Compare the fractions and put an appropriate sign.
(a) $ \frac{3}{6} \square \frac{5}{6} $
(b) $ \frac{1}{7} \square \frac{1}{4} $
(c) $ \frac{4}{5} \square \frac{5}{5} $
(d) $ \frac{3}{5} \square \frac{3}{7} $

To do:

We have to compare the given fractions and put appropriate signs.

Solution:

To compare we need to convert the given fractions into fractions with equal denominators.

(a) Here,

$\frac{3}{6}$ and $\frac{5}{6}$ have equal denominators.

$3<5$

Therefore,

$\frac{3}{6} < \frac{5}{6}$

(b)

LCM of denominators 7 and 4 is 28.

Multiply $\frac{1}{7}$ by $\frac{4}{4}$

This implies, 

$\frac{1}{7}\times\frac{4}{4}=\frac{4}{28}$

Multiply $\frac{1}{4}$ by $\frac{7}{7}$

$\frac{1}{4}\times\frac{7}{7}=\frac{7}{28}$

$4<7$

Therefore,

$\frac{4}{28} < \frac{7}{28}$

This implies,

 $\frac{1}{7} < \frac{1}{4}$

(c) Here,

$\frac{4}{5}$ and $\frac{5}{5}$ have equal denominators.

$4<5$

Therefore,

$\frac{4}{5} < \frac{5}{5}$

(d) LCM of denominators 5 and 7 is 35.

Multiply $\frac{3}{5}$ by $\frac{7}{7}$

This implies, 

$\frac{3}{5}\times\frac{7}{7}=\frac{21}{35}$

Multiply $\frac{3}{7}$ by $\frac{5}{5}$

$\frac{3}{7}\times\frac{5}{5}=\frac{15}{35}$

$15<21$

Therefore,

$\frac{15}{35} < \frac{21}{35}$

This implies,

 $\frac{3}{7} < \frac{3}{5}$