Карточка № 42. Сократите дроби 35 20 70 36 196 84 44.36 42' 25' 84' 72' 84' 56' 27.55 13.36.21 45.12.15 3.5+7.5 24.28.39'60.81·18' 25

Разберем дроби и сократим их:

1. $$\frac{35}{42} = \frac{5 \cdot 7}{6 \cdot 7} = \frac{5}{6}$$
2. $$\frac{20}{25} = \frac{4 \cdot 5}{5 \cdot 5} = \frac{4}{5}$$
3. $$\frac{70}{84} = \frac{5 \cdot 14}{6 \cdot 14} = \frac{5}{6}$$
4. $$\frac{36}{72} = \frac{1 \cdot 36}{2 \cdot 36} = \frac{1}{2}$$
5. $$\frac{196}{84} = \frac{14 \cdot 14}{6 \cdot 14} = \frac{14}{6} = \frac{7 \cdot 2}{3 \cdot 2} = \frac{7}{3} = 2\frac{1}{3}$$
6. $$\frac{84}{56} = \frac{12 \cdot 7}{8 \cdot 7} = \frac{12}{8} = \frac{4 \cdot 3}{4 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}$$
7. $$\frac{44 \cdot 36}{27 \cdot 55} = \frac{4 \cdot 11 \cdot 4 \cdot 9}{3 \cdot 9 \cdot 5 \cdot 11} = \frac{4 \cdot 4}{3 \cdot 5} = \frac{16}{15} = 1\frac{1}{15}$$
8. $$\frac{13 \cdot 36 \cdot 21}{24 \cdot 28 \cdot 39} = \frac{13 \cdot 12 \cdot 3 \cdot 7 \cdot 3}{12 \cdot 2 \cdot 7 \cdot 4 \cdot 13 \cdot 3} = \frac{3}{2 \cdot 4} = \frac{3}{8}$$
9. $$\frac{45 \cdot 12 \cdot 15}{60 \cdot 81 \cdot 18} = \frac{15 \cdot 3 \cdot 3 \cdot 4 \cdot 15}{15 \cdot 4 \cdot 9 \cdot 9 \cdot 2 \cdot 9} = \frac{3 \cdot 15}{9 \cdot 2 \cdot 9} = \frac{3 \cdot 3 \cdot 5}{9 \cdot 2 \cdot 9} = \frac{5}{2 \cdot 9} = \frac{5}{18}$$
10. $$\frac{3 \cdot 5 + 7 \cdot 5}{25} = \frac{5 \cdot (3 + 7)}{25} = \frac{5 \cdot 10}{5 \cdot 5} = \frac{10}{5} = 2$$

Ответ: $$\frac{5}{6}, \frac{4}{5}, \frac{5}{6}, \frac{1}{2}, 2\frac{1}{3}, 1\frac{1}{2}, 1\frac{1}{15}, \frac{3}{8}, \frac{5}{18}, 2$$