Question
By what number should $\frac{-33}{8}$ be divided to get $\frac{-11}{2}?$
✓
Answer
Let required number $= x$
Then,
$\frac{-33}{8}\div\text{x}=\frac{-11}{2}$
$\Rightarrow\frac{-33}{8}\times\frac{1}{\text{x}}=\frac{-11}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-11}{2}\div\frac{-33}{8}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-11}{2}\times\frac{8}{-33}$
$=\frac{-88}{-66}=\frac{88}{66}$
$=\text{x}=\frac{66}{88}$
$=\frac{66\div22}{88\div22}$
$=\frac{3}{4}$
$\therefore$ Required number $=\frac{3}{4}$
Then,
$\frac{-33}{8}\div\text{x}=\frac{-11}{2}$
$\Rightarrow\frac{-33}{8}\times\frac{1}{\text{x}}=\frac{-11}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-11}{2}\div\frac{-33}{8}$
$\Rightarrow\frac{1}{\text{x}}=\frac{-11}{2}\times\frac{8}{-33}$
$=\frac{-88}{-66}=\frac{88}{66}$
$=\text{x}=\frac{66}{88}$
$=\frac{66\div22}{88\div22}$
$=\frac{3}{4}$
$\therefore$ Required number $=\frac{3}{4}$
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