Question

Which ratio is Greater

$1:2\mathrm{or}13:27$

Answer 1

As ratios are $1:2or13:27$

Here,

$$\begin{gathered} 1:2=\frac{1}{2}\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}27 \\ \Rightarrow \frac{1\times 27}{2\times 27}=\frac{27}{54} \\ \mathrm{Also},13:27=\frac{13}{27}\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}2 \\ \Rightarrow \frac{13\times 2}{27\times 2}=\frac{26}{54} \end{gathered}$$

On comparing we can say

$$\begin{gathered} \frac{27}{54}>\frac{26}{54}i.e\frac{1}{2}>\frac{13}{27} \\ Hence,1:2>13:27 \end{gathered}$$