Question

Which fraction is smaller?

1.$\frac{2}{10},\frac{2}{7}$

2.$\frac{5}{7},\frac{5}{9}$

3.$\frac{13}{14},\frac{5}{6}$

4.$\frac{3}{13},\frac{4}{14}$

Answer 1

$\left(a\right)10>7$

$\Rightarrow \frac{10}{2}>\frac{7}{2}$

$\Rightarrow \frac{2}{10}<\frac{2}{7}$

$\therefore \frac{2}{10}$ is smaller

$\left(b\right)9>7$

$\Rightarrow \frac{9}{5}>\frac{7}{5}$

$\Rightarrow \frac{5}{9}<\frac{5}{7}$

$\therefore \frac{5}{9}$ is smaller

$\left(c\right)\frac{13}{14},\frac{5}{6}$

$\frac{13}{14}\times \frac{6}{6},\frac{5}{6}\times \frac{14}{14}$

$\frac{78}{84}\frac{70}{84}$ by making the denominators same

$\Rightarrow 78>70$

$\Rightarrow \frac{78}{84}>\frac{70}{84}$

$\Rightarrow \frac{13}{14}>\frac{5}{6}$

$\Rightarrow \frac{5}{6}<\frac{13}{14}$

$\therefore \frac{5}{6}$ is smaller.

$\left(d\right)\frac{3}{14},\frac{4}{14}$

$\Rightarrow \frac{3}{13},\frac{2}{7}$

L.C.M of $(13,7)=91$

$\Rightarrow \frac{3\times 7}{13\times 7},\frac{2\times 13}{7\times 13}$

$\Rightarrow \frac{21}{91},\frac{26}{91}$

$\Rightarrow \frac{21}{91}<\frac{26}{91}$

$\Rightarrow \frac{3}{13}<\frac{2}{7}$

$\therefore \frac{3}{13}$ is smaller.