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$4 \frac{1}{7} *14-1 \frac{1}{4}*1 \frac{1}{6}-1 \frac{2}{9}*2 \frac{5}{8}=53 \frac{1}{3}$

1) $4 \frac{1}{7}*14= \frac{4*7+1}{7}* \frac{14}{1}= \frac{29}{7}* \frac{14}{1}= \frac{29}{1}*\frac{2}{1}= 58$

2) $1 \frac{1}{4}*1\frac{1}{6}= \frac{1*4+1}{4}*\frac{1*6+1}{6}=\frac{5}{4}*\frac{7}{6}= \frac{35}{24}$

3) $1\frac{2}{9}*2\frac{5}{8} =\frac{1*9+2}{9}*\frac{2*8+5}{8}= \frac{11}{9}*\frac{21}{8}=\frac{11}{3}*\frac{7}{8}= \frac{77}{24}$

4) $58- \frac{35}{24}= \frac{24*58}{24}-\frac{35}{24}= \frac{1392-35}{24}= \frac{1357}{24}$

5) $\frac{1357}{24}-\frac{77}{24}= \frac{1357-77}{24}= \frac{1280}{24}= \frac{160}{3}=53 \frac{1}{3}$