We have, \(3\frac{1}{2}\div \frac{8}{3}=(\frac{3\times 2+1}{2})\div \frac{8}{3}=(\frac{6+1}{2})\times \frac{3}{8}\)
=\(\frac{7}{2} \times \frac{3}{8}=\frac{7\times 3}{2\times 8}=\frac{21}{16}\)

We have, \(\frac{6}{13} \div 7=\frac{6}{13}+\frac{7}{1}=\frac{6}{13} \times \frac{7}{1}=\frac{6\times 14}{13\times 7}=\frac{6}{91}\)

We have, \(\frac{4}{5}\times \frac{12}{7}\times \frac{4\times12 }{5\times 7}=\frac{48}{35}=1\frac{13}{35}\)

\(\frac{1}{2}\)of 10=\(\frac{1}{2}\times 10=\frac{10}{2}=5\)   [∵ 'of' represents multiplication]

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.

We have 
\(4\frac { 2 }{ 3 } -3\frac { 1 }{ 4 } +2\frac { 1 }{ 6 } \)=\(\frac { 14 }{ 3 } -\frac { 13 }{ 4 } +\frac { 13 }{ 6 } \)
= \(\frac { 14\times 4 }{ 3\times 4 } -\frac { 13\times 3 }{ 4\times 3 } +\frac { 13\times 2 }{ 6\times 2 } \)
∵ LCM of 3, 4 and 6 is 12, so we convert each fraction into an equivalent fraction with denominator 12
i,e  \(\frac { 56 }{ 12 } -\frac { 39 }{ 12 } +\frac { 26 }{ 12 } =\frac { 56-39+26 }{ 12 } \)
= \(\frac { 82-39 }{ 12 } =\frac { 43 }{ 12 } =3\frac { 7 }{ 12 } \)

(a) No. of students like to study English
= \(\frac { 1 }{ 5 } \times 40\)
= 8
(b) No. of students like to study Maths
= \(\frac { 2 }{ 5 } \times 40\)
= 2\(\times\) 8
= 16
(c) No. of students who like to study Science
=40 - (8 + 16)
= 40-24
= 16
In part (ii), we know
\(\frac { 2 }{ 5 } \times 40\) = 16
So,\(\frac { 2 }{ 5 } \)of the total number of students like to study Science

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

Given, number of boys in the school \(=\frac{5}{6}\) of the total number of students in the school
ஃ Fraction of boys in the school+ Fraction of girls in the school = 1
i.e. \((\frac{5}{6})+\)[fraction of girls in the school]=1
So, Fraction of girls in the school
\(=1-\frac{5}{6}=\frac{1}{1}-\frac{5}{6}=\frac{6-5}{6}=\frac{1}{6}\)
We know that, the number of girls in the school is equal to 240.
So, \(\frac{1}{6}\)of the total number of students in the school =240
⇒ \(\frac{1}{6}\)x Total number of students = 240
So, Total number of students = \(240 \times \frac{6}{1}\)
=240x6=1440
∴ Total number of students in the school
= Total number of boys students in the school + Total number of girls students in the school
⇒ 1440= Total number of boys students in the school + 240
Hence, total number of boys students in the school
=1440 - 240 =1200

We have
Cost of 1 kg of sugar = Rs.17\(\frac { 3 }{ 4 } \)=Rs\(\frac { 71 }{ 4 } \)k
∴ Cost of 8 kg of sugar = Rs \(\left( \frac { 71 }{ 4 } \times 8\frac { 1 }{ 2 } \right) \)
=Rs \(\left( \frac { 71 }{ 4 } \times \frac { 17 }{ 2 } \right) =Rs.\left( \frac { 71\times 17 }{ 4\times 2 } \right) \)
=Rs\(\left( \frac { 1207 }{ 8 } \right) \) =Rs.150\(\frac { 7 }{ 8 } \)
Hence, the cost of 8\(\frac { 1 }{ 2 } \) kg of sugar is Rs.150\(\frac { 7 }{ 8 } \)

\(\frac{1}{4}\)

\(1-\frac{3}{5}=\frac{5}{5}-\frac{3}{5}=\frac{5-3}{5}=\frac{2}{5}\)