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МатематикаВопрос:
19. Выполните умножение: a) 1 \(\frac{2}{7}\) \(\cdot\) 1 \(\frac{1}{4}\) б) 4 \(\frac{2}{3}\) \(\cdot\) \(\frac{2}{5}\) в) 1 \(\frac{3}{5}\) \(\cdot\) 3 \(\frac{3}{4}\) г) \(\frac{4}{9}\) \(\cdot\) 2 \(\frac{3}{4}\) д) 2 \(\frac{3}{4}\) \(\cdot\) \(\frac{4}{11}\) e) 1 \(\frac{3}{4}\) \(\cdot\) 1 \(\frac{5}{7}\) ж) 3 \(\frac{1}{4}\) \(\cdot\) 4 3) 10 \(\cdot\) 5 \(\frac{2}{5}\) и) 3 \(\frac{5}{6}\) \(\cdot\) 1 \(\frac{7}{23}\) к) 1 \(\frac{2}{3}\) \(\cdot\) 2 \(\frac{2}{5}\) л) 7 \(\frac{3}{11}\) \(\cdot\) 2 \(\frac{19}{40}\) м) 2 \(\frac{1}{2}\) \(\cdot\) 2 \(\frac{2}{15}\) н) 0 \(\cdot\) 1 \(\frac{4}{9}\) o) 1 \(\frac{5}{7}\) \(\cdot\) 1 п) 3 \(\frac{8}{9}\) \(\cdot\) 0.
Ответ:
Решение:
- а) \( 1\frac{2}{7} \cdot 1\frac{1}{4} = \frac{9}{7} \cdot \frac{5}{4} = \frac{45}{28} = 1\frac{17}{28} \)
- б) \( 4\frac{2}{3} \cdot \frac{2}{5} = \frac{14}{3} \cdot \frac{2}{5} = \frac{28}{15} = 1\frac{13}{15} \)
- в) \( 1\frac{3}{5} \cdot 3\frac{3}{4} = \frac{8}{5} \cdot \frac{15}{4} = \frac{2}{1} \cdot \frac{3}{1} = 6 \)
- г) \( \frac{4}{9} \cdot 2\frac{3}{4} = \frac{4}{9} \cdot \frac{11}{4} = \frac{1}{9} \cdot \frac{11}{1} = \frac{11}{9} = 1\frac{2}{9} \)
- д) \( 2\frac{3}{4} \cdot \frac{4}{11} = \frac{11}{4} \cdot \frac{4}{11} = 1 \)
- е) \( 1\frac{3}{4} \cdot 1\frac{5}{7} = \frac{7}{4} \cdot \frac{12}{7} = \frac{1}{4} \cdot \frac{12}{1} = 3 \)
- ж) \( 3\frac{1}{4} \cdot 4 = \frac{13}{4} \cdot 4 = 13 \)
- з) \( 10 \cdot 5\frac{2}{5} = 10 \cdot \frac{27}{5} = 2 \cdot 27 = 54 \)
- и) \( 3\frac{5}{6} \cdot 1\frac{7}{23} = \frac{23}{6} \cdot \frac{30}{23} = \frac{1}{6} \cdot \frac{30}{1} = 5 \)
- к) \( 1\frac{2}{3} \cdot 2\frac{2}{5} = \frac{5}{3} \cdot \frac{12}{5} = \frac{1}{3} \cdot \frac{12}{1} = 4 \)
- л) \( 7\frac{3}{11} \cdot 2\frac{19}{40} = \frac{80}{11} \cdot \frac{99}{40} = \frac{2}{11} \cdot \frac{99}{1} = 2 \cdot 9 = 18 \)
- м) \( 2\frac{1}{2} \cdot 2\frac{2}{15} = \frac{5}{2} \cdot \frac{32}{15} = \frac{1}{2} \cdot \frac{32}{3} = \frac{16}{3} = 5\frac{1}{3} \)
- н) \( 0 \cdot 1\frac{4}{9} = 0 \)
- о) \( 1\frac{5}{7} \cdot 1 = \frac{12}{7} \cdot 1 = \frac{12}{7} = 1\frac{5}{7} \)
- п) \( 3\frac{8}{9} \cdot 0 = 0 \)
Ответ: а) \( 1\frac{17}{28} \); б) \( 1\frac{13}{15} \); в) 6; г) \( 1\frac{2}{9} \); д) 1; е) 3; ж) 13; з) 54; и) 5; к) 4; л) 18; м) \( 5\frac{1}{3} \); н) 0; о) \( 1\frac{5}{7} \); п) 0.
