Question

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

Answer 1

Hint: We have to find the number which when divided by $\dfrac{{ - 1}}{8}$ we get the answer $\dfrac{{ - 3}}{{10}}$. We will assume the number which will be divided as ‘x’. Then, either we divide ‘x’ by $\dfrac{{ - 1}}{8}$ or we multiply $\dfrac{{ - 1}}{8}$ with the reciprocal of ‘x’ and write it in LHS. We will equate it with $\dfrac{{ - 3}}{{10}}$ in RHS forming a linear equation with variable x. Then, by simplifying we will find the value of ‘x’.

Complete step-by-step solution:
Assume the number which we divide by $\dfrac{{ - 1}}{8}$ to get $\dfrac{{ - 3}}{{10}}$ as $x$.
We will multiply the reciprocal of $x$ with the term $\dfrac{{ - 1}}{8}$ and equate it with $\dfrac{{ - 3}}{{10}}$.
By using these conditions, we will form a linear equation with variable $x$.
$\dfrac{1}{x} \times \left( {\dfrac{{ - 1}}{8}} \right) = \dfrac{{ - 3}}{{10}}$
$\dfrac{{ - 1}}{{8x}} = \dfrac{{ - 3}}{{10}}$
Now, by cross multiplying we get,
$ - 1 \times 10 = - 3 \times 8x$
$10 = 24x$
$x = \dfrac{{10}}{{24}}$
$x = \dfrac{5}{{12}}$
So, $\dfrac{5}{{12}}$ should be divided by $\dfrac{{ - 1}}{8}$ to get $\dfrac{{ - 3}}{{10}}$.

Note: The linear equation in one variable is an equation which is expressed in the form of $ax + b = 0$, where $a$ and $b$ are two integers, and $x$ is a variable and has only one solution.
LHS is an informal shorthand for the left-hand side of an equation. Similarly, RHS is the right-hand side of the equation.
We can also check whether the answer is correct or not. We will divide $\dfrac{5}{{12}}$ with $\dfrac{{ - 1}}{8}$ and if the answer comes $\dfrac{{ - 3}}{{10}}$. Then, the solution we did above is correct. So, we will check it now.
Rather than dividing $\dfrac{5}{{12}}$ we will multiply its reciprocal to make the calculations easier.
$ = \dfrac{{ - 1}}{8} \times \dfrac{{12}}{5}$
$ = \dfrac{{ - 1}}{2} \times \dfrac{3}{5}$
Now we will multiply the numerators with each other and denominators with each other.
$ = \dfrac{{ - 3}}{{10}}$
The answer is $\dfrac{{ - 3}}{{10}}$. Which means the solution we did above is correct.