ГДЗ по Математике 5 Класс Часть 2 Номер 326 Петерсон — Подробные Ответы

Легенда рассказывает, что в древности великий Архимед соорудил систему блоков, с помощью которой один человек смог спустить на воду огромный корабль «Сиракосия». Крылатыми стали произнесённые тогда слова Архимеда. Расшифруй их. (Буквы соответствуют полученным значениям х.)

При

$a = \frac{1}{6}$

:

$$\frac{1}{6} + \frac{5}{12} = \frac{2}{12} + \frac{5}{12} = \frac{7}{12} \leq 2 \frac{1}{3}$$

$$\frac{7}{12} + \frac{1}{4} = \frac{7}{12} + \frac{3}{12} = \frac{10}{12} = \frac{5}{6}$$

При

$a = \frac{1}{3}$

:

$$\frac{1}{3} + \frac{5}{12} = \frac{4}{12} + \frac{5}{12} = \frac{9}{12} = \frac{3}{4} \leq 2 \frac{1}{3}$$

$$\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$$

При

$a = \frac{1}{2}$

:

$$\frac{1}{2} + \frac{5}{12} = \frac{6}{12} + \frac{5}{12} = \frac{11}{12} \leq 2 \frac{1}{3}$$

$$\frac{11}{12} + 1 = \frac{11}{12} + \frac{3}{12} = \frac{14}{12} = 1 \frac{1}{6}$$

При

$a = \frac{7}{12}$

:

$$\frac{7}{12} + \frac{5}{12} = \frac{12}{12} = 1 \leq 2 \frac{1}{3}$$

$$1 + \frac{1}{4} = \frac{5}{4} = 1 \frac{1}{4}$$

при

$a = \frac{5}{8}$

:

$$\frac{5}{8} + \frac{5}{12} = \frac{15}{24} + \frac{10}{24} = \frac{25}{24} = 1 \frac{1}{24} \leq 2 \frac{1}{3} \Rightarrow \text{подходит}$$

$$1 \frac{1}{24} + \frac{1}{4} = \frac{6}{24} + \frac{1}{24} = \frac{7}{24} + 1 = 2 \frac{7}{24}$$

при

$a = \frac{3}{4}$

:

$$\frac{3}{4} + \frac{5}{12} = \frac{9}{12} + \frac{5}{12} = \frac{14}{12} = 1 \frac{1}{6} \leq 2 \frac{1}{3} \Rightarrow \text{подходит}$$

$$1 \frac{1}{6} + \frac{1}{4} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12} + 2 = 2 \frac{5}{12}$$

при

$a = 1 \frac{2}{3}$

:

$$1 \frac{2}{3} + \frac{5}{12} = \frac{8}{12} + \frac{5}{12} = \frac{13}{12} + 1 = 2 \frac{1}{12} \leq 2 \frac{1}{3} \Rightarrow \text{подходит}$$

$$2 \frac{1}{12} + \frac{1}{4} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12} + 3 = 3 \frac{5}{12}$$

при

$a = \frac{5}{6}$

:

$$\frac{5}{6} + \frac{5}{12} = \frac{10}{12} + \frac{5}{12} = \frac{15}{12} = 1 \frac{1}{4} \leq 2 \frac{1}{3} \Rightarrow \text{подходит}$$

$$2 \frac{1}{4} + \frac{1}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} + 2 = 3 \frac{1}{2}$$

при

$a = 1 \frac{11}{12}$

:

$$1 \frac{11}{12} + \frac{5}{12} = \frac{16}{12} + 1 = 2 \frac{1}{3} \leq 2 \frac{1}{3} \Rightarrow \text{подходит}$$

$$2 \frac{1}{3} + \frac{1}{2} = \frac{4}{12} + \frac{3}{12} + 3 = 3 \frac{7}{12}$$

при

$a = 2$

:

$$2 + \frac{5}{12} = 2 \frac{5}{12} > 2 \frac{1}{3} \Rightarrow \text{не подходит}$$

$$2 \frac{5}{12} — \frac{5}{6} = \frac{17}{12} — \frac{10}{12} = \frac{7}{12}$$

при

$a = \frac{23}{24}$

:

$$\frac{23}{24} + \frac{5}{12} = \frac{10}{24} + \frac{23}{24} = \frac{33}{24} = 1 \frac{9}{24} = 2 \frac{9}{24} > 2 \frac{1}{3} \Rightarrow \text{не подходит}$$

$$2\frac{19}{24}-\frac{5}{6}=\frac{43}{24}-\frac{20}{24}=\frac{23}{24}$$

при

$a = 2 \frac{4}{9}$

:

$$\frac{4}{9} + \frac{5}{12} = \frac{16}{36} + \frac{15}{36} = \frac{31}{36}, \quad 2 \frac{31}{36} > 2 \frac{1}{3} \Rightarrow \text{нет}$$

$$2 \frac{31}{36} — \frac{5}{6} = \frac{31}{36} — \frac{30}{36} = \frac{1}{36}$$

при

$a = 2 \frac{7}{12}$

:

$$\frac{7}{12} + \frac{5}{12} = \frac{12}{12} = 1, \quad 2 + 1 = 3 > 2 \frac{1}{3} \Rightarrow \text{нет}$$

$$3 — \frac{5}{6} = \frac{18 — 5}{6} = \frac{13}{6} = 2 \frac{1}{6}$$

при

$a = 3 \frac{1}{2}$

:

$$\frac{1}{2} + \frac{5}{12} = \frac{6 + 5}{12} = \frac{11}{12}, \quad 3 + \frac{11}{12} = 3 \frac{11}{12} > 2 \frac{1}{3} \Rightarrow \text{нет}$$

$$3 \frac{11}{12} — \frac{5}{6} = \frac{11}{12} — \frac{10}{12} = \frac{1}{12}, \quad 3 + \frac{1}{12} = 3 \frac{1}{12}$$

при

$a = 3 \frac{3}{4}$

:

$$\frac{3}{4} + \frac{5}{12} = \frac{9 + 5}{12} = \frac{14}{12} = 1 \frac{1}{6}, \quad 3 + \frac{7}{6} = 4 \frac{1}{6} > 2 \frac{1}{3} \Rightarrow \text{нет}$$

$$4 \frac{1}{6} — \frac{5}{6} = \frac{25 — 5}{6} = \frac{20}{6} = 3 \frac{1}{3}$$

при

$a = 3 \frac{7}{8}$

:

$$\frac{7}{8} + \frac{5}{12} = \frac{21 + 10}{24} = \frac{31}{24}, \quad 3 + \frac{31}{24} = 4 \frac{7}{24} > 2 \frac{1}{3} \Rightarrow \text{нет}$$

$$4 \frac{7}{24} — \frac{5}{6} = \frac{103 — 20}{24} = \frac{83}{24} = 3 \frac{11}{24}$$

при

$a = 4 \frac{1}{12}$

:

$$\frac{1}{12} + \frac{5}{12} = \frac{6}{12} = \frac{1}{2}, \quad 4 + \frac{1}{2} = 4 \frac{1}{2} > 2 \frac{1}{3} \Rightarrow \text{нет}$$

$$4 \frac{1}{2} — \frac{5}{6} = \frac{27 — 10}{6} = \frac{17}{6} = 2 \frac{5}{6}$$

2 \frac{19}{24} — \frac{5}{6} = \frac{43}{24} — \frac{20}{24} = \frac{23}{24}

при

$a = 4 \frac{5}{8}$

:

$$\frac{5}{8} + \frac{5}{12} = \frac{15}{24} + \frac{10}{24} = \frac{25}{24},\quad 4 + \frac{25}{24} = 5 \frac{1}{24} > 2 \frac{1}{3} \Rightarrow \text{не подходит}$$

$$5 \frac{1}{24} — \frac{5}{6} = \frac{25}{24} — \frac{20}{24} = \frac{5}{24} + 3 = 3 \frac{5}{24}$$

при

$a = 5 \frac{7}{12}$

:

$$\frac{7}{12} + \frac{5}{12} = 1,\quad 5 + 1 = 6 > 2 \frac{1}{3} \Rightarrow \text{не подходит}$$

$$6 — \frac{5}{6} = 5 \frac{1}{6}$$

при

$a = 5 \frac{3}{4}$

:

$$\frac{3}{4} + \frac{5}{12} = \frac{9}{12} + \frac{5}{12} = \frac{14}{12},\quad 5 + \frac{14}{12} = 6 \frac{1}{6} > 2 \frac{1}{3} \Rightarrow \text{не подходит}$$

$$6 \frac{1}{6} — \frac{5}{6} = \frac{37}{6} — \frac{5}{6} = \frac{32}{6} = 5 \frac{1}{3}$$

при a = 1/6:
1/6 + 5/12 = 2/12 + 5/12 = 7/12, 7/12 ≤ 2 1/3 — да
7/12 + 1/4 = 7/12 + 3/12 = 10/12 = 5/6

при a = 1/3:
1/3 + 5/12 = 4/12 + 5/12 = 9/12 = 3/4, 3/4 ≤ 2 1/3 — да
3/4 + 1/4 = 1

при a = 1/2:
1/2 + 5/12 = 6/12 + 5/12 = 11/12, 11/12 ≤ 2 1/3 — да
11/12 + 1 = 11/12 + 3/12 = 14/12 = 1 1/6

при a = 7/12:
7/12 + 5/12 = 12/12 = 1, 1 ≤ 2 1/3 — да
1 + 1/4 = 5/4 = 1 1/4

при a = 5/8:
5/8 + 5/12 = 15/24 + 10/24 = 25/24 = 1 1/24, 1 1/24 ≤ 2 1/3 — да
1 1/24 + 1/4 = 6/24 + 1/24 = 7/24, 1 + 7/24 = 2 7/24

при a = 3/4:
3/4 + 5/12 = 9/12 + 5/12 = 14/12 = 1 1/6, 1 1/6 ≤ 2 1/3 — да
1 1/6 + 1/4 = 2/12 + 3/12 = 5/12, 2 + 5/12 = 2 5/12

при a = 1 2/3:
1 2/3 + 5/12 = 8/12 + 5/12 = 13/12, 1 + 13/12 = 2 1/12 ≤ 2 1/3 — да
2 1/12 + 1/4 = 2/12 + 3/12 = 5/12, 3 + 5/12 = 3 5/12

при a = 5/6:
5/6 + 5/12 = 10/12 + 5/12 = 15/12 = 1 1/4, 2 1/4 ≤ 2 1/3 — да
2 1/4 + 1/4 = 2/4 + 3/4 = 5/4, 2 + 1 1/2 = 3 1/2

при a = 1 11/12:
1 11/12 + 5/12 = 16/12 + 1 = 2 1/3 ≤ 2 1/3 — да
2 1/3 + 1/2 = 4/12 + 3/12 = 7/12, 3 + 7/12 = 3 7/12

при a = 2:
2 + 5/12 = 2 5/12 > 2 1/3 — нет
2 5/12 − 5/6 = 17/12 − 10/12 = 7/12

при a = 23/24:
23/24 + 5/12 = 10/24 + 23/24 = 33/24 = 1 9/24, 2 9/24 > 2 1/3 — нет
2 19/24 − 5/6 = 43/24 − 20/24 = 23/24

при a = 2 4/9:
4/9 + 5/12 = 16/36 + 15/36 = 31/36, 2 31/36 > 2 1/3 — нет
2 31/36 − 5/6 = 31/36 − 30/36 = 1/36

при a = 2 7/12:
7/12 + 5/12 = 12/12 = 1, 2 + 1 = 3 > 2 1/3 — нет
3 − 5/6 = 18/6 − 5/6 = 13/6 = 2 1/6

при a = 3 1/2:
1/2 + 5/12 = 6/12 + 5/12 = 11/12, 3 + 11/12 = 3 11/12 > 2 1/3 — нет
3 11/12 − 5/6 = 11/12 − 10/12 = 1/12, 3 + 1/12 = 3 1/12

при a = 3 3/4:
3/4 + 5/12 = 9/12 + 5/12 = 14/12 = 1 1/6, 3 + 7/6 = 4 1/6 > 2 1/3 — нет
4 1/6 − 5/6 = 25/6 − 5/6 = 20/6 = 3 1/3

при a = 3 7/8:
7/8 + 5/12 = 21/24 + 10/24 = 31/24, 3 + 31/24 = 4 7/24 > 2 1/3 — нет
4 7/24 − 5/6 = 103/24 − 20/24 = 83/24 = 3 11/24

при a = 4 1/12:
1/12 + 5/12 = 6/12 = 1/2, 4 + 1/2 = 4 1/2 > 2 1/3 — нет
4 1/2 − 5/6 = 27/6 − 10/6 = 17/6 = 2 5/6

при a = 4 5/8:
5/8 + 5/12 = 15/24 + 10/24 = 25/24, 4 + 25/24 = 5 1/24 > 2 1/3 — нет
5 1/24 − 5/6 = 25/24 − 20/24 = 5/24, 3 + 5/24 = 3 5/24

при a = 5 7/12:
7/12 + 5/12 = 12/12 = 1, 5 + 1 = 6 > 2 1/3 — нет
6 − 5/6 = 5 1/6

при a = 5 3/4:
3/4 + 5/12 = 9/12 + 5/12 = 14/12, 5 + 14/12 = 6 1/6 > 2 1/3 — нет
6 1/6 − 5/6 = 37/6 − 5/6 = 32/6 = 5 1/3