Evaluate :
(i) (3)/(4)-(4)/(5)`
(ii) `-3-(4)/(7)`
(iii) `(7)/(24)-(19)/(36)`
(iv) `(14)/(15)-(13)/(20)`
(v) `(4)/(9)-(2)/(-3)`
(vi) `(7)/(11)- (-4)/(-11)`
(vii) `(-5)/(14)`-(-2)/(7)`
(viii) ` (-5)/(-8)-(-3)/(4)`

Answer

Let's evaluate each expression step by step:

### (i) \( \frac{3}{4} - \frac{4}{5} \)

1. **Find the LCM of the denominators (4 and 5)**:
- LCM(4, 5) = 20.

2. **Convert each fraction to have the same denominator**:
- \( \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \)
- \( \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} \)

3. **Subtract the fractions**:
- \( \frac{15}{20} - \frac{16}{20} = \frac{15 - 16}{20} = \frac{-1}{20} \)

### (ii) \( -3 - \frac{4}{7} \)

1. **Convert -3 to a fraction**:
- \( -3 = \frac{-21}{7} \)

2. **Combine the fractions**:
- \( \frac{-21}{7} - \frac{4}{7} = \frac{-21 - 4}{7} = \frac{-25}{7} \)

### (iii) \( \frac{7}{24} - \frac{19}{36} \)

1. **Find the LCM of the denominators (24 and 36)**:
- LCM(24, 36) = 72.

2. **Convert each fraction**:
- \( \frac{7}{24} = \frac{7 \times 3}{24 \times 3} = \frac{21}{72} \)
- \( \frac{19}{36} = \frac{19 \times 2}{36 \times 2} = \frac{38}{72} \)

3. **Subtract the fractions**:
- \( \frac{21}{72} - \frac{38}{72} = \frac{21 - 38}{72} = \frac{-17}{72} \)

### (iv) \( \frac{14}{15} - \frac{13}{20} \)

1. **Find the LCM of the denominators (15 and 20)**:
- LCM(15, 20) = 60.

2. **Convert each fraction**:
- \( \frac{14}{15} = \frac{14 \times 4}{15 \times 4} = \frac{56}{60} \)
- \( \frac{13}{20} = \frac{13 \times 3}{20 \times 3} = \frac{39}{60} \)

3. **Subtract the fractions**:
- \( \frac{56}{60} - \frac{39}{60} = \frac{56 - 39}{60} = \frac{17}{60} \)

### (v) \( \frac{4}{9} - \frac{2}{-3} \)

1. **Convert \( \frac{2}{-3} \) to \( -\frac{2}{3} \)**:
- So, \( \frac{4}{9} + \frac{2}{3} \).

2. **Find the LCM of the denominators (9 and 3)**:
- LCM(9, 3) = 9.

3. **Convert \( \frac{2}{3} \)**:
- \( \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \)

4. **Add the fractions**:
- \( \frac{4}{9} + \frac{6}{9} = \frac{4 + 6}{9} = \frac{10}{9} \)

### (vi) \( \frac{7}{11} - \frac{-4}{-11} \)

1. **Convert \( \frac{-4}{-11} \) to \( \frac{4}{11} \)**:
- So, \( \frac{7}{11} - \frac{4}{11} \).

2. **Subtract the fractions**:
- \( \frac{7}{11} - \frac{4}{11} = \frac{7 - 4}{11} = \frac{3}{11} \)

### (vii) \( \frac{-5}{14} - \left(-\frac{2}{7}\right) \)

1. **Convert \( -\frac{2}{7} \) to \( +\frac{2}{7} \)**:
- So, \( \frac{-5}{14} + \frac{2}{7} \).

2. **Find the LCM of the denominators (14 and 7)**:
- LCM(14, 7) = 14.

3. **Convert \( \frac{2}{7} \)**:
- \( \frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14} \)

4. **Add the fractions**:
- \( \frac{-5}{14} + \frac{4}{14} = \frac{-5 + 4}{14} = \frac{-1}{14} \)

### (viii) \( \frac{-5}{-8} - \frac{-3}{4} \)

1. **Convert \( \frac{-5}{-8} \) to \( \frac{5}{8} \)** and \( -\frac{-3}{4} \) to \( +\frac{3}{4} \):
- So, \( \frac{5}{8} + \frac{3}{4} \).

2. **Find the LCM of the denominators (8 and 4)**:
- LCM(8, 4) = 8.

3. **Convert \( \frac{3}{4} \)**:
- \( \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \)

4. **Add the fractions**:
- \( \frac{5}{8} + \frac{6}{8} = \frac{5 + 6}{8} = \frac{11}{8} \)

### Summary of Answers:
1. \( \frac{-1}{20} \)
2. \( \frac{-25}{7} \)
3. \( \frac{-17}{72} \)
4. \( \frac{17}{60} \)
5. \( \frac{10}{9} \)
6. \( \frac{3}{11} \)
7. \( \frac{-1}{14} \)
8. \( \frac{11}{8} \)