36. Сравните дроби (>, <, =).

Решение:

Для сравнения дробей приведём их к общему знаменателю или преобразуем в десятичные дроби.

Сравнение:

1. \(\frac{1}{3}\) ? \(\frac{1}{4}\) \(\implies 0.33... > 0.25\) → \(>\)
2. \(\frac{1}{5}\) ? \(\frac{1}{7}\) \(\implies 0.2 > 0.14...\) → \(>\)
3. \(\frac{1}{8}\) ? \(\frac{3}{5}\) \(\implies 0.125 < 0.6\) → \(<\)
4. \(\frac{1}{3}\) ? \(\frac{1}{5}\) \(\implies 0.33... > 0.2\) → \(>\)
5. \(\frac{1}{100}\) ? \(\frac{1}{99}\) \(\implies 0.01 < 0.0101...\) → \(<\)
6. \(\frac{5}{6}\) ? \(\frac{7}{6}\) \(\implies \frac{5}{6} < \frac{7}{6}\) → \(<\)
7. \(\frac{7}{18}\) ? \(\frac{1}{3}\) \(\implies \frac{7}{18} < \frac{6}{18}\) → \(<\)
8. \(\frac{12}{33}\) ? \(\frac{10}{13}\) \(\implies \frac{4}{11} \approx 0.36; \frac{10}{13} \approx 0.77\) → \(<\)
9. \(\frac{1}{2}\) ? \(\frac{3}{8}\) \(\implies \frac{4}{8} > \frac{3}{8}\) → \(>\)

Сравнение:

1. \(\frac{2}{5}\) ? \(\frac{1}{3}\) \(\implies \frac{6}{15} > \frac{5}{15}\) → \(>\)
2. \(\frac{9}{10}\) ? \(\frac{12}{11}\) \(\implies 0.9 < 1.09...\) → \(<\)
3. \(\frac{5}{9}\) ? \(\frac{3}{8}\) \(\implies \frac{40}{72} > \frac{27}{72}\) → \(>\)
4. \(2\frac{13}{2}\) ? \(2\frac{1}{2}\) \(\implies 2.65 > 2.5\) → \(>\)
5. \(4\frac{2}{3}\) ? \(4.5\) \(\implies 4.66... > 4.5\) → \(>\)
6. \(2.3\) ? \(2\frac{1}{3}\) \(\implies 2.3 > 2.33...\) → \(<\)
7. \(0.66\) ? \(\frac{3}{5}\) \(\implies 0.66 > 0.6\) → \(>\)
8. \(3.25\) ? \(\frac{13}{4}\) \(\implies 3.25 = 3.25\) → \(=\); \(\frac{13}{4} = 3\frac{1}{4}\)
9. \(3.6\) ? \(3\frac{3}{5}\) \(\implies 3.6 = 3.6\) → \(=\); \(3\frac{3}{5} = 3.6\)

Сравнение:

1. \(\frac{8}{9}\) ? \(0.8\) \(\implies 0.88... > 0.8\) → \(>\)
2. \(12.4\) ? \(\frac{63}{5}\) \(\implies 12.4 > 12.6\) → \(<\)
3. \(5\frac{2}{3}\) ? \(5.8\) \(\implies 5.66... < 5.8\) → \(<\)
4. \(8.8\) ? \(8\frac{3}{4}\) \(\implies 8.8 > 8.75\) → \(>\)
5. \(9\frac{2}{5}\) ? \(\frac{83}{9}\) \(\implies 9.4 > 9.22...\) → \(>\)
6. \(\frac{15}{4}\) ? \(\frac{3}{7}\) \(\implies 3.75 > 0.42...\) → \(>\)
7. \(-1.4\) ? \(0.44\) \(\implies -1.4 < 0.44\) → \(<\)
8. \(-\frac{4}{7}\) ? \(\frac{3}{4}\) \(\implies -0.57... < 0.75\) → \(<\)
9. \(-\frac{9}{8}\) ? \(1.01\) \(\implies -1.125 < 1.01\) → \(<\)

Сравнение:

1. \(-8.94\) ? \(-9.02\) \(\implies -8.94 > -9.02\) → \(>\)
2. \(4.32\) ? \(-4.33\) \(\implies 4.32 > -4.33\) → \(>\)
3. \(-3.71\) ? \(3.7\) \(\implies -3.71 < 3.7\) → \(<\)
4. \(2.3\) ? \(-2\frac{1}{2}\) \(\implies 2.3 > -2.5\) → \(>\)
5. \(0.01\) ? \(112.5\) \(\implies 0.01 < 112.5\) → \(<\)
6. \(-4\frac{3}{8}\) ? \(-0.01\) \(\implies -4.375 < -0.01\) → \(<\)
7. \(2.12\) ? \(-\frac{1}{2}\) \(\implies 2.12 > -0.5\) → \(>\)
8. \(-2\frac{3}{4}\) ? \(\frac{2}{5}\) \(\implies -2.75 < 0.4\) → \(<\)
9. \(-6.1\) ? \(-6.2\) \(\implies -6.1 > -6.2\) → \(>\)