ГДЗ по Математике 6 Класс Вариант 4 Номер 56 Мерзляк, Полонский — Подробные Ответы

Преобразуйте десятичные дроби в обыкновенные и вычислите:

1) \(\frac{7}{9} — 0,6\);

2) \(0,34 + \frac{8}{11}\);

3) \(7 \frac{5}{36} — 4,55\);

4) \(5,375 — 1 \frac{3}{19}\).

1)
\[
\frac{7}{9} — 0{,}6 = \frac{8}{45}
\]

2)
\[
0{,}34 + \frac{8}{11} = 1 \frac{37}{550}
\]

3)
\[
7 \frac{5}{36} — 4{,}55 = 2 \frac{53}{90}
\]

4)
\[
5{,}375 — 1 \frac{3}{19} = 4 \frac{33}{152}
\]

1)
\[
0{,}6 = \frac{6}{10} = \frac{3}{5}
\]

\[
\frac{7}{9} — \frac{3}{5}
\]

\[
\frac{7 \cdot 5}{9 \cdot 5} — \frac{3 \cdot 9}{5 \cdot 9}
\]

\[
\frac{35}{45} — \frac{27}{45}
\]

\[
\frac{8}{45}
\]

2)
\[
0{,}34 = \frac{34}{100}
\]

\[
\frac{34}{100} + \frac{8}{11}
\]

\[
\frac{34 \cdot 11}{100 \cdot 11} + \frac{8 \cdot 100}{11 \cdot 100}
\]

\[
\frac{374}{1100} + \frac{800}{1100}
\]

\[
\frac{1174}{1100}
\]

\[
1 \frac{74}{1100}
\]

\[
1 \frac{37}{550}
\]

3)
\[
4{,}55 = \frac{455}{100}
\]

\[
7 \frac{5}{36} = \frac{7 \cdot 36 + 5}{36} = \frac{257}{36}
\]

\[
\frac{257}{36} — \frac{455}{100}
\]

\[
\frac{257 \cdot 25}{36 \cdot 25} — \frac{455 \cdot 9}{100 \cdot 9}
\]

\[
\frac{6425}{900} — \frac{4095}{900}
\]

\[
\frac{2330}{900}
\]

\[
\frac{233}{90}
\]

\[
2 \frac{53}{90}
\]

4)
\[
5{,}375 = \frac{5375}{1000}
\]

\[
\frac{5375}{1000} = \frac{43}{8}
\]

\[
1 \frac{3}{19} = \frac{22}{19}
\]

\[
\frac{43}{8} — \frac{22}{19}
\]

\[
\frac{43 \cdot 19}{8 \cdot 19} — \frac{22 \cdot 8}{19 \cdot 8}
\]

\[
\frac{817}{152} — \frac{176}{152}
\]

\[
\frac{641}{152}
\]

\[
4 \frac{33}{152}
\]