Tính bằng cách hợp lí:

Let's solve the problems step by step:

### 5. Tính bằng cách hợp lí:

a)
\[ \frac{204}{215} + \frac{2021}{2022} - \frac{204}{215} + \frac{1}{2022} \]

Simplify:
\[ \left( \frac{204}{215} - \frac{204}{215} \right) + \left( \frac{2021}{2022} + \frac{1}{2022} \right) = 0 + \frac{2022}{2022} = 1 \]

b)
\[ \frac{2}{3} \times \left( -\frac{3}{7} \right) - \frac{4}{3} \times \frac{5}{10} + \left( -\frac{4}{7} \right) \times \frac{7}{10} \]

Simplify:
\[ \frac{2 \times -3}{3 \times 7} - \frac{4 \times 5}{3 \times 10} + \frac{-4 \times 7}{7 \times 10} = -\frac{6}{21} - \frac{20}{30} - \frac{28}{70} \]
\[ = -\frac{2}{7} - \frac{2}{3} - \frac{2}{5} \]
Find common denominator (105):
\[ = -\frac{30}{105} - \frac{70}{105} - \frac{42}{105} = -\frac{142}{105} \]

c)
\[ \left( -\frac{1}{2} \right) \times \left( -\frac{1}{3} \right) \times \left( -\frac{1}{4} \right) \times \left( -\frac{1}{5} \right) \times \left( -\frac{1}{6} \right) \]

Simplify:
\[ = \frac{1}{2} \times \frac{1}{3} \times \frac{1}{4} \times \frac{1}{5} \times \frac{1}{6} = \frac{1}{720} \]

d)
\[ 2022 - \frac{2}{151} + \frac{6}{151} - \frac{2}{50} - \left( 20 - \frac{8}{151} + \frac{3}{50} \right) \]

Simplify:
\[ = 2022 - \frac{2 - 6 + 8}{151} - \frac{2 - 3}{50} - 20 \]
\[ = 2022 - \frac{4}{151} - \frac{-1}{50} - 20 \]
\[ = 2022 - \frac{4}{151} + \frac{1}{50} - 20 \]

### 6. Điền dấu (> , < , =) thích hợp vào ô trống.

a)
\[ \left( -\frac{3}{18} \right) \quad ? \quad \left( \frac{15}{-18} \right) \]
\[ -\frac{1}{6} \quad = \quad -\frac{5}{6} \]

b)
\[ \left( \frac{5}{-66} \right) \quad ? \quad \left( -\frac{13}{66} \right) \]
\[ -\frac{5}{66} \quad > \quad -\frac{13}{66} \]

c)
\[ \left( \frac{19}{-88} \right) + \left( \frac{5}{88} \right) \quad ? \quad \frac{30}{-66} \]
\[ -\frac{19}{88} + \frac{5}{88} = -\frac{14}{88} = -\frac{7}{44} \]
\[ -\frac{7}{44} \quad < \quad -\frac{15}{33} = -\frac{5}{11} \]

d)
\[ \frac{2}{3} - \left( -\frac{1}{4} \right) \quad ? \quad \frac{1}{2} + \left( -\frac{1}{6} \right) \]
\[ \frac{2}{3} + \frac{1}{4} \quad ? \quad \frac{1}{2} - \frac{1}{6} \]
\[ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \quad > \quad \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \]

### 7. Tìm x, biết:

a)
\[ x + \frac{3}{5} = -\frac{1}{4} \]
\[ x = -\frac{1}{4} - \frac{3}{5} = -\frac{5}{20} - \frac{12}{20} = -\frac{17}{20} \]

b)
\[ x - \frac{1}{2} = \frac{-3}{10} \]
\[ x = \frac{-3}{10} + \frac{1}{2} = \frac{-3}{10} + \frac{5}{10} = \frac{2}{10} = \frac{1}{5} \]

c)
\[ \frac{4}{5} x = \frac{-12}{17} \]
\[ x = \frac{-12}{17} \times \frac{5}{4} = \frac{-60}{68} = \frac{-30}{34} = \frac{-15}{17} \]

d)
\[ x : \left( -\frac{2}{3} \right) = \frac{4}{5} \]
\[ x = \frac{4}{5} \times \left( -\frac{3}{2} \right) = \frac{-12}{10} = \frac{-6}{5} \]

e)
\[ -0.25x = \frac{1}{4} \]
\[ x = \frac{1}{4} \div -0.25 = \frac{1}{4} \times -4 = -1 \]

g)
\[ -2 : x = 0.75 \]
\[ x = -2 \div 0.75 = -2 \times \frac{4}{3} = -\frac{8}{3} \]

### 8. Viết số hữu tỉ dưới dạng tích của hai số hữu tỉ theo sáu cách khác nhau.

a)
\[ -\frac{5}{88} = \left( -\frac{1}{2} \right) \times \left( \frac{5}{44} \right) \]
\[ = \left( -\frac{5}{11} \right) \times \left( \frac{1}{8} \right) \]
\[ = \left( -\frac{5}{22} \right) \times \left( \frac{1}{4} \right) \]
\[ = \left( -\frac{5}{8} \right) \times \left( \frac{1}{11} \right) \]
\[ = \left( -\frac{5}{4} \right) \times \left( \frac{1}{22} \right) \]
\[ = \left( -\frac{5}{2} \right) \times \left( \frac{1}{44} \right) \]

b)
\[ -\frac{6}{11} = \left( -\frac{3}{11} \right) \times \left( 2 \right) \]
\[ = \left( -\frac{6}{1} \right) \times \left( \frac{1}{11} \right) \]
\[ = \left( -\frac{6}{2} \right) \times \left( \frac{2}{11} \right) \]
\[ = \left( -\frac{6}{3} \right) \times \left( \frac{3}{11} \right) \]
\[ = \left( -\frac{6}{6} \right) \times \left( \frac{6}{11} \right) \]
\[ = \left( -\frac{6}{12} \right) \times \left( \frac{12}{11} \right) \]