Write down the reciprocal of (i) 6/7 (ii) 9 (iii) 1/14 (iv) 12 3/5. 2. Simplify (i) 4/7 + 9/14 (ii) 7/10 + 3/5 (iii) 8/9 + 16

$$
\frac{4}{7} = \frac{4 \times 2}{7 \times 2} = \frac{8}{14}
$$

$$
\frac{8}{14} + \frac{9}{14} = \frac{8+9}{14} = \boxed{\frac{17}{14}}
$$

$$
\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
$$

$$
\frac{7}{10} + \frac{6}{10} = \frac{7+6}{10} = \boxed{\frac{13}{10}}
$$

$$
16 = \frac{16 \times 9}{9} = \frac{144}{9}
$$

$$
\frac{8}{9} + \frac{144}{9} = \frac{8+144}{9} = \boxed{\frac{152}{9}}
$$

$$
9 = \frac{9 \times 3}{3} = \frac{27}{3}
$$

$$
\frac{27}{3} + \frac{1}{3} = \frac{27+1}{3} = \boxed{\frac{28}{3}}
$$

$$
24 \div \frac{6}{7} = 24 \times \frac{7}{6}
$$

$$
24 \times \frac{7}{6} = \frac{24}{6} \times 7 = 4 \times 7 = \boxed{28}
$$

$$
3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15+3}{5} = \frac{18}{5}
$$

$$
\frac{18}{5} + \frac{4}{5} = \frac{18+4}{5} = \boxed{\frac{22}{5}}
$$

$$
3\frac{3}{7} = \frac{3 \times 7 + 3}{7} = \frac{21+3}{7} = \frac{24}{7}
$$

$$
\frac{24}{7} = \frac{24 \times 3}{7 \times 3} = \frac{72}{21}
$$

$$
\frac{72}{21} + \frac{8}{21} = \frac{72+8}{21} = \boxed{\frac{80}{21}}
$$

$$
5\frac{4}{7} = \frac{5 \times 7 + 4}{7} = \frac{35+4}{7} = \frac{39}{7}
$$
$$
1\frac{3}{10} = \frac{1 \times 10 + 3}{10} = \frac{10+3}{10} = \frac{13}{10}
$$

$$
\frac{39}{7} = \frac{39 \times 10}{7 \times 10} = \frac{390}{70}
$$
$$
\frac{13}{10} = \frac{13 \times 7}{10 \times 7} = \frac{91}{70}
$$

$$
\frac{390}{70} + \frac{91}{70} = \frac{390+91}{70} = \boxed{\frac{481}{70}}
$$

$$
15\frac{3}{7} = \frac{15 \times 7 + 3}{7} = \frac{105+3}{7} = \frac{108}{7}
$$
$$
1\frac{23}{49} = \frac{1 \times 49 + 23}{49} = \frac{49+23}{49} = \frac{72}{49}
$$

$$
\frac{108}{7} \div \frac{72}{49} = \frac{108}{7} \times \frac{49}{72}
$$

$$
\frac{108}{7} \times \frac{49}{72} = \frac{108}{72} \times \frac{49}{7} = \frac{3 \times 36}{2 \times 36} \times \frac{7 \times 7}{7} = \frac{3}{2} \times 7 = \frac{21}{2}
$$
$$
\boxed{\frac{21}{2}}
$$