Question 1: 

Which of the following fraction is arranged in ascending order of their value?

a) \(\frac{1}{4} \) , \(\frac{2}{7} \) , \(\frac{3}{4} \) , \(\frac{4}{7} \) , \(\frac{5}{7} \) , \(\frac{6}{5} \)

b) \(\frac{1}{4} \) ,\(\frac{2}{7} \) ,\(\frac{4}{7} \) ,\(\frac{5}{7} \) ,\(\frac{3}{4} \) ,\(\frac{6}{5} \)

c) \(\frac{2}{7} \) ,\(\frac{1}{4} \) ,\(\frac{4}{7} \) ,\(\frac{3}{4} \) ,\(\frac{5}{7} \) ,\(\frac{6}{5} \)

d) \(\frac{2}{7} \) ,\(\frac{1}{4} \) ,\(\frac{4}{7} \) ,\(\frac{5}{7} \) ,\(\frac{3}{4} \) ,\(\frac{6}{5} \)

Answer : b) \(\frac{1}{4} \) ,\(\frac{2}{7} \) ,\(\frac{4}{7} \) ,\(\frac{5}{7} \) ,\(\frac{3}{4} \) ,\(\frac{6}{5} \)

Solution :

Converting the given fractions into decimal numbers, we have

\(\frac{1}{4} \)  = 0.25

\(\frac{2}{7} \) = 0.28

\(\frac{3}{4} \)  = 0.75

\(\frac{4}{7} \)  = 0.57

\(\frac{5}{7} \)  = 0.71

\(\frac{6}{5} \)  = 1.2

So, 0.25 < 0.28 < 0.57 < 0.71 < 0.75 < 1.2

Corresponding fraction is \(\frac{1}{4} \)  < \(\frac{2}{7} \) < \(\frac{4}{7} \) < \(\frac{5}{7} \)  < \(\frac{3}{4} \)  < \(\frac{6}{5} \)

Hence the answer is option b.

Question 2: 

Which of the following fraction is the largest?

a) \(\frac{8}{9} \)

b) \(\frac{18}{23} \)

c) \(\frac{16}{21} \)

d) \(\frac{14}{17} \)

Answer : a) \(\frac{8}{9} \)

Solution :

Converting the given fractions into decimal form, we have,

\(\frac{8}{9} \)  = 0.88

\(\frac{18}{23} \)  = 0.78

\(\frac{16}{21} \)  = 0.76

\(\frac{14}{17} \)  = 0.82

From the above, 0.88 is the largest.
Corresponding fraction is \(\frac{8}{9} \) .

Question 3:  

Which of the following fraction is greater than \(\frac{4}{5} \)  and less than \(\frac{6}{7} \) ?

a) \(\frac{2}{3} \)

b) \(\frac{3}{4} \)

c) \(\frac{5}{6} \)

d) \(\frac{10}{11} \)

Answer : c)\(\frac{5}{6} \)

Solution :

We have to find X such that \(\frac{4}{5} \)  < X < \(\frac{6}{7} \)

Converting each fraction into decimal form, we get:

\(\frac{4}{5} \)  = 0.8

\(\frac{6}{7} \)  = 0.85

We have to find the fraction which is greater than 0.8and less than 0.85.
Now,

\(\frac{2}{3} \)  = 0.66

\(\frac{3}{4} \) = 0.75

\(\frac{5}{6} \)  = 0.83

\(\frac{10}{11} \)  = 0.91

Clearly, 0.83 lies between 0.8 and 0.85.
Required fraction is  \(\frac{5}{6} \)

Question 4: 

Which of the following fraction does not lie between \(\frac{5}{6} \)  and \(\frac{8}{15} \) ?

a)\(\frac{2}{3} \)

b)\(\frac{3}{4} \)

c)\(\frac{4}{5} \)

d)\(\frac{6}{7} \)

Answer : d) \(\frac{6}{7} \)

Solution :

Converting each of the given fractions into decimal form, we get,

\(\frac{5}{6} \)  = 0.83

\(\frac{8}{15} \)  = 0.53

\(\frac{2}{3} \)  = 0.66

\(\frac{3}{4} \) = 0.75

\(\frac{4}{5} \)  = 0.8

\(\frac{6}{7} \)  = 0.85

Clearly, 0.85 does not lie between 0.83 and 0.53
Hence the required fraction is\(\frac{6}{7} \) .