$$(11\frac{1}{13}-1\frac{3}{8})+2\frac{7}{8}$$
$\frac{327}{26}\approx 12.576923077$
$$\frac{143+1}{13}-\frac{1\times 8+3}{8}+\frac{2\times 8+7}{8}$$
$$\frac{144}{13}-\frac{1\times 8+3}{8}+\frac{2\times 8+7}{8}$$
$$\frac{144}{13}-\frac{8+3}{8}+\frac{2\times 8+7}{8}$$
$$\frac{144}{13}-\frac{11}{8}+\frac{2\times 8+7}{8}$$
$$\frac{1152}{104}-\frac{143}{104}+\frac{2\times 8+7}{8}$$
$$\frac{1152-143}{104}+\frac{2\times 8+7}{8}$$
$$\frac{1009}{104}+\frac{2\times 8+7}{8}$$
$$\frac{1009}{104}+\frac{16+7}{8}$$
$$\frac{1009}{104}+\frac{23}{8}$$
$$\frac{1009}{104}+\frac{299}{104}$$
$$\frac{1009+299}{104}$$
$$\frac{1308}{104}$$
$$\frac{327}{26}$$
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$\frac{3 \cdot 109}{2 \cdot 13} = 12\frac{15}{26} = 12.576923076923077$
