Question

How do you solve $\dfrac{1.1}{1.2}=\dfrac{n}{3.6}$?

Answer 1

Hint: In this problem we need to calculate the value of $n$ such that the given equation is satisfied. We can observe that all the values we have in the equations are decimals at the same time fractions also. So, we will first apply cross multiplication to the given fractions. Here we will simplify the equation by calculating the product of the two decimal values. Now we will perform arithmetic operations to solve the given equation. After applying arithmetic operations, we will simplify the equation to get the required result.

Complete step by step solution:
Given equation, $\dfrac{1.1}{1.2}=\dfrac{n}{3.6}$.
Applying the cross-multiplication rule to the above equation, then we will get
$\Rightarrow 1.1\left( 3.6 \right)=1.2\times n$
Considering the left-hand side of the above equation which is $1.1\times 3.6$. We can say that the above value is a product of the two decimal values. We know that multiplication of the decimals is similar to the multiplication of numbers but we will place the decimal value after the sum of the number of digits after the decimal point in both the values. Hence the value of $1.1\times 3.6$ will be $1.1\times 3.6=3.96$. Substituting this value in the above equation, then we will get
$\Rightarrow 3.96=1.2\times n$
We can observe that $1.2$ is in multiplication in the above equation, so dividing the above equation with $1.2$ on both sides, then we will get
$\begin{align}
  & \Rightarrow \dfrac{3.96}{1.2}=\dfrac{1.2n}{1.2} \\
 & \Rightarrow n=3.3 \\
\end{align}$

Hence the solution for the given equation $\dfrac{1.1}{1.2}=\dfrac{n}{3.6}$ is $n=3.3$.

Note: We can also follow another method to solve the above equation. We can say that $3.6$ is in division on RHS of the given equation, so multiplying the whole equation with $3.6$ on both sides, then we will get
$\Rightarrow 3.6\times \dfrac{1.1}{1.2}=\dfrac{n}{3.6}\times 3.6$
Cancelling the all the possible values in the above equation, then we will have
$\begin{align}
  & \Rightarrow 3\times 1.1=n \\
 & \Rightarrow n=3.3 \\
\end{align}$
From both the methods we got the same result.