Question

How do you solve the given equation $\dfrac{10}{12}=\dfrac{2}{n}$?

Answer 1

Hint: We start solving the problem by recalling the fact that if $\dfrac{a}{b}=\dfrac{c}{d}$, then $a\times d=b\times c$. We use this fact for the given equation to proceed through the problem. We then make the necessary calculations which includes multiplication and division operations to get the required value of n.

Complete step-by-step answer:
According to the problem, we are asked to solve the given equation $\dfrac{10}{12}=\dfrac{2}{n}$.
We have given the equation $\dfrac{10}{12}=\dfrac{2}{n}$ ---(1).
We know that if $\dfrac{a}{b}=\dfrac{c}{d}$, then $a\times d=b\times c$. Let us use this result in equation (1).
$\Rightarrow 10\times n=12\times 2$.
$\Rightarrow 10n=24$.
$\Rightarrow n=\dfrac{24}{10}$.
$\Rightarrow n=2.4$.
So, we have found the solution of the given equation $\dfrac{10}{12}=\dfrac{2}{n}$ (i.e., the value of n) as 2.4.
$\therefore $ The solution of the given equation $\dfrac{10}{12}=\dfrac{2}{n}$ (i.e., the value of n) as 2.4.

Note: We should not make calculation mistakes while solving this problem. We should not report the answer as $\dfrac{5}{6}$ because we need the numerator of the rational number in R.H.S (Right Hand Side) which should be avoided while solving this type of problem. We can also solve the given problem as shown below:
We have given the equation $\dfrac{10}{12}=\dfrac{2}{n}$ ---(2).
Let us multiply the numerator and denominator in the R.H.S (Right Hand Side) of the equation (2) with 5.
$\Rightarrow \dfrac{10}{12}=\dfrac{2}{n}\times \dfrac{5}{5}$.
$\Rightarrow \dfrac{10}{12}=\dfrac{10}{5n}$ ---(3).
We can see that the numerator is the same on both sides of the equation (3). So, the value of the denominator in R.H.S must be equal to 12 in order to attain equality.
So, we have $5n=12$.
$\Rightarrow n=\dfrac{12}{5}$.
$\Rightarrow n=2.4$.