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

Answer

Let's solve the given questions step by step.

### Question (i):
Fill in the blank: `(….) divide ((-7)/(5)) = (10)/(19)`

1. Let the blank be represented by \( x \).
2. The equation can be rewritten as:
\[ x \div \left(-\frac{7}{5}\right) = \frac{10}{19} \]
3. To eliminate the division, multiply both sides by \(-\frac{7}{5}\):
\[ x = \frac{10}{19} \times \left(-\frac{7}{5}\right) \]
4. Now, multiply the fractions:
\[ x = \frac{10 \times -7}{19 \times 5} = \frac{-70}{95} \]
5. Simplifying \(-70/95\) by dividing both the numerator and denominator by 5:
\[ x = \frac{-14}{19} \]

**Final Answer for (i):** \( x = \frac{-14}{19} \)

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### Question (ii):
Fill in the blank: `(……) divide (-3) = (-4)/(15)`

1. Let the blank be represented by \( x \).
2. The equation can be rewritten as:
\[ x \div (-3) = \frac{-4}{15} \]
3. To eliminate the division, multiply both sides by \(-3\):
\[ x = \frac{-4}{15} \times (-3) \]
4. Now, multiply the fractions:
\[ x = \frac{-4 \times -3}{15} = \frac{12}{15} \]
5. Simplifying \(12/15\) by dividing both the numerator and denominator by 3:
\[ x = \frac{4}{5} \]

**Final Answer for (ii):** \( x = \frac{4}{5} \)

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### Question (iii):
Fill in the blank: `(9)/(8) divide (……) = (-3)/(2)`

1. Let the blank be represented by \( x \).
2. The equation can be rewritten as:
\[ \frac{9}{8} \div x = \frac{-3}{2} \]
3. To eliminate the division, multiply both sides by \( x \):
\[ \frac{9}{8} = \frac{-3}{2} \times x \]
4. Now, isolate \( x \) by multiplying both sides by the reciprocal of \(-\frac{3}{2}\):
\[ x = \frac{9}{8} \div \left(-\frac{3}{2}\right) = \frac{9}{8} \times \left(-\frac{2}{3}\right) \]
5. Now, multiply the fractions:
\[ x = \frac{9 \times -2}{8 \times 3} = \frac{-18}{24} \]
6. Simplifying \(-18/24\) by dividing both the numerator and denominator by 6:
\[ x = \frac{-3}{4} \]

**Final Answer for (iii):** \( x = \frac{-3}{4} \)

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### Question (iv):
Fill in the blank: `(-12) + (……) = (-6)/(5)`

1. Let the blank be represented by \( x \).
2. The equation can be rewritten as:
\[ -12 + x = \frac{-6}{5} \]
3. To isolate \( x \), add 12 to both sides:
\[ x = \frac{-6}{5} + 12 \]
4. Convert 12 to a fraction with a denominator of 5:
\[ 12 = \frac{12 \times 5}{5} = \frac{60}{5} \]
5. Now, combine the fractions:
\[ x = \frac{-6 + 60}{5} = \frac{54}{5} \]

**Final Answer for (iv):** \( x = \frac{54}{5} \)

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### Summary of Answers:
1. (i) \( x = \frac{-14}{19} \)
2. (ii) \( x = \frac{4}{5} \)
3. (iii) \( x = \frac{-3}{4} \)
4. (iv) \( x = \frac{54}{5} \)

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