$$1 \frac { 1 } { 2 } \div ( 3 \frac { 1 } { 3 } + 4 \frac { 1 } { 5 } - 6 \frac { 1 } { 2 }$$
$\frac{45}{31}\approx 1.451612903$
$$\frac{\frac{2+1}{2}}{\frac{3\times 3+1}{3}+\frac{4\times 5+1}{5}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{3\times 3+1}{3}+\frac{4\times 5+1}{5}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{9+1}{3}+\frac{4\times 5+1}{5}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{10}{3}+\frac{4\times 5+1}{5}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{10}{3}+\frac{20+1}{5}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{10}{3}+\frac{21}{5}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{50}{15}+\frac{63}{15}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{50+63}{15}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{113}{15}-\frac{6\times 2+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{113}{15}-\frac{12+1}{2}}$$
$$\frac{\frac{3}{2}}{\frac{113}{15}-\frac{13}{2}}$$
$$\frac{\frac{3}{2}}{\frac{226}{30}-\frac{195}{30}}$$
$$\frac{\frac{3}{2}}{\frac{226-195}{30}}$$
$$\frac{\frac{3}{2}}{\frac{31}{30}}$$
$$\frac{3}{2}\times \frac{30}{31}$$
$$\frac{3\times 30}{2\times 31}$$
$$\frac{90}{62}$$
$$\frac{45}{31}$$
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$\frac{3 ^ {2} \cdot 5}{31} = 1\frac{14}{31} = 1.4516129032258065$
