Question

Find the ratio of the following in the simplest form 3m 5cm to 35cm.

Answer 1

Hint: Convert the measurements into the same units. First measurement is given as a combination of 2 units. So, combine them and make them into one unit. Now change the second measurement also into the same unit. Now when 2 measurements are in the same units then you apply algebraic property directly, there are no conditions applied. So, find the ratio as out find for normal numbers, cancel the units as they are the same and mention the answer ratio without any units. Ratio of 2 similar measurements never has units. Convert everything into metres. 1 centimetre is equal to 0.01 metres. So, multiply with 0.01 to make it into metres $1cm=0.01m$.

Complete step-by-step answer:
Given measurements in the question, which we need to solve are:
3m 5cm : 35cm
Let us divide these 2 into different measurements denoted by A, B.
Let us assume the value of A to be 3m 5cm.
Let us assume the value of B to be 35cm.
As per question, we need the ratio of A to B.
Required expression $=A:B$
According to algebra, we can apply properties normally if and only if the units are the same.
Now we will convert both A, B into units of m.
Case-1: Solving the measurement A. Converting into m.
By basic knowledge of measurements, we can say that the units:
$kcm=\left( 0.01\times k \right)m$
By applying this condition to measurement A, we will get:
$3m\text{ }5cm=3m+5cm=3m+0.05m$
By simplifying this condition, we get the value of A to be:
$A=3.05m$
Case-2: Solving the measurement B. Converting into m.
By basic knowledge of measurements, we can say that the units:
$kcm=\left( 0.01\times k \right)m$
By applying this condition to measurement B, we will get:
$35cm=35\times 0.01m$
By simplifying this condition, we get the value of B to be:
$B=0.35m$
We need the ratio of these two measurements:
$\begin{align}
  & A:B=3.05:0.35 \\
 & =\dfrac{3.05}{0.35} \\
\end{align}$
By simplifying above fraction, we get:
$\dfrac{3.05}{0.35}=\dfrac{0.61}{0.07}=\dfrac{61}{7}$
$\dfrac{A}{B}=\dfrac{61}{7}$
By converting fraction into ratio, we get
$A:B=61:7$
Therefore, required ratio is $61:7$

Note: Alternative method is to convert first measurement into cm. It is done by dividing 0.01 on both sides of the measurement equation. We know 1 metre is 100 centimetre. Now you have both measurements in centimetres. Then take the ratio of 2 measurements in cm. However the measurements cancel in the ratio. So, you will reach the same result.