$\text{a)}$  

$4,2+3\frac{1}{5}=4\frac{2}{10}+3\frac{1}{5}=4\frac{1}{5}+3\frac{1}{5}=7\frac{2}{5}=7\frac{4}{10}=7,4$  

$3,75+2\frac{3}{4}=3\frac{3}{4}+2\frac{3}{4}=5\frac{6}{4}=5\frac{3}{2}=6\frac{1}{2}=6,5$  

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$\text{b)}$  

$6\frac{1}{4}-3,05=6,25-3,05=3,2=3\frac{2}{10}=3\frac{1}{5}$  

$10,0-5\frac{1}{2}=10,0-5,5=4,5=4\frac{1}{2}$  

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$\text{c)}$  

$4,5\cdot \frac{2}{5}=4\frac{1}{2}\cdot \frac{2}{5}=\frac{9}{2}\cdot \frac{2}{5}=\frac{9}{5}=1\frac{4}{5}=1\frac{8}{10}=1,8$  

$\frac{3}{11}\cdot 0,22=\frac{3}{11}\cdot \frac{22}{100}=\frac{3}{50}=\frac{6}{100}=0,06$  

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$\text{d)}$  

$5,1:\frac{17}{100}=5\frac{1}{10}:\frac{17}{100}=\frac{51}{10}\cdot \frac{100}{17}=30$  

$\frac{3}{4}:0,25=\frac{3}{4}:\frac{1}{4}=\frac{3}{4}\cdot 4=3$