Question

By what number should we divide $-\dfrac{1}{8}$ to get $-\dfrac{3}{10}$?

Answer 1

Hint: In the above problem, we have given $-\dfrac{1}{8}$ and are asked the number which we divide by that number will give us $-\dfrac{3}{10}$. So, let us say, “x” is that number which in division with $-\dfrac{1}{8}$ will give $-\dfrac{3}{10}$. Now, we are going to divide $-\dfrac{1}{8}$ by x which will look as follows: $-\dfrac{\dfrac{1}{8}}{x}$. After that, we are going to equate this division with $-\dfrac{3}{10}$, and from this equation, we will get the value of x.


Complete step by step solution:
The number which we have to divide by some other number so that the final result will become $-\dfrac{3}{10}$ is as follows:
$-\dfrac{1}{8}$
Now, let us assume that the number which in division with $-\dfrac{1}{8}$ will give $-\dfrac{3}{10}$ is equal to “x”. We are going to divide x by $-\dfrac{1}{8}$ and it will look as follows:
$-\dfrac{\dfrac{1}{8}}{x}$
Rearranging the above fraction will give us:
$-\dfrac{1}{8x}$
Equating the above expression to $-\dfrac{3}{10}$ we get,
$-\dfrac{1}{8x}=-\dfrac{3}{10}$
In the above equation, negative sign will get canceled out from both the sides and we get,
$\dfrac{1}{8x}=\dfrac{3}{10}$
On cross-multiplying the above equation we get,
$\begin{align}
  & \Rightarrow 10=3\left( 8x \right) \\
 & \Rightarrow 10=24x \\
\end{align}$
Now, to simplify the above expression we are going to divide 24 into both the sides and we get,
$\dfrac{10}{24}=x$
From the above solution, we got the number $\left( =\dfrac{10}{24} \right)$ which on division with $-\dfrac{1}{8}$ will give $-\dfrac{3}{10}$.

Note:You can check the number which we are getting in the above solution which on division with $-\dfrac{1}{8}$ will give us $-\dfrac{3}{10}$ is equal to $\dfrac{10}{24}$ is correct or not by dividing $\dfrac{10}{24}$ to $-\dfrac{1}{8}$ and we get,
$\begin{align}
  & -\dfrac{\dfrac{1}{8}}{\dfrac{10}{24}} \\
 & =-\dfrac{1}{8}\times \dfrac{24}{10} \\
\end{align}$
Simplifying the above expression will give us:
$=-\dfrac{3}{10}$
Hence, the number which we found in the above solution is correct.