Question

By what number should $\frac{-33}{8}$ be divided to get $\frac{-11}{2}$ ?

Answer 1

Let $\frac{-33}{8}$ be divided by $x$ to get $\frac{-11}{2}$.

So,

$\begin{array}{rcl}\frac{-33}{8}÷x& =& \frac{-11}{2}\\ & \Rightarrow & x=\frac{-33}{8}÷\frac{-11}{2}\\ & \Rightarrow & x=\frac{-33}{8}\times \frac{2}{-11}\\ & \Rightarrow & x=\frac{-33\times 2}{8\times -11}\\ & \Rightarrow & x=\frac{-66}{-88}\\ & \Rightarrow & x=\frac{-66\times -1}{-88\times -1}\\ & \Rightarrow & x=\frac{66}{88}\\ & \Rightarrow & x=\frac{66÷22}{88÷22}\\ & \Rightarrow & x=\frac{3}{4}\end{array}$

Hence, the required value is $\frac{3}{4}$