac{23}{15} \cdot \frac{11}{4} = \frac{253}{60} = 4\frac{13}{60} \)
• \( \frac{117}{22} \cdot \frac{78}{23} = \frac{9126}{506} = 18\frac{36}{506} = 18\frac{18}{253} \)
• \( \frac{41}{9} \cdot \frac{1}{2} = \frac{41}{18} = 2\frac{5}{18} \)
• \( \frac{15}{11} \cdot \frac{15}{11} = \frac{225}{121} = 1\frac{104}{121} \)
• \( \frac{17}{3} \cdot \frac{14}{3} = \frac{238}{9} = 26\frac{4}{9} \)
• \( \frac{29}{10} \cdot \frac{9}{10} = \frac{261}{100} = 2\frac{61}{100} \)

Сравниваем полученные результаты:

• \( 4\frac{13}{60} \) и \( 18\frac{18}{253} \). \( 4\frac{13}{60} < 18\frac{18}{253} \)
• \( 2\frac{5}{18} \) и \( 1\frac{104}{121} \). \( 2\frac{5}{18} > 1\frac{104}{121} \)
• \( 26\frac{4}{9} \) и \( 2\frac{61}{100} \). \( 26\frac{4}{9} > 2\frac{61}{100} \)

Ответ: 1) \( 1\frac{8}{15} \(\cdot\) \( 2\frac{3}{4} = 4\frac{13}{60} \) ; 2) \( 5\frac{7}{22} \(\cdot\) \( 3\frac{9}{23} = 18\frac{18}{253} \) ; 3) \( 4\frac{5}{9} \(\cdot\) \( \frac{7}{14} = 2\frac{5}{18} \) ; 4) \( 1\frac{4}{11} \(\cdot\) \( \frac{15}{11} = 1\frac{104}{121} \) ; 5) \( \frac{17}{3} \(\cdot\) \( 4\frac{2}{3} = 26\frac{4}{9} \) ; 6) \( \frac{29}{10} \(\cdot\) \( \frac{9}{10} = 2\frac{61}{100} \).