Упр.921 ГДЗ Мерзляк Полонский 5 класс (Математика)
- Вычислите: 1) $$6\frac{4}{9}+3\frac{5}{9}$$; 2) $$10\frac{11}{19}+5\frac{14}{19}$$; 3) $$2\frac{3}{13}+2\frac{11}{13}$$; 4) $$1\frac{5}{8}+3\frac{7}{8}$$; 5) $$1-\frac{3}{11}$$; 6) $$1-\frac{13}{40}$$; 7) $$4-1\frac{4}{7}$$; 8) $$10-9\frac{3}{10}$$; 9) $$5\frac{2}{7}-2\frac{5}{7}$$; 10) $$14\frac{6}{20}-8\frac{12}{20}$$; 11) $$8\frac{3}{14}-5\frac{9}{14}$$; 12) $$7\frac{10}{21}-4\frac{16}{21}$$; 13) $$14\frac{8}{31}-6\frac{8}{31}$$; 14) $$\left(12\frac{5}{22}+7\frac{17}{22}\right)-\left(13\frac{7}{23}-9\frac{15}{23}\right)$$.
- Вычислите площадь теннисного корта, длина и ширина которого равны $$23{,}75\ \text{м}$$ и $$10{,}92\ \text{м}$$. Округлите ответ до единиц.
1) $$6 \frac{4}{9} + 3 \frac{5}{9} = (6+3) + \left(\frac{4}{9}+\frac{5}{9}\right) = 9 + \frac{9}{9} = 9 + 1 = 10.$$
2) $$10 \frac{11}{19} + 5 \frac{14}{19} = (10+5) + \left(\frac{11}{19}+\frac{14}{19}\right) = 15 + \frac{25}{19} = 15 + 1 \frac{6}{19} = 16 \frac{6}{19}.$$
3) $$2 \frac{3}{13} + 2 \frac{11}{13} = (2+2) + \left(\frac{3}{13}+\frac{11}{13}\right) = 4 + \frac{14}{13} = 4 + 1 \frac{1}{13} = 5 \frac{1}{13}.$$
4) $$1 \frac{5}{8} + 3 \frac{7}{8} = (1+3) + \left(\frac{5}{8}+\frac{7}{8}\right) = 4 + \frac{12}{8} = 4 + 1 \frac{4}{8} = 5 \frac{4}{8} = 5 \frac{1}{2}.$$
5) $$1 — \frac{3}{11} = \frac{11}{11} — \frac{3}{11} = \frac{8}{11}.$$
6) $$1 — \frac{13}{40} = \frac{40}{40} — \frac{13}{40} = \frac{27}{40}.$$
7) $$4 — 1 \frac{4}{7} = 3 \frac{7}{7} — 1 \frac{4}{7} = (3-1) + \left(\frac{7}{7}-\frac{4}{7}\right) = 2 + \frac{3}{7} = 2 \frac{3}{7}.$$
8) $$10 — 9 \frac{3}{10} = 9 \frac{10}{10} — 9 \frac{3}{10} = (9-9) + \left(\frac{10}{10}-\frac{3}{10}\right) = \frac{7}{10}.$$
9) $$5 \frac{2}{7} — 2 \frac{5}{7} = 4 \frac{9}{7} — 2 \frac{5}{7} = (4-2) + \left(\frac{9}{7}-\frac{5}{7}\right) = 2 + \frac{4}{7} = 2 \frac{4}{7}.$$
10) $$14 \frac{6}{20} — 8 \frac{12}{20} = 13 \frac{26}{20} — 8 \frac{12}{20} = (13-8) + \left(\frac{26}{20}-\frac{12}{20}\right) = 5 + \frac{14}{20} = 5 \frac{14}{20} = 5 \frac{7}{10}.$$
11) $$8 \frac{3}{14} — 5 \frac{9}{14} = 7 \frac{17}{14} — 5 \frac{9}{14} = (7-5) + \left(\frac{17}{14}-\frac{9}{14}\right) = 2 + \frac{8}{14} = 2 \frac{4}{7}.$$
12) $$7 \frac{10}{21} — 4 \frac{16}{21} = 6 \frac{31}{21} — 4 \frac{16}{21} = (6-4) + \left(\frac{31}{21}-\frac{16}{21}\right) = 2 + \frac{15}{21} = 2 \frac{5}{7}.$$
13) $$14 \frac{8}{31} — 6 \frac{8}{31} = (14-6) + \left(\frac{8}{31}-\frac{8}{31}\right) = 8 + 0 = 8.$$
14) $$\left(12 \frac{5}{22} + 7 \frac{17}{22}\right) — \left(13 \frac{7}{23} — 9 \frac{15}{23}\right)$$
$$= \left(19 + \frac{22}{22}\right) — \left(13 \frac{7}{23} — 9 \frac{15}{23}\right) = 20 — \left(13 \frac{7}{23} — 9 \frac{15}{23}\right).$$
$$13 \frac{7}{23} — 9 \frac{15}{23} = 12 \frac{30}{23} — 9 \frac{15}{23} = (12-9) + \left(\frac{30}{23}-\frac{15}{23}\right) = 3 \frac{15}{23}.$$
Тогда
$$20 — 3 \frac{15}{23} = 19 \frac{23}{23} — 3 \frac{15}{23} = (19-3) + \left(\frac{23}{23}-\frac{15}{23}\right) = 16 + \frac{8}{23} = 16 \frac{8}{23}.$$
Ответ
1) $$10$$; 2) $$16 \frac{6}{19}$$; 3) $$5 \frac{1}{13}$$; 4) $$5 \frac{1}{2}$$; 5) $$\frac{8}{11}$$; 6) $$\frac{27}{40}$$; 7) $$2 \frac{3}{7}$$; 8) $$\frac{7}{10}$$; 9) $$2 \frac{4}{7}$$; 10) $$5 \frac{7}{10}$$; 11) $$2 \frac{4}{7}$$; 12) $$2 \frac{5}{7}$$; 13) $$8$$; 14) $$16 \frac{8}{23}$$.
