Fill in the blanks .
(i)`(……..)+((-7)/(5))=(-2)/(3)`
(ii)` ((-65)/(14))divide(…….)=2(1)/(2)`
(iii)`(-3)/(8)+(……)=(5)/(12)`
(iv) Multiplicate inverse of `-1(3)/(4)`is ……….

Answer

Let's solve each part step by step:

### (i) \((\ldots) + \left(-\frac{7}{5}\right) = -\frac{2}{3}\)

1. Let \( x = \ldots \).
2. We can rewrite the equation as:
\[ x = -\frac{2}{3} + \frac{7}{5} \]
3. To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 5 is 15.
4. Convert each fraction:
\[ -\frac{2}{3} = -\frac{10}{15} \quad \text{and} \quad \frac{7}{5} = \frac{21}{15} \]
5. Now, add the fractions:
\[ x = -\frac{10}{15} + \frac{21}{15} = \frac{11}{15} \]
6. Therefore, the answer is:
\[ \frac{11}{15} \]

### (ii) \(\left(-\frac{65}{14}\right) \div (\ldots) = 2\frac{1}{2}\)

1. Let \( x = \ldots \).
2. Convert \( 2\frac{1}{2} \) to an improper fraction:
\[ 2\frac{1}{2} = \frac{5}{2} \]
3. Rewrite the equation:
\[ -\frac{65}{14} \div x = \frac{5}{2} \]
4. This can be rewritten as:
\[ -\frac{65}{14} = x \cdot \frac{5}{2} \]
5. To find \( x \), multiply both sides by the reciprocal of \(\frac{5}{2}\):
\[ x = -\frac{65}{14} \cdot \frac{2}{5} \]
6. Simplifying gives:
\[ x = -\frac{130}{70} = -\frac{13}{7} \]
7. Therefore, the answer is:
\[ -\frac{13}{7} \]

### (iii) \(-\frac{3}{8} + (\ldots) = \frac{5}{12}\)

1. Let \( x = \ldots \).
2. Rewrite the equation:
\[ x = \frac{5}{12} + \frac{3}{8} \]
3. Find a common denominator for 12 and 8, which is 24.
4. Convert each fraction:
\[ \frac{5}{12} = \frac{10}{24} \quad \text{and} \quad \frac{3}{8} = \frac{9}{24} \]
5. Now add the fractions:
\[ x = \frac{10}{24} + \frac{9}{24} = \frac{19}{24} \]
6. Therefore, the answer is:
\[ \frac{19}{24} \]

### (iv) The multiplicative inverse of \(-1\frac{3}{4}\)

1. Convert \(-1\frac{3}{4}\) to an improper fraction:
\[ -1\frac{3}{4} = -\frac{7}{4} \]
2. The multiplicative inverse of a number \( a \) is \(\frac{1}{a}\):
\[ \text{Multiplicative inverse} = -\frac{4}{7} \]
3. Therefore, the answer is:
\[ -\frac{4}{7} \]

### Summary of Answers:
(i) \(\frac{11}{15}\)
(ii) \(-\frac{13}{7}\)
(iii) \(\frac{19}{24}\)
(iv) \(-\frac{4}{7}\)