4.209. Выполните деление: 11 A) 3:2- 23 E) 5:32 4 3 Й) 103:123 5 30 0) 3:27 :- 12

Решение:

A) $$3\frac{1}{2}:2\frac{1}{3}=\frac{3 \cdot 2+1}{2}:\frac{2 \cdot 3+1}{3}=\frac{7}{2}:\frac{7}{3}=\frac{7}{2} \cdot \frac{3}{7}=\frac{7 \cdot 3}{2 \cdot 7}=\frac{3}{2}=1\frac{1}{2}$$

E) $$5\frac{2}{4}:3\frac{2}{3}=\frac{5 \cdot 4+2}{4}:\frac{3 \cdot 3+2}{3}=\frac{22}{4}:\frac{11}{3}=\frac{22}{4} \cdot \frac{3}{11}=\frac{22 \cdot 3}{4 \cdot 11}=\frac{2 \cdot 3}{4}=\frac{6}{4}=\frac{3}{2}=1\frac{1}{2}$$

Й) $$10\frac{3}{5}:1\frac{23}{30}=\frac{10 \cdot 5+3}{5}:\frac{1 \cdot 30+23}{30}=\frac{53}{5}:\frac{53}{30}=\frac{53}{5} \cdot \frac{30}{53}=\frac{53 \cdot 30}{5 \cdot 53}=\frac{30}{5}=6$$

O) $$3\frac{3}{11}:\frac{27}{44}=\frac{3 \cdot 11+3}{11}:\frac{27}{44}=\frac{36}{11}:\frac{27}{44}=\frac{36}{11} \cdot \frac{44}{27}=\frac{36 \cdot 44}{11 \cdot 27}=\frac{4 \cdot 4}{3}=\frac{16}{3}=5\frac{1}{3}$$

Ответ: A) $$1\frac{1}{2}$$, E) $$1\frac{1}{2}$$, Й) $$6$$, O) $$5\frac{1}{3}$$