$$3:1\frac{1}{2}+5:1\frac{1}{4}=$$
$6$
$$\frac{3\times 2}{1\times 2+1}+\frac{5}{\frac{1\times 4+1}{4}}$$
$$\frac{6}{1\times 2+1}+\frac{5}{\frac{1\times 4+1}{4}}$$
$$\frac{6}{2+1}+\frac{5}{\frac{1\times 4+1}{4}}$$
$$\frac{6}{3}+\frac{5}{\frac{1\times 4+1}{4}}$$
$$2+\frac{5}{\frac{1\times 4+1}{4}}$$
$$2+\frac{5\times 4}{1\times 4+1}$$
$$2+\frac{20}{1\times 4+1}$$
$$2+\frac{20}{4+1}$$
$$2+\frac{20}{5}$$
$$2+4$$
$$6$$
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$2\times 3$
