Which of the following fraction is the smallest ? 7/6,\,7/9,\,4/5,\,5/7

Answer: Option D

$$\frac{7}{6},\frac{7}{9},\frac{4}{5},\frac{5}{7}$$
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 :
$$\begin{array}{rl}& \frac{7}{6}=1.166,\\ & \frac{7}{6}=0.777\\ & \frac{4}{5}=0.8,\\ & \frac{5}{7}=0.714\\ & \text{Thus }\frac{5}{7}\text{ is the smallest}\text{.}\end{array}$$