$$1\frac{1}{5}\times5\frac{3}{4}$$
$\frac{69}{10}=6.9$
$$\frac{5+1}{5}\times \frac{5\times 4+3}{4}$$
$$\frac{6}{5}\times \frac{5\times 4+3}{4}$$
$$\frac{6}{5}\times \frac{20+3}{4}$$
$$\frac{6}{5}\times \frac{23}{4}$$
$$\frac{6\times 23}{5\times 4}$$
$$\frac{138}{20}$$
$$\frac{69}{10}$$
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$\frac{3 \cdot 23}{2 \cdot 5} = 6\frac{9}{10} = 6.9$