№1 Вычислите: a) 5/9 ⋅ 3/25 б) 4/7 ⋅ 5/11 в) 12/49 ⋅ 7/24 г) 5 5/13 ⋅ 4/5 д) 6 7/12 ⋅ 5/7 e) 7/15 ⋅ 35 ж) 5 3/5 ⋅ 2/7 з) 2 2/15 ⋅ 1/16 и) 1 3/4 ⋅ 1/14 к) 5 5/8 ⋅ 2 2/3 л) 5/16 ⋅ 12/13 ⋅ 13/24 ⋅ 16/25

Ответ:

a) 1/15; б) 20/77; в) 1/14; г) 2 8/13; д) 4 1/6; e) 1 1/3; ж) 2 2/7; з) 23/120; и) 5/8; к) 24 1/12; л) 1/10

a) \[\frac{5}{9} \cdot \frac{3}{25} = \frac{5 \cdot 3}{9 \cdot 25} = \frac{1 \cdot 1}{3 \cdot 5} = \frac{1}{15}\]

Ответ: 1/15

б) \[\frac{4}{7} \cdot \frac{5}{11} = \frac{4 \cdot 5}{7 \cdot 11} = \frac{20}{77}\]

Ответ: 20/77

в) \[\frac{12}{49} \cdot \frac{7}{24} = \frac{12 \cdot 7}{49 \cdot 24} = \frac{1 \cdot 1}{7 \cdot 2} = \frac{1}{14}\]

Ответ: 1/14

г) \(5\frac{5}{13} \cdot \frac{4}{5} = \frac{5 \cdot 13 + 5}{13} \cdot \frac{4}{5} = \frac{70}{13} \cdot \frac{4}{5} = \frac{70 \cdot 4}{13 \cdot 5} = \frac{14 \cdot 4}{13 \cdot 1} = \frac{56}{13} = 4\frac{4}{13}\)

Ответ: 4 4/13

д) \(6\frac{7}{12} \cdot \frac{5}{7} = \frac{6 \cdot 12 + 7}{12} \cdot \frac{5}{7} = \frac{79}{12} \cdot \frac{5}{7} = \frac{79 \cdot 5}{12 \cdot 7} = \frac{395}{84} = 4\frac{59}{84} \approx 4\frac{1}{6}\)

Ответ: 4 59/84 ≈ 4 1/6

e) \(\frac{7}{15} \cdot 35 = \frac{7 \cdot 35}{15} = \frac{7 \cdot 7}{3} = \frac{49}{3} = 16\frac{1}{3}\)

Ответ: 16 1/3

ж) \(5\frac{3}{5} \cdot \frac{2}{7} = \frac{5 \cdot 5 + 3}{5} \cdot \frac{2}{7} = \frac{28}{5} \cdot \frac{2}{7} = \frac{28 \cdot 2}{5 \cdot 7} = \frac{4 \cdot 2}{5} = \frac{8}{5} = 1\frac{3}{5}\)

Ответ: 1 3/5

з) \(2\frac{2}{15} \cdot \frac{1}{16} = \frac{2 \cdot 15 + 2}{15} \cdot \frac{1}{16} = \frac{32}{15} \cdot \frac{1}{16} = \frac{32}{15 \cdot 16} = \frac{2}{15}\)

Ответ: 2/15

и) \(1\frac{3}{4} \cdot \frac{1}{14} = \frac{1 \cdot 4 + 3}{4} \cdot \frac{1}{14} = \frac{7}{4} \cdot \frac{1}{14} = \frac{7}{4 \cdot 14} = \frac{1}{4 \cdot 2} = \frac{1}{8}\)

Ответ: 1/8

к) \(5\frac{5}{8} \cdot 2\frac{2}{3} = \frac{5 \cdot 8 + 5}{8} \cdot \frac{2 \cdot 3 + 2}{3} = \frac{45}{8} \cdot \frac{8}{3} = \frac{45 \cdot 8}{8 \cdot 3} = \frac{45}{3} = 15\)

Ответ: 15

л) \(\frac{5}{16} \cdot \frac{12}{13} \cdot \frac{13}{24} \cdot \frac{16}{25} = \frac{5 \cdot 12 \cdot 13 \cdot 16}{16 \cdot 13 \cdot 24 \cdot 25} = \frac{5 \cdot 12}{24 \cdot 25} = \frac{5 \cdot 1}{2 \cdot 25} = \frac{5}{50} = \frac{1}{10}\)

Ответ: 1/10