4. Решите пропорцию: a) 3$$\frac{2}{3}$$ : x = 5$$\frac{3}{4}$$ = 2$$\frac{11}{23}$$ : 5$$\frac{2}{11}$$; B) 4$$\frac{5}{7}$$ : x = 2$$\frac{1}{13}$$ = 2$$\frac{8}{9}$$ : 3$$\frac{3}{11}$$.

a) Решим пропорцию 3$$\frac{2}{3}$$ : x = 5$$\frac{3}{4}$$ = 2$$\frac{11}{23}$$ : 5$$\frac{2}{11}$$:

3$$\frac{2}{3}$$ = $$\frac{3 * 3 + 2}{3}$$ = $$\frac{11}{3}$$

5$$\frac{3}{4}$$ = $$\frac{5 * 4 + 3}{4}$$ = $$\frac{23}{4}$$

2$$\frac{11}{23}$$ = $$\frac{2 * 23 + 11}{23}$$ = $$\frac{57}{23}$$

5$$\frac{2}{11}$$ = $$\frac{5 * 11 + 2}{11}$$ = $$\frac{57}{11}$$

$$\frac{11}{3}$$ : x = $$\frac{23}{4}$$ = $$\frac{57}{23}$$ : $$\frac{57}{11}$$

$$\frac{11}{3}$$ : x = $$\frac{23}{4}$$ = $$\frac{57}{23}$$ * $$\frac{11}{57}$$

$$\frac{11}{3}$$ : x = $$\frac{23}{4}$$ = $$\frac{11}{23}$$

$$\frac{23}{4}$$ * x = $$\frac{11}{3}$$

x = $$\frac{\frac{11}{3}}{\frac{23}{4}}$$ = $$\frac{11}{3}$$ * $$\frac{4}{23}$$ = $$\frac{44}{69}$$

Ответ: x = $$\frac{44}{69}$$

b) Решим пропорцию 4$$\frac{5}{7}$$ : x = 2$$\frac{1}{13}$$ = 2$$\frac{8}{9}$$ : 3$$\frac{3}{11}$$:

4$$\frac{5}{7}$$ = $$\frac{4 * 7 + 5}{7}$$ = $$\frac{33}{7}$$

2$$\frac{1}{13}$$ = $$\frac{2 * 13 + 1}{13}$$ = $$\frac{27}{13}$$

2$$\frac{8}{9}$$ = $$\frac{2 * 9 + 8}{9}$$ = $$\frac{26}{9}$$

3$$\frac{3}{11}$$ = $$\frac{3 * 11 + 3}{11}$$ = $$\frac{36}{11}$$

$$\frac{33}{7}$$ : x = $$\frac{27}{13}$$ = $$\frac{26}{9}$$ : $$\frac{36}{11}$$

$$\frac{33}{7}$$ : x = $$\frac{27}{13}$$ = $$\frac{26}{9}$$ * $$\frac{11}{36}$$

$$\frac{33}{7}$$ : x = $$\frac{27}{13}$$ = $$\frac{13 * 11}{9 * 18}$$ = $$\frac{143}{162}$$

$$\frac{27}{13}$$ * x = $$\frac{33}{7}$$

x = $$\frac{\frac{33}{7}}{\frac{27}{13}}$$ = $$\frac{33}{7}$$ * $$\frac{13}{27}$$ = $$\frac{11 * 13}{7 * 9}$$ = $$\frac{143}{63}$$

Ответ: x = $$\frac{143}{63}$$