Which of the following fraction is the smallest ?
$$\frac{7}{6},\,\frac{7}{9},\,\frac{4}{5},\,\frac{5}{7}$$

$$\frac{7}{6},\,\frac{7}{9},\,\frac{4}{5},\,\frac{5}{7}$$
Step 1 : Compare two fractions
$$\frac{{7}}{{6}}$$ ⤩ $$\frac{{7}}{{9}}$$
Cross multiply
63 , 42
 ↑      ↑
$$\frac{7}{6}$$ ⤩ $$\frac{7}{9}$$
42 is smaller than 63
So, $$\frac{7}{9}$$ is smaller than $$\frac{7}{6}$$
Step 2 : Compare
(i) $$\frac{7}{9},\frac{4}{5}$$
(ii) $$\frac{7}{9}$$ ⤩ $$\frac{4}{5}$$
Cross multiply it
35 , 36
 ↑      ↑
$$\frac{7}{9}$$ ⤩ $$\frac{4}{5}$$
35 is smaller than 36
So, $$\frac{7}{9}$$ is smaller than $$\frac{4}{5}$$
Step 3 : Compare
(i) $$\frac{7}{9},\frac{5}{7}$$
(ii) $$\frac{7}{9}$$ ⤩ $$\frac{5}{7}$$
Cross multiply it
49 , 45
 ↑      ↑
$$\frac{7}{9}$$ ⤩ $$\frac{5}{7}$$
45 is smaller than 49
S0, $$\frac{5}{7}$$ is the smallest

Alternate :
$$\eqalign{ & \frac{7}{6} = 1.166, \cr & \frac{7}{6} = 0.777 \cr & \frac{4}{5} = 0.8, \cr & \frac{5}{{7\,}} = 0.714 \cr & {\text{Thus }}\frac{5}{7}{\text{ is the smallest}}{\text{.}} \cr} $$