Question

By what number should $-\dfrac{33}{16}$ be divided to get $-\dfrac{11}{4}$ ?

Answer 1

Hint: Here we have been given a number and a value and we have to find what number when dividing it gives the value. Firstly we will let that number as an unknown variable then we will form an equation where we will divide the number by the unknown variable and put it equal to the value given. Finally we will solve the obtained equation and get the desired answer.

Complete step-by-step solution:
The number is given as follows:
$-\dfrac{33}{16}$…..$\left( 1 \right)$
We have to find what should be divided by above number to get the below value,
$-\dfrac{11}{4}$……$\left( 2 \right)$
Let the number be $x$ which when divide the number in equation (1) gives the value in equation (2).
So we get the equation by dividing equation (1) by $x$ and substituting it equal to equation (2) as follows:
$\dfrac{-\dfrac{33}{16}}{x}=-\dfrac{11}{4}$
$\Rightarrow -\dfrac{33}{16x}=-\dfrac{11}{4}$
Now take the unknown variable on one side and rest value on another as follows:
$\Rightarrow x=-\dfrac{33}{16}\times -\dfrac{4}{11}$
$\Rightarrow x=\dfrac{132}{176}$
Simplifying the value further by dividing the numerator and denominator by $44$ we get,
$\Rightarrow x=\dfrac{3}{4}$
Hence when $-\dfrac{33}{16}$ is divided by $\dfrac{3}{4}$ we get the value $-\dfrac{11}{4}$.

Note: In this type of question we always let the value that is to be found and form an equation according to the statement given in the question then we simplify the equation and get our answer. Fractions are defined as a part of a whole; this whole value can be any number or any-thing. We can cross check our answer by dividing the number $-\dfrac{33}{16}$ by the value $\dfrac{3}{4}$ we obtained as follows:
$\begin{align}
  & \Rightarrow \dfrac{-\dfrac{33}{16}}{\dfrac{3}{4}} \\
 & \Rightarrow -\dfrac{33\times 4}{3\times 16} \\
\end{align}$
On solving we get,
$\Rightarrow -\dfrac{11}{4}$
So our answer is correct.