Упр.1031 ГДЗ Ткачёва 5 класс (Математика)
1) 6/7 : (1 2/7 + 2 1/7); 2) (1 1/2 + 1 1/4) : 2 1/2;
3) (3 5/12 — 1 1/4) : 1 5/12; 4) (5 8/15 — 2 1/3) : 8/15;
5) (3/8 — 1/6) : (1 1/4 — 5/6); 6) (2/5 + 3/10) : (1 1/15 — 7/10);
7) (2 3/5 + 2/3) : (14/15 — 2/3); 8) (3 1/6 — 1 1/2) : (11/12 — 3/4).
1) $$\frac{6}{7} : \left(1\frac{2}{7} + 2\frac{1}{7}\right) = \frac{6}{7} : 3\frac{3}{7} = \frac{6}{7} : \frac{24}{7} = \frac{6}{7} \cdot \frac{7}{24} = \frac{1}{4}.$$
2) $$\left(1\frac{1}{2} + 1\frac{1}{4}\right) : 2\frac{1}{2} = 2\frac{3}{4} : \frac{5}{2} = \frac{11}{4} \cdot \frac{2}{5} = \frac{11}{10} = 1\frac{1}{10}.$$
3) $$\left(3\frac{5}{12} — 1\frac{1}{4}\right) : 1\frac{5}{12} = \left(3\frac{5}{12} — 1\frac{3}{12}\right) : \frac{17}{12} = 2\frac{2}{12} : \frac{17}{12} = \frac{26}{12} \cdot \frac{12}{17} = \frac{26}{17} = 1\frac{9}{17}.$$
4) $$\left(5\frac{8}{15} — 2\frac{1}{3}\right) : \frac{8}{15} = \left(5\frac{8}{15} — 2\frac{5}{15}\right) : \frac{8}{15} = 3\frac{3}{15} : \frac{8}{15} = \frac{48}{15} \cdot \frac{15}{8} = 6.$$
5) $$\left(\frac{3}{8} — \frac{1}{6}\right) : \left(1\frac{1}{4} — \frac{5}{6}\right) = \left(\frac{9}{24} — \frac{4}{24}\right) : \left(\frac{15}{12} — \frac{10}{12}\right) = \frac{5}{24} : \frac{5}{12} = \frac{5}{24} \cdot \frac{12}{5} = \frac{1}{2}.$$
6) $$\left(\frac{2}{5} + \frac{3}{10}\right) : \left(1\frac{1}{15} — \frac{7}{10}\right) = \left(\frac{4}{10} + \frac{3}{10}\right) : \left(\frac{16}{15} — \frac{21}{30}\right) = \frac{7}{10} : \frac{11}{30} = \frac{7}{10} \cdot \frac{30}{11} = \frac{21}{11} = 1\frac{10}{11}.$$
7) $$\left(2\frac{3}{5} + \frac{2}{3}\right) : \left(\frac{14}{15} — \frac{2}{3}\right) = \left(2\frac{9}{15} + \frac{10}{15}\right) : \left(\frac{14}{15} — \frac{10}{15}\right) = 3\frac{4}{15} : \frac{4}{15} = \frac{49}{15} \cdot \frac{15}{4} = \frac{49}{4} = 12\frac{1}{4}.$$
8) $$\left(3\frac{1}{6} — 1\frac{1}{2}\right) : \left(\frac{11}{12} — \frac{3}{4}\right) = \left(3\frac{2}{12} — 1\frac{6}{12}\right) : \left(\frac{11}{12} — \frac{9}{12}\right) = 1\frac{8}{12} : \frac{2}{12} = 1\frac{2}{3} : \frac{1}{6} = \frac{5}{3} \cdot 6 = 10.$$
Ответ
1) $$\frac{1}{4}$$; 2) $$1\frac{1}{10}$$; 3) $$1\frac{9}{17}$$; 4) $$6$$; 5) $$\frac{1}{2}$$; 6) $$1\frac{10}{11}$$; 7) $$12\frac{1}{4}$$; 8) $$10$$.
