# Fill in the blanks:

Question:

Fill in the blanks:

(i) $\frac{9}{8}+(\ldots)=\frac{-3}{2}$

(ii) $(\ldots) \div\left(\frac{-7}{5}\right)=\frac{10}{19}$

(iii) $(\ldots) \div(-3)=\frac{-4}{15}$

(iv) $(-12) \div(\ldots)=\frac{-6}{5}$

Solution:

(i) Let $\frac{9}{8} \div \mathrm{x}=\frac{-3}{2}$

$\Rightarrow \frac{9}{8} \times \frac{1}{\mathrm{x}}=\frac{-3}{2}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-3}{2} \div \frac{9}{8}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-3}{2} \times \frac{8}{9}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-24}{18}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-4}{3}$

$\Rightarrow \mathrm{x}=\frac{-3}{4}$             $\left[\right.$ Reciprocal of $\left.\frac{-4}{3}\right]$

(ii) Let $\mathrm{x} \div\left(\frac{-7}{5}\right)=\frac{10}{19}$

$\Rightarrow \mathrm{x} \times\left(\frac{5}{-7}\right)=\frac{10}{19}$

$\Rightarrow \mathrm{x}=\left(\frac{10}{19}\right) \div\left(\frac{5}{-7}\right)$

$\Rightarrow \mathrm{x}=\frac{10}{19} \times \frac{-7}{5}$

$\Rightarrow \mathrm{x}=\frac{-70}{95}$

$\Rightarrow \mathrm{x}=\frac{-14}{19}$

(iii) Let $\mathrm{x} \div(-3)=\frac{-4}{15}$

$\Rightarrow \mathrm{x} \times\left(\frac{1}{-3}\right)=\frac{-4}{15}$

$\Rightarrow \mathrm{x}=\frac{-4}{15} \times(-3)$

$\Rightarrow \mathrm{x}=\frac{12}{15}$

$\Rightarrow \mathrm{X}=\frac{4}{5}$

(iv) Let $(-12) \div \mathrm{x}=\frac{-6}{5}$

$\Rightarrow(-12) \times \frac{1}{\mathrm{x}}=\frac{-6}{5}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-6}{5} \div(-12)$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{-6}{5} \times \frac{1}{-12}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{10}$

$\Rightarrow \mathrm{x}=10$