$$\frac { 1 } { 3 } + \frac { 1 } { 7 } \frac { 1 } { 4 \frac { 2 } { 7 } } + \frac { 1 } { 3 \frac { 1 } { 13 } } { 3 \frac { 16 } { 16 } }$$
$\frac{5}{3}\approx 1.666666667$
$$\frac{1}{3}+\frac{1}{7}\times \frac{7}{4\times 7+2}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{1}{3}+\frac{1}{7}\times \frac{7}{28+2}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{1}{3}+\frac{1}{7}\times \frac{7}{30}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{1}{3}+\frac{1\times 7}{7\times 30}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{1}{3}+\frac{1}{30}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{10}{30}+\frac{1}{30}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{10+1}{30}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{11}{30}+\frac{1}{\frac{3\times 13+1}{13}}\times \frac{3\times 16+16}{16}$$
$$\frac{11}{30}+\frac{13}{3\times 13+1}\times \frac{3\times 16+16}{16}$$
$$\frac{11}{30}+\frac{13}{39+1}\times \frac{3\times 16+16}{16}$$
$$\frac{11}{30}+\frac{13}{40}\times \frac{3\times 16+16}{16}$$
$$\frac{11}{30}+\frac{13}{40}\times \frac{48+16}{16}$$
$$\frac{11}{30}+\frac{13}{40}\times \frac{64}{16}$$
$$\frac{11}{30}+\frac{13}{40}\times 4$$
$$\frac{11}{30}+\frac{13\times 4}{40}$$
$$\frac{11}{30}+\frac{52}{40}$$
$$\frac{11}{30}+\frac{13}{10}$$
$$\frac{11}{30}+\frac{39}{30}$$
$$\frac{11+39}{30}$$
$$\frac{50}{30}$$
$$\frac{5}{3}$$
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$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$
