Question

Write the following ratio in the simplest form: - Rupees 6.30: Rupees 16.80.

Answer 1

Hint: Assume the given ratio as R. Consider Rupees 6.30 as the numerator and Rupees 168 as the denominator of the fraction. Cancel the unit Rupees from the numerator and the denominator. Remove the decimal point by multiplying the numerator and the denominator with 100. Cancel the common factors to simplify the fraction and get the simplest form of the ratio.

Complete step by step answer:
Here we have been asked to find the simplest form of the ratio Rupees 6.30: Rupees 16.80. That means we have to cancel the common factors present in the numbers given. Let us assume the given ration as R, so we have,
$\Rightarrow $ R = Rupees 6.30: Rupees 16.80
Converting the ratio into the fraction we must have Rupees 6.30 as the numerator and Rupees 168 as the denominator of the fraction, so we get,
$\Rightarrow R=\dfrac{\text{Rupees }6.30}{\text{Rupees }16.80}$
Here we can cancel the unit of money that is rupees so we get,
$\Rightarrow R=\dfrac{6.30}{16.80}$
Now, multiplying the numerator and the denominator of the fraction with 100 to remove the decimal point we get,
$\begin{align}
  & \Rightarrow R=\dfrac{6.30}{16.80}\times \dfrac{100}{100} \\
 & \Rightarrow R=\dfrac{630}{1680} \\
\end{align}$
Cancelling the common factors to simplify the above fraction we get,
\[\begin{align}
  & \Rightarrow R=\dfrac{63}{168} \\
 & \Rightarrow R=\dfrac{3\times 3\times 7}{3\times 7\times 8} \\
 & \Rightarrow R=\dfrac{3}{8} \\
\end{align}\]
Converting the simplified form of the fraction back into the ratio we get,
$\therefore $ R = 3:8
Hence, the simplest form of the given ratio is 3:8.

Note: Note that the ratio is a pure number that means it has no units. When we multiply a fraction with 100 then it becomes a percentage. In the above solution we have multiplied the numerator and the denominator of the fraction with 100 because there were two digits after the decimal point and we did not require to balance the fraction because we were multiplying both the terms with the same number.