Question

Find the ratio of 3.2 metres to 56 metres.

Answer 1

Hint: We know that a ratio indicates how many times one number contains another number. We can also say that the simplest fractional form which indicates how many times one number contains another number. It is also a dimensionless quantity. Let us assume the value of x is equal to 3.2 metres. Now we will consider this as equation (1). Let us also assume the value of y is equal to 56 metres. Now let us consider this as equation (2). Now by using equation (1) and equation (2), we can find the value of the ratio of 3.2 metres and 56 metres.

Complete step-by-step answer:
Before solving the question, we know that a ratio indicates how many times one number contains another number. We can also say that the simplest fractional form which indicates how many times one number contains another number. It is also a dimensionless quantity.
The ratio of x and y is said to be equal to \[\text{a:b}\] where \[\text{a:b}\] is the simplest ratio possible.
Let us assume the value of x is equal to 3.2 metres. Let us also assume the value of y is equal to 56 metres.
\[\begin{align}
  & x=3.2.....(1) \\
 & y=56......(2) \\
\end{align}\]
Now by using equation (1) and equation (2), we can find the ratio of x and y.
\[\Rightarrow \dfrac{x}{y}=\dfrac{3.2}{56}\]
We know that 3.2 can be written as \[\dfrac{32}{10}\].
\[\Rightarrow \dfrac{x}{y}=\dfrac{32}{560}\]
\[\Rightarrow \dfrac{x}{y}=\dfrac{16}{280}\]
\[\Rightarrow \dfrac{x}{y}=\dfrac{8}{140}\]
\[\Rightarrow \dfrac{x}{y}=\dfrac{4}{70}\]
\[\Rightarrow \dfrac{x}{y}=\dfrac{2}{35}......(3)\]
Finally, from equation (3) we have obtained the ratio of x and y.
So, the ratio of 3.2 metres and 56 metres is equal to \[2:35\].

Note: Students should be careful at calculation part of this question. If a small mistake is made, then it is not possible to get a correct final answer. So, one should do the calculation part in a perfect manner. This is also important to solve this problem. Some students may write the final answer as \[2m:35\] considering that ratio is having a unit. We know that ratio is a dimensionless quantity. So, this type of misconceptions should be avoided.