Question

460. 1) 4 1/2:2 1/4 2) 2 4/5:1 2/5 3) 7/9:2 1/3 4) 8 1/2:19/20 ​

Answer 1

Пошаговое объяснение:

1)

$4 \frac{1}{2} \div 2 \frac{1}{4} = \frac{1 + 4 \times 2}{2} \div \frac{1 + 2 \times 4}{4} = \frac{9}{2} \div \frac{9}{4} = \frac{9}{2} \times \frac{4}{9} = \frac{9 \times 4}{2 \times 9} = \frac{36}{18} = \frac{2 \times 18}{18} = 2$

2)

$2 \frac{4}{5} \div 1 \frac{2}{5} = \frac{4 + 2 \times 5}{5} \div \frac{2 + 1 \times 5}{5} = \frac{14}{5} \div \frac{7}{5} = \frac{14}{5} \times \frac{5}{7} = \frac{14 \times 5}{5 \times 7} = \frac{70}{35} = \frac{2 \times 35}{35} = 2$

3)

$\frac{7}{9} \div 2 \frac{1}{3} = \frac{7}{9} \div \frac{1 + 2 \times 3}{3} = \frac{7}{9} \div \frac{7}{3} = \frac{7}{9} \times \frac{3}{7} = \frac{7 \times 3}{9 \times 7} = \frac{21}{63} = \frac{1 \times 21}{3 \times 21} = \frac{1}{3}$

4)

$8 \frac{1}{2} \div \frac{19}{20} = \frac{1 + 8 \times 2}{2} \div \frac{19}{20} = \frac{17}{2} \div \frac{19}{20} = \frac{17}{2} \times \frac{20}{19} = \frac{17 \times 20}{2 \times 19} = \frac{340}{38} = \frac{170 \times 2}{19 \times 2} = \frac{170}{19} = \frac{8 \times 19 + 18}{19} = 8 \frac{18}{19}$