Question

A rectangle sheet of paper is of length $1.2m$ and width $21cm$. Find the ratio of width of the paper to its length.

Answer 1

Hint: In this problem we need to calculate the ratio to the width of the paper to the length of the paper. We can observe that the given dimensions are not in the same unit that means the length is given in meters and the width is given in centimeters. To calculate the ratio of any two variables we need to have units of those variables as the same. So, we need to convert either length into centimeters or width into meters. Among this converting length into centimeters will be simple by using the relation $1m=100cm$. So, we will multiply $100$ to the given length of the paper to convert it into centimeters. Now we will write the ratio of the width and length and simplify it by cancelling the common factors.

Complete step by step solution:
The length of the paper is $1.2m$.
Width of the paper is $21cm$.

We can observe that the units of both the given dimensions are not the same. So, converting the length into centimeters. From the relation $1m=100cm$ , to convert meters into centimeters we need to multiply the length with $100$. Hence
$\begin{align}
  & l=1.2\times 100cm \\
 & \Rightarrow l=120cm \\
\end{align}$
Now the ratio of the width to length can be written as
$b:l=21:120$
We can observe that both the numbers have the common factor which is $3$. So, cancelling the $3$ in the given ratio, then we will get
$b:l=7:40$
Hence the required ratio is $7:40$.

Note: We can also convert the centimeters into meters by using the relation $1cm=0.01m$. So, we will multiply the given length with $0.01$ to convert it into meters. For this problem we have small value in centimeters, so converting it into meters will give decimals. Decimals in ratios are not preferable ones in calculations so we are not converting the centimeters into meters.