The distance from school to Library via Bus Stop.
= \(\left[ \cfrac { 3 }{ 4 } +3\cfrac { 1 }{ 2 } \right] \)
= \(\cfrac { 3 }{ 4 } +\cfrac { 7 }{ 2 } \)
= \(\cfrac { 3+(7\times 2) }{ 4 } =\cfrac { 3+14 }{ 4 } =\cfrac { 17 }{ 4 } \)
= \(4\frac { 1 }{ 4 } \) km
The distance between school and library via Hospital
= \(\left( 4\frac { 1 }{ 2 } +1\frac { 1 }{ 4 } \right) \)
= \(\cfrac { 9 }{ 2 } +\cfrac { 5 }{ 4 } \)
= \(\cfrac { (9\times 2) }{ 4 } =\cfrac { 18+5 }{ 4 } =\cfrac { 23 }{ 4 } \)
= \(5\frac { 3 }{ 4 } \)
(iii) The shortest between (i) and (ii)
via Bus stop = \(4\frac { 1 }{ 4 } \)
via Hospital = \(5\frac { 3 }{ 4 } \)
Ans: via Bus stop.
(iv) Distance between School and Hospital = \(4\frac { 1 }{ 2 }\ km \)
Distance between School and Bus stop = \(\frac{3}{4}\ km\)
Required  Answer = \(4 \frac{1}{2} \div \frac{3}{4}\)
\(=\frac{9}{2} \div \frac{3}{4}=\frac{9}{2} \times \frac{4}{3}=6\)
The distance between school and Hospital is 6 times the distance between school and Bus stop.

Given:
A painter painted = \(\cfrac { 3 }{ 8 } \) of the wall
Yellow colour painted = \(\cfrac { 1 }{ 3 } \times \cfrac { 3 }{ 8 } =\cfrac { 1 }{ 8 } \)
\(\therefore \cfrac { 1 }{ 8 } \) is the yellow colour of the entire wall

(i) \(\cfrac { 3 }{ 7 } \div 4\)
= \(\cfrac { 3 }{ 7 } \times \cfrac { 1 }{ 4 } =\cfrac { 3\times 1 }{ 7\times 4 } =\cfrac { 3 }{ 28 } \)
(ii) \(\cfrac { 4 }{ 3 } \div \cfrac { 5 }{ 9 } \)
= \(\cfrac { 4 }{ 3 } \times \cfrac { 9 }{ 5 } \)
= \(\cfrac { 4\times 3 }{ 5 } =\cfrac { 12 }{ 5 } =2\cfrac { 2 }{ 5 } \)
(iii) \(4\cfrac { 1 }{ 5 } \div 3\cfrac { 3 }{ 4 } \)
= \(\cfrac { 21 }{ 5 } \div \cfrac { 15 }{ 4 } \)

= \(\cfrac { 21 }{ 5 } \times \cfrac { 4 }{ 15 } =\cfrac { 7\times 4 }{ 5\times 5 } =\cfrac { 28 }{ 25 } =1\cfrac { 3 }{ 25 } \)

(iv) \(9\cfrac { 2 }{ 3 } \div 1\cfrac { 2 }{ 3 } \)
= \(\cfrac { 29 }{ 3 } \div \cfrac { 5 }{ 3 } \)
= \(\cfrac { 29 }{ 3 } \times \cfrac { 3 }{ 5 } =\cfrac { 29 }{ 5 } 5\cfrac { 4 }{ 5 } \) 

(i) \(3\cfrac { 7 }{ 8 } \)
Improper fraction = \(\cfrac { \left( 3\times 18 \right) +7 }{ 18 } \)
= \(\cfrac { 54+7 }{ 18 } =\cfrac { 61 }{ 18 } \)
(ii) \(\cfrac { 99 }{ 7 } \)
\(Mixed\ fraction=Qutient+\frac { Remainder }{ Divisor } \)
= \(14+\cfrac { 1 }{ 7 } \)
= \(14\cfrac { 1 }{ 7 } \)
(iii) \(\cfrac { 47 }{ 6 } \)
Mixed fraction = \(7\cfrac { 5 }{ 6 } \)
(iv) \(12\cfrac { 1 }{ 9 } \)
Mixed fraction = \(\cfrac { \left( 12\times 9 \right) +1 }{ 9 } \)
= \(\cfrac { 108+1 }{ 9 } =\cfrac { 109 }{ 9 }\)