ГДЗ по Математике 6 Класс Вариант 1 Номер 47 Мерзляк, Полонский — Подробные Ответы

Вычислите:

1) \( \frac{2}{3} + \frac{5}{8} = \frac{16}{24} + \frac{15}{24} = \frac{31}{24} = 1 \frac{7}{24} \)

2) \( \frac{7}{12} — \frac{3}{8} = \frac{14}{24} — \frac{9}{24} = \frac{5}{24} \)

3) \( \frac{11}{16} — \frac{5}{8} = \frac{11}{16} — \frac{10}{16} = \frac{1}{16} \)

4) \( \frac{6}{35} + \frac{3}{10} = \frac{12}{70} + \frac{21}{70} = \frac{33}{70} \)

5) \( \frac{8}{15} — \frac{4}{9} = \frac{24}{45} — \frac{20}{45} = \frac{4}{45} \)

6) \( \frac{4}{15} + \frac{7}{12} = \frac{16}{60} + \frac{35}{60} = \frac{51}{60} \)

7) \( \frac{11}{48} — \frac{5}{36} = \frac{33}{144} — \frac{20}{144} = \frac{13}{144} \)

8) \( \frac{4}{5} — \frac{2}{3} + \frac{4}{15} = \frac{12}{15} — \frac{10}{15} + \frac{4}{15} = \frac{2}{15} + \frac{4}{15} = \frac{6}{15} = \frac{2}{5} \)

9) \( \frac{7}{8} + \frac{11}{12} — \frac{5}{6} = \frac{21}{24} + \frac{22}{24} — \frac{20}{24} = \frac{43}{24} — \frac{20}{24} = \frac{23}{24} \)

1) $\frac{2}{3} + \frac{5}{8}$

Находим наименьший общий знаменатель (НОК) для 3 и 8:
$\text{НОК}(3, 8) = 24$

Приводим дроби к общему знаменателю:

$$\frac{2}{3} = \frac{16}{24}, \quad \frac{5}{8} = \frac{15}{24}$$

Складываем:

$$\frac{16}{24} + \frac{15}{24} = \frac{31}{24} = 1 \frac{7}{24}$$

2) $\frac{7}{12} — \frac{3}{8}$

Находим НОК(12, 8) = 24

$$\frac{7}{12} = \frac{14}{24}, \quad \frac{3}{8} = \frac{9}{24}$$

$$\frac{14}{24} — \frac{9}{24} = \frac{5}{24}$$

3) $\frac{11}{16} — \frac{5}{8}$

Приведём к общему знаменателю:

$$\frac{5}{8} = \frac{10}{16}$$

$$\frac{11}{16} — \frac{10}{16} = \frac{1}{16}$$

4) $\frac{6}{35} + \frac{3}{10}$

НОК(35, 10) = 70

$$\frac{6}{35} = \frac{12}{70}, \quad \frac{3}{10} = \frac{21}{70}$$

$$\frac{12}{70} + \frac{21}{70} = \frac{33}{70}$$

5) $\frac{8}{15} — \frac{4}{9}$

НОК(15, 9) = 45

$$\frac{8}{15} = \frac{24}{45}, \quad \frac{4}{9} = \frac{20}{45}$$

$$\frac{24}{45} — \frac{20}{45} = \frac{4}{45}$$

6) $\frac{4}{15} + \frac{7}{12}$

НОК(15, 12) = 60

$$\frac{4}{15} = \frac{16}{60}, \quad \frac{7}{12} = \frac{35}{60}$$

$$\frac{16}{60} + \frac{35}{60} = \frac{51}{60}$$

7) $\frac{11}{48} — \frac{5}{36}$

НОК(48, 36) = 144

$$\frac{11}{48} = \frac{33}{144}, \quad \frac{5}{36} = \frac{20}{144}$$

$$\frac{33}{144} — \frac{20}{144} = \frac{13}{144}$$

8) $\frac{4}{5} — \frac{2}{3} + \frac{4}{15}$

НОК(5, 3, 15) = 15

$$\frac{4}{5} = \frac{12}{15}, \quad \frac{2}{3} = \frac{10}{15}, \quad \frac{4}{15} = \frac{4}{15}$$

$$12 — 10 + 4 = 6 \Rightarrow \frac{6}{15} = \frac{2}{5}$$

9) $\frac{7}{8} + \frac{11}{12} — \frac{5}{6}$

НОК(8, 12, 6) = 24

$$\frac{7}{8} = \frac{21}{24}, \quad \frac{11}{12} = \frac{22}{24}, \quad \frac{5}{6} = \frac{20}{24}$$

$$21 + 22 = 43, \quad 43 — 20 = \frac{23}{24}$$