УМНОЖЕНИЕ ДРОБИ НА НАТУРАЛЬНОЕ ЧИСЛО И НА СМЕШАННУЮ ДРОБЬ Вычислите (№ 595-597): 595 a) 3/7 ⋅ 2; б) 3 ⋅ 1/6; в) 9 ⋅ 5/6; г) 2/5 ⋅ 15; д) 1/4 ⋅ 4; e) 5 ⋅ 1/3 596 a) 2 1/3 ⋅ 2; б) 4 ⋅ 1 1/2; в) 1 1/3 ⋅ 9; г) 3/7 ⋅ 2 1/3; д) 1 1/3 ⋅ 1 1/2. 597 a) 12 ⋅ 1/6 ⋅ 1 1/2 ⋅ 3 3/4 ⋅ 4/5; б) 3 ⋅ 5 1/4 ⋅ 1 1/7 ⋅ 5 1/2 ⋅ 4/11.

№ 595

• а) \[ \frac{3}{7} \cdot 2 = \frac{3 \cdot 2}{7} = \frac{6}{7} \]
• б) \[ 3 \cdot \frac{1}{6} = \frac{3 \cdot 1}{6} = \frac{3}{6} = \frac{1}{2} \]
• в) \[ 9 \cdot \frac{5}{6} = \frac{9 \cdot 5}{6} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2} \]
• г) \[ \frac{2}{5} \cdot 15 = \frac{2 \cdot 15}{5} = \frac{30}{5} = 6 \]
• д) \[ \frac{1}{4} \cdot 4 = \frac{1 \cdot 4}{4} = \frac{4}{4} = 1 \]
• e) \[ 5 \cdot \frac{1}{3} = \frac{5 \cdot 1}{3} = \frac{5}{3} = 1\frac{2}{3} \]

№ 596

• а) \[ 2\frac{1}{3} \cdot 2 = \frac{7}{3} \cdot 2 = \frac{7 \cdot 2}{3} = \frac{14}{3} = 4\frac{2}{3} \]
• б) \[ 4 \cdot 1\frac{1}{2} = 4 \cdot \frac{3}{2} = \frac{4 \cdot 3}{2} = \frac{12}{2} = 6 \]
• в) \[ 1\frac{1}{3} \cdot 9 = \frac{4}{3} \cdot 9 = \frac{4 \cdot 9}{3} = \frac{36}{3} = 12 \]
• г) \[ \frac{3}{7} \cdot 2\frac{1}{3} = \frac{3}{7} \cdot \frac{7}{3} = \frac{3 \cdot 7}{7 \cdot 3} = \frac{21}{21} = 1 \]
• д) \[ 1\frac{1}{3} \cdot 1\frac{1}{2} = \frac{4}{3} \cdot \frac{3}{2} = \frac{4 \cdot 3}{3 \cdot 2} = \frac{12}{6} = 2 \]

№ 597

• а) \[ 12 \cdot \frac{1}{6} \cdot 1\frac{1}{2} \cdot 3\frac{3}{4} \cdot \frac{4}{5} = 12 \cdot \frac{1}{6} \cdot \frac{3}{2} \cdot \frac{15}{4} \cdot \frac{4}{5} = \frac{12 \cdot 1 \cdot 3 \cdot 15 \cdot 4}{6 \cdot 2 \cdot 4 \cdot 5} = \frac{2160}{240} = 9 \]
• б) \[ 3 \cdot 5\frac{1}{4} \cdot 1\frac{1}{7} \cdot 5\frac{1}{2} \cdot \frac{4}{11} = 3 \cdot \frac{21}{4} \cdot \frac{8}{7} \cdot \frac{11}{2} \cdot \frac{4}{11} = \frac{3 \cdot 21 \cdot 8 \cdot 11 \cdot 4}{4 \cdot 7 \cdot 2 \cdot 11} = \frac{22176}{616} = 36 \]

Ответ: См. решение выше