УПРАЖНЕНИЯ УМНОЖЕНИЕ ДРОБИ НА ДРОБЬ Вычислите (№ 592-594): a) 1/3 ⋅ 2/7; б) 1/2 ⋅ 5/6; в) 3/4 ⋅ 1/4; г) 2/5 ⋅ 7/5; д) 1/2 ⋅ 1/3; 592 593 a) 4/5 ⋅ 5/7; б) 8/9 ⋅ 3/5; в) 9/2 ⋅ 2/9; г) 8/21 ⋅ 7/10; д) 8/15 ⋅ 25/28; 594 a) 3/5 ⋅ 1/2 ⋅ 4/9; в) 1/2 ⋅ 2/3 ⋅ 3/4 ⋅ 4/5; д) 4/7 ⋅ 35/36 ⋅ 3/5; б) 4/5 ⋅ 10/27 ⋅ 15/16; г) 6/7 ⋅ 7/8 ⋅ 8/9 ⋅ 9/10 ⋅ 10/11; e) 1/2 ⋅ 2/3 ⋅ 3/4 ... 23/24 ⋅ 24/25;

№ 592

• а) \[ \frac{1}{3} \cdot \frac{2}{7} = \frac{1 \cdot 2}{3 \cdot 7} = \frac{2}{21} \]
• б) \[ \frac{1}{2} \cdot \frac{5}{6} = \frac{1 \cdot 5}{2 \cdot 6} = \frac{5}{12} \]
• в) \[ \frac{3}{4} \cdot \frac{1}{4} = \frac{3 \cdot 1}{4 \cdot 4} = \frac{3}{16} \]
• г) \[ \frac{2}{5} \cdot \frac{7}{5} = \frac{2 \cdot 7}{5 \cdot 5} = \frac{14}{25} \]
• д) \[ \frac{1}{2} \cdot \frac{1}{3} = \frac{1 \cdot 1}{2 \cdot 3} = \frac{1}{6} \]

№ 593

• а) \[ \frac{4}{5} \cdot \frac{5}{7} = \frac{4 \cdot 5}{5 \cdot 7} = \frac{20}{35} = \frac{4}{7} \]
• б) \[ \frac{8}{9} \cdot \frac{3}{5} = \frac{8 \cdot 3}{9 \cdot 5} = \frac{24}{45} = \frac{8}{15} \]
• в) \[ \frac{9}{2} \cdot \frac{2}{9} = \frac{9 \cdot 2}{2 \cdot 9} = \frac{18}{18} = 1 \]
• г) \[ \frac{8}{21} \cdot \frac{7}{10} = \frac{8 \cdot 7}{21 \cdot 10} = \frac{56}{210} = \frac{4}{15} \]
• д) \[ \frac{8}{15} \cdot \frac{25}{28} = \frac{8 \cdot 25}{15 \cdot 28} = \frac{200}{420} = \frac{10}{21} \]

№ 594

• а) \[ \frac{3}{5} \cdot \frac{1}{2} \cdot \frac{4}{9} = \frac{3 \cdot 1 \cdot 4}{5 \cdot 2 \cdot 9} = \frac{12}{90} = \frac{2}{15} \]
• б) \[ \frac{4}{5} \cdot \frac{10}{27} \cdot \frac{15}{16} = \frac{4 \cdot 10 \cdot 15}{5 \cdot 27 \cdot 16} = \frac{600}{2160} = \frac{5}{18} \]
• в) \[ \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} = \frac{1 \cdot 2 \cdot 3 \cdot 4}{2 \cdot 3 \cdot 4 \cdot 5} = \frac{24}{120} = \frac{1}{5} \]
• г) \[ \frac{6}{7} \cdot \frac{7}{8} \cdot \frac{8}{9} \cdot \frac{9}{10} \cdot \frac{10}{11} = \frac{6 \cdot 7 \cdot 8 \cdot 9 \cdot 10}{7 \cdot 8 \cdot 9 \cdot 10 \cdot 11} = \frac{30240}{55440} = \frac{6}{11} \]
• д) \[ \frac{4}{7} \cdot \frac{35}{36} \cdot \frac{3}{5} = \frac{4 \cdot 35 \cdot 3}{7 \cdot 36 \cdot 5} = \frac{420}{1260} = \frac{1}{3} \]
• е) \[ \frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdot ... \cdot \frac{23}{24} \cdot \frac{24}{25} = \frac{1 \cdot 2 \cdot 3 \cdot ... \cdot 23 \cdot 24}{2 \cdot 3 \cdot 4 \cdot ... \cdot 24 \cdot 25} = \frac{1}{25} \]

Ответ: См. решение выше