$$2\frac{1}{27}+2\frac{1}{7}$$
$\frac{790}{189}\approx 4.17989418$
$$\frac{54+1}{27}+\frac{2\times 7+1}{7}$$
$$\frac{55}{27}+\frac{2\times 7+1}{7}$$
$$\frac{55}{27}+\frac{14+1}{7}$$
$$\frac{55}{27}+\frac{15}{7}$$
$$\frac{385}{189}+\frac{405}{189}$$
$$\frac{385+405}{189}$$
$$\frac{790}{189}$$
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$\frac{2 \cdot 5 \cdot 79}{3 ^ {3} \cdot 7} = 4\frac{34}{189} = 4.1798941798941796$
