Question

From each of the given pairs, find which ratio is larger:

(i) $(3:4)$ or $(9:16)$

(ii) $(5:12)$ or $(17:30)$

(iii) $(3:7)$ or $(4:9)$

(iv) $(1:2)$ or $(13:27)$

Answer 1

(i) $(3:4)$ or $(9:16)$

Making the denominators equal:

$\frac{3\times 4}{4\times 4}=\frac{12}{16}$

and, $\frac{12}{16}>\frac{9}{16}$

$\therefore (3:4)>(9:16)$

(ii) $(5:12)$ or $(17:30)$

Making the denominators equal:

$\frac{5\times 5}{12\times 5}=\frac{25}{60}$

and, $\frac{17\times 2}{30\times 2}=\frac{34}{60}$

$\Rightarrow \frac{25}{60}<\frac{34}{60}$

$\therefore (5:12)<(17:30)$

(iii) $(3:7)$ or $(4:9)$

Making the denominators equal:

$\frac{3\times 9}{7\times 9}=\frac{27}{63}$

and, $\frac{4\times 7}{9\times 7}=\frac{28}{63}$

$\Rightarrow \frac{27}{63}<\frac{28}{63}$

$(3:7)<(4:9)$

(iv) $(1:2)$ or $(13:27)$

Making the denominators equal:

$\frac{1\times 27}{2\times 27}=\frac{27}{54}$

and, $\frac{13\times 2}{27\times 2}=\frac{26}{54}$

$\Rightarrow \frac{27}{54}>\frac{26}{54}$

$(1:2)>(13:27)$