$$\frac{15}{56}\cdot1\frac{1}{7}:\frac{2}{15}\cdot24\frac{1}{2}:7\frac{1}{2}$$
$\frac{15}{2}=7.5$
$$\frac{\frac{\frac{15}{56}\times \frac{7+1}{7}}{\frac{2}{15}}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{\frac{15}{56}\times \frac{8}{7}}{\frac{2}{15}}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{\frac{15\times 8}{56\times 7}}{\frac{2}{15}}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{\frac{120}{392}}{\frac{2}{15}}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{\frac{15}{49}}{\frac{2}{15}}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{15}{49}\times \frac{15}{2}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{15\times 15}{49\times 2}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{225}{98}\times \frac{24\times 2+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{225}{98}\times \frac{48+1}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{225}{98}\times \frac{49}{2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{225\times 49}{98\times 2}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{11025}{196}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{225}{4}}{\frac{7\times 2+1}{2}}$$
$$\frac{\frac{225}{4}}{\frac{14+1}{2}}$$
$$\frac{\frac{225}{4}}{\frac{15}{2}}$$
$$\frac{225}{4}\times \frac{2}{15}$$
$$\frac{225\times 2}{4\times 15}$$
$$\frac{450}{60}$$
$$\frac{15}{2}$$
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$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$
