2\(\frac{3}{5}\)x10  =\(\frac{13}{5}\)x10 ==\(\frac { 13\times 2 }{ 1 } \)=26

\(\frac { 2 }{ 5 } \div \frac { 1 }{ 2 } \)=\(\frac { 2 }{ 5 } \times \frac { 2 }{ 1 } \)=\(\frac { 4 }{ 5 } \)

We have,  4+\(\frac{7}{8}\)=\(\frac{4}{1}+\frac{7}{8}=\frac{4\times 8+7\times1}{8}​​\)  [∵ LCM of 8and 1=8]
=\(\frac{10-3}{5}=\frac{7}{5}\)

The given frraacctnions are \(\frac{2}{5},\frac{3}{10},\frac{9}{14} , \frac{16}{35}\)
LCM of 5,10, 14,35 = 70

Now, \(\frac{2}{5}=\frac{2\times 14}{5\times 14}=\frac{21}{70},\frac{9}{14}=\frac{9\times5 }{14\times 5}=\frac{45}{70}\) and \(\frac{16}{35}=\frac{16\times 2}{35 \times 2}=\frac{32}{70}\)
Clearly, \(\frac{21}{70}<\frac{28}{70}<\frac{32}{70}<\frac{45}{70}\) So, \(\frac{3}{10}<\frac{2}{5}<\frac{16}{35}<\frac{9}{14}\)
Hence, thee zgiiven firacn..ons in ascendimg order are \(\frac{3}{10}<\frac{2}{5}<\frac{16}{35}<\frac{9}{14}\)
Now, let us change each of the given fractions into an equivalent fraction having 70 as its denominator.

Total hours spend by Ritika for studies =11\(\frac { 1 }{ 3 } \) hours =\(\frac { 34 }{ 3 } \)hours
 Total hours devoted by Ritika for Hindi and Sanskrit 5\(\frac { 3 }{ 5 } \)= \(\frac { 28 }{ 5 } \)hours
Total hours devoted by Ritika for other subjects
= \(\frac { 34 }{ 3 } -\frac { 28 }{ 5 } \)
= \(\frac { 170-84 }{ 15 } =\frac { 86 }{ 15 } \)
=5\(\frac { 11 }{ 15 } \) hours

Time taken by Michael to finished colouring the picture \(\frac{7}{12}\)hr
Time taken by Vaibhav to finished colouring the picture = \(\frac{3}{4}\)hr

LCM of 12 and 4 = 3 X 4 = 12
On converting these fractions into like fractions, we get
\(\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12} and \frac{7}{12}=\frac{7}{12}\)
It is clear, 9>7 [numerators of fractions]
So, \(\frac{9}{12}>\frac{7}{12} i.e., \frac{3}{4}>\frac{7}{12}\)
So, Vaibhav takes longer time to finish colouring the picture. Difference between time taken by Vaibhav and Michael
\(=\frac{3}{4}-\frac{7}{12}\)

LCM of 4 and 12 = 2 x 2 x3 = 12
\(=\frac{3}{4}-\frac{7}{12}=\frac{3\times 3-7\times 1}{12}\)
=\(\frac{9-7}{12}=\frac{2}{12}=\frac{1}{6}\) [dividing numerator and denominator by 2]
Hence, Vaibhav takes \(\frac{1}{6}\) h more than Michael.

We have
\(5\times \frac { 3 }{ 20 } \times \frac { 2 }{ 15 } \)=\(\frac { 5 }{ 1 } \times \frac { 3 }{ 20 } \times \frac { 2 }{ 15 } =\frac { 5\times 3\times 2 }{ 1\times 20\times 15 } =\frac { 1\times 1\times 2 }{ 1\times 4\times 5 } \)
= \(\frac { 1 }{ 2\times 5 } =\frac { 1 }{ 10 } \)

\(\frac{11}{5}\)