ГДЗ по Математике 6 Класс Вариант 3 Номер 47 Мерзляк, Полонский — Подробные Ответы

Вычислите:

1) \( \frac{3}{4} + \frac{5}{7} \)

2) \( \frac{9}{14} — \frac{3}{4} \)

3) \( \frac{11}{12} — \frac{2}{3} \)

4) \( \frac{7}{25} + \frac{4}{10} \)

5) \( \frac{11}{18} — \frac{5}{12} \)

6) \( \frac{13}{18} + \frac{7}{15} \)

7) \( \frac{19}{24} — \frac{25}{36} \)

8) \( \frac{5}{6} — \frac{3}{4} + \frac{5}{24} \)

9) \( \frac{5}{8} + \frac{11}{28} — \frac{9}{14} \)

1) \( \frac{3}{4} + \frac{5}{7} = \frac{21}{28} + \frac{20}{28} = \frac{41}{28} = 1\frac{13}{28} \)

2) \( \frac{9}{14} — \frac{3}{4} = \frac{18}{28} — \frac{21}{28} = -\frac{3}{28} \)

3) \( \frac{11}{12} — \frac{2}{3} = \frac{11}{12} — \frac{8}{12} = \frac{3}{12} = \frac{1}{4} \)

4) \( \frac{7}{25} + \frac{4}{10} = \frac{7}{25} + \frac{2}{5} = \frac{7}{25} + \frac{10}{25} = \frac{17}{25} \)

5) \( \frac{11}{18} — \frac{5}{12} = \frac{22}{36} — \frac{15}{36} = \frac{7}{36} \)

6) \( \frac{13}{18} + \frac{7}{15} = \frac{65}{90} + \frac{42}{90} = \frac{107}{90} = 1\frac{17}{90} \)

7) \( \frac{19}{24} — \frac{25}{36} = \frac{57}{72} — \frac{50}{72} = \frac{7}{72} \)

8) \( \frac{5}{6} — \frac{3}{4} + \frac{5}{24} = \frac{20}{24} — \frac{18}{24} + \frac{5}{24} = \frac{7}{24} \)

9) \( \frac{5}{8} + \frac{11}{28} — \frac{9}{14} = \frac{35}{56} + \frac{22}{56} — \frac{36}{56} = \frac{21}{56} = \frac{3}{8} \)

1) \( \frac{3}{4} + \frac{5}{7} \)

\[
\frac{3}{4} = \frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28}, \quad
\frac{5}{7} = \frac{5 \cdot 4}{7 \cdot 4} = \frac{20}{28}
\]

\[
\frac{21}{28} + \frac{20}{28} = \frac{41}{28} = 1\frac{13}{28}
\]

Ответ:\( 1\frac{13}{28} \)

2) \( \frac{9}{14} — \frac{3}{4} \)

\[
\frac{9}{14} = \frac{9 \cdot 2}{14 \cdot 2} = \frac{18}{28}, \quad
\frac{3}{4} = \frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28}
\]

\[
\frac{18}{28} — \frac{21}{28} = -\frac{3}{28}
\]

Ответ:\( -\frac{3}{28} \)

3)\( \frac{11}{12} — \frac{2}{3} \)

\[
\frac{2}{3} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12}
\]

\[
\frac{11}{12} — \frac{8}{12} = \frac{3}{12} = \frac{1}{4}
\]

Ответ: \( \frac{1}{4} \)

4) \( \frac{7}{25} + \frac{4}{10} \)

\[
\frac{4}{10} = \frac{2}{5}, \quad
\frac{2}{5} = \frac{2 \cdot 5}{5 \cdot 5} = \frac{10}{25}
\]

\[
\frac{7}{25} + \frac{10}{25} = \frac{17}{25}
\]

Ответ:\( \frac{17}{25} \)

5)\( \frac{11}{18} — \frac{5}{12} \)

\[
\frac{11}{18} = \frac{11 \cdot 2}{18 \cdot 2} = \frac{22}{36}, \quad
\frac{5}{12} = \frac{5 \cdot 3}{12 \cdot 3} = \frac{15}{36}
\]

\[
\frac{22}{36} — \frac{15}{36} = \frac{7}{36}
\]

Ответ:\( \frac{7}{36} \)

6) \( \frac{13}{18} + \frac{7}{15} \)

\[
\frac{13}{18} = \frac{13 \cdot 5}{18 \cdot 5} = \frac{65}{90}, \quad
\frac{7}{15} = \frac{7 \cdot 6}{15 \cdot 6} = \frac{42}{90}
\]

\[
\frac{65}{90} + \frac{42}{90} = \frac{107}{90} = 1\frac{17}{90}
\]

Ответ: \( 1\frac{17}{90} \)

7)\( \frac{19}{24} — \frac{25}{36} \)

\[
\frac{19}{24} = \frac{19 \cdot 3}{24 \cdot 3} = \frac{57}{72}, \quad
\frac{25}{36} = \frac{25 \cdot 2}{36 \cdot 2} = \frac{50}{72}
\]

\[
\frac{57}{72} — \frac{50}{72} = \frac{7}{72}
\]

Ответ: \( \frac{7}{72} \)

8) \( \frac{5}{6} — \frac{3}{4} + \frac{5}{24} \)

\[
\frac{5}{6} = \frac{5 \cdot 4}{6 \cdot 4} = \frac{20}{24}, \quad
\frac{3}{4} = \frac{3 \cdot 6}{4 \cdot 6} = \frac{18}{24}
\]

\[
\frac{20}{24} — \frac{18}{24} + \frac{5}{24} = \frac{7}{24}
\]

Ответ: \( \frac{7}{24} \)

9) \( \frac{5}{8} + \frac{11}{28} — \frac{9}{14} \)

\[
\frac{5}{8} = \frac{5 \cdot 7}{8 \cdot 7} = \frac{35}{56}, \quad
\frac{11}{28} = \frac{11 \cdot 2}{28 \cdot 2} = \frac{22}{56}, \quad
\frac{9}{14} = \frac{9 \cdot 4}{14 \cdot 4} = \frac{36}{56}
\]

\[
\frac{35}{56} + \frac{22}{56} — \frac{36}{56} = \frac{21}{56} = \frac{3}{8}
\]

\( \frac{3}{8} \)

Окончательные ответы:

\[
\begin{array}{ll}
1)\ 1\frac{13}{28} & 4)\ \frac{17}{25} & 7)\ \frac{7}{72} \\
2)\ -\frac{3}{28} & 5)\ \frac{7}{36} & 8)\ \frac{7}{24} \\
3)\ \frac{1}{4} & 6)\ 1\frac{17}{90} & 9)\ \frac{3}{8} \\
\end{array}
\]