Question

Which ratio is greater?

(i) (5 : 6) or (7 : 9)
(ii) (2 : 3) or (4 : 7)
(iii) (1 : 2) or (4 : 7)
(iv) (3 : 5) or (8 : 13)

Answer 1

(i) The LCM of 6 and 9 is 18.

$$\begin{gathered} \frac{5}{6}=\frac{5\times 3}{6\times 3}=\frac{15}{18} \\ \frac{7}{9}=\frac{7\times 2}{9\times 2}=\frac{14}{18}\mathrm{Clearly},\frac{14}{18}<\frac{15}{18} \end{gathered}$$

∴ (7 : 9) $<$ (5 : 6)

(ii) The LCM of 3 and 7 is 21.

$$\begin{gathered} \frac{2}{3}=\frac{2\times 7}{3\times 7}=\frac{14}{21} \\ \frac{4}{7}=\frac{4\times 3}{7\times 3}=\frac{12}{21} \\ \mathrm{Clearly},\frac{12}{21}<\frac{14}{21} \end{gathered}$$

∴ (4 : 7) $<$ (2 : 3)

(iii) The LCM of 2 and 7 is 14.

$$\begin{gathered} \frac{1\times 7}{2\times 7}=\frac{7}{14} \\ \frac{4\times 2}{7\times 2}=\frac{8}{14} \end{gathered}$$

Clearly, $\frac{7}{14}<\frac{8}{14}$

∴ (1 : 2) $<$ (4 : 7)

(iv) The LCM of 5 and 13 is 65.

$$\begin{gathered} \frac{3}{5}=\frac{3\times 13}{5\times 13}=\frac{39}{65} \\ \frac{8}{13}=\frac{8\times 5}{13\times 5}=\frac{40}{65} \\ \mathrm{Clearly},\frac{39}{65}<\frac{40}{65} \end{gathered}$$

∴ (3 : 5) $<$ (8 : 13)