Упр.65 Часть 1 ГДЗ Дорофеев Петерсон 6 класс (Математика)

1) 10 5/6 : 5 + 2 5/9 : (3 2/9 — 3 · 2/9) — 1 3/4;
2) 15/28 : [4 1/8 — 3 1/8 : (4 5/12 — 2 13/24) + 19 : 6].

1) Упростим выражение:

$$10\frac{5}{6}:5+2\frac{5}{9}:(3\frac{2}{9}-3\cdot\frac{2}{9})-1\frac{3}{4}$$

$$3\cdot\frac{2}{9}=\frac{2}{3}$$

$$3\frac{2}{9}-\frac{2}{3}=3\frac{2}{9}-\frac{6}{9}=2\frac{5}{9}$$

$$10\frac{5}{6}:5=\frac{65}{6}\cdot\frac{1}{5}=\frac{13}{6}=2\frac{1}{6}$$

$$2\frac{5}{9}:2\frac{5}{9}=1$$

$$2\frac{1}{6}+1=3\frac{1}{6}$$

$$3\frac{1}{6}-1\frac{3}{4}=3\frac{2}{12}-1\frac{9}{12}=2\frac{14}{12}-1\frac{9}{12}=1\frac{5}{12}$$

$$1\frac{5}{12}=1{,}4166\ldots \approx 1{,}4 \approx 1{,}42 \approx 1{,}417$$

2) Упростим выражение:

$$\frac{15}{28}:\left[4\frac{1}{8}-3\frac{1}{8}:(4\frac{5}{12}-2\frac{13}{24})+19:6\right]$$

$$4\frac{5}{12}-2\frac{13}{24}=4\frac{10}{24}-2\frac{13}{24}=3\frac{34}{24}-2\frac{13}{24}=1\frac{21}{24}=1\frac{7}{8}$$

$$3\frac{1}{8}:1\frac{7}{8}=\frac{25}{8}:\frac{15}{8}=\frac{25}{8}\cdot\frac{8}{15}=\frac{5}{3}=1\frac{2}{3}$$

$$19:6=\frac{19}{6}=3\frac{1}{6}$$

$$4\frac{1}{8}-1\frac{2}{3}+3\frac{1}{6}=4\frac{3}{24}-1\frac{16}{24}+3\frac{4}{24}=5\frac{5}{8}$$

$$\frac{15}{28}:5\frac{5}{8}=\frac{15}{28}:\frac{45}{8}=\frac{15}{28}\cdot\frac{8}{45}=\frac{2}{21}$$

$$\frac{2}{21}=0{,}095238\ldots \approx 0{,}1 \approx 0{,}10 \approx 0{,}095$$

Ответ

1) $$1{,}4$$; $$1{,}42$$; $$1{,}417$$.

2) $$0{,}1$$; $$0{,}10$$; $$0{,}095$$.