Question
Fill in the blank: $\frac{9}{8}\div(....)=\frac{-3}{2}$
✓
Answer
Let required number $= x$
Then,
$\frac{9}{8}\div\text{x}=\frac{-3}{2}$
$\Rightarrow\frac{9}{8}\times\frac{1}{\text{x}}=\frac{-3}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-3}{2}\div\frac{9}{8}$
$\Rightarrow\frac{-3}{2}\times\frac{8}{9}=\frac{-24}{18}$
$\Rightarrow\text{x}=\frac{18}{-24}$
$\Rightarrow\frac{18\div6}{-24\div6}$
$=\frac{3}{-4}$
$=\frac{-3}{4}$
$\therefore$ Required number $=\frac{-3}{4}$
Then,
$\frac{9}{8}\div\text{x}=\frac{-3}{2}$
$\Rightarrow\frac{9}{8}\times\frac{1}{\text{x}}=\frac{-3}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-3}{2}\div\frac{9}{8}$
$\Rightarrow\frac{-3}{2}\times\frac{8}{9}=\frac{-24}{18}$
$\Rightarrow\text{x}=\frac{18}{-24}$
$\Rightarrow\frac{18\div6}{-24\div6}$
$=\frac{3}{-4}$
$=\frac{-3}{4}$
$\therefore$ Required number $=\frac{-3}{4}$
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