Fill in the blanks:
(i) `(9)/(8) divide (........)=(-3)/(2)`
(ii) `(.......)divide ((-7)/(5))=(10)/(19)`
(iii) `(.......) divide (-3)=(-4)/(15)`
(iv) `(-12) divide (.........) = (-6)/(5)`

Answer

To solve the given problems, we will use the property of division of rational numbers. The property states that if \( a \div b = c \), then \( a = b \times c \). We will rearrange the equations to find the missing values.

### Solution Steps:

(i) **Given:**
\[ \frac{9}{8} \div \text{(blank)} = \frac{-3}{2} \]
**Step 1:** Rearranging the equation:
\[ \text{(blank)} = \frac{9}{8} \div \frac{-3}{2} \]

**Step 2:** Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \text{(blank)} = \frac{9}{8} \times \frac{-2}{3} \]

**Step 3:** Multiply the fractions:
\[ \text{(blank)} = \frac{9 \times -2}{8 \times 3} = \frac{-18}{24} \]

**Step 4:** Simplifying the fraction:
\[ \text{(blank)} = \frac{-3}{4} \]

---

(ii) **Given:**
\[ \text{(blank)} \div \frac{-7}{5} = \frac{10}{19} \]
**Step 1:** Rearranging the equation:
\[ \text{(blank)} = \frac{10}{19} \times \frac{-7}{5} \]

**Step 2:** Multiply the fractions:
\[ \text{(blank)} = \frac{10 \times -7}{19 \times 5} = \frac{-70}{95} \]

**Step 3:** Simplifying the fraction:
\[ \text{(blank)} = \frac{-14}{19} \]

---

(iii) **Given:**
\[ \text{(blank)} \div (-3) = \frac{-4}{15} \]
**Step 1:** Rearranging the equation:
\[ \text{(blank)} = \frac{-4}{15} \times (-3) \]

**Step 2:** Multiply the fractions:
\[ \text{(blank)} = \frac{-4 \times -3}{15} = \frac{12}{15} \]

**Step 3:** Simplifying the fraction:
\[ \text{(blank)} = \frac{4}{5} \]

---

(iv) **Given:**
\[ -12 \div \text{(blank)} = \frac{-6}{5} \]
**Step 1:** Rearranging the equation:
\[ \text{(blank)} = -12 \div \frac{-6}{5} \]

**Step 2:** Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \text{(blank)} = -12 \times \frac{-5}{6} \]

**Step 3:** Multiply the numbers:
\[ \text{(blank)} = \frac{-12 \times -5}{6} = \frac{60}{6} \]

**Step 4:** Simplifying the fraction:
\[ \text{(blank)} = 10 \]

### Final Answers:
(i) \(\frac{-3}{4}\)
(ii) \(\frac{-14}{19}\)
(iii) \(\frac{4}{5}\)
(iv) \(10\)