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[latex]2 \frac{5}{18}-5 \frac{1}{12}=2+ \frac{5}{18}-(5+ \frac{1}{12})= 2+ \frac{5}{18}-5- \frac{1}{12}= 2-5+ \frac{5}{18}- \frac{1}{12}=[/latex] [latex]=-3+\frac{5}{6*3}-\frac{1}{6*2} =-3+\frac{1}{6}*\frac{5}{3}-\frac{1}{6}*\frac{1}{2} =-3+\frac{1}{6}*(\frac{5}{3}-\frac{1}{2})=[/latex] [latex]=-3+\frac{1}{6}*(\frac{5*2}{3*2}-\frac{3*1}{3*2}) =-3+\frac{1}{6}*(\frac{5*2-3*1}{3*2}) =-3+\frac{1}{6}*(\frac{10-3}{6})=[/latex] [latex]=-3+\frac{1}{6}*\frac{7}{6}=-3+ \frac{1*7}{6*6}=-3+ \frac{7}{36}=-3* \frac{1}{1}+ \frac{7}{36}=[/latex] [latex]=(-3)* \frac{36}{36}+ \frac{7}{36}= \frac{(-3)*36}{36}+ \frac{7}{36}= \frac{(-3)*36+7}{36}= \frac{-108+7}{36}= \frac{-101}{36}=[/latex] [latex]=- \frac{101}{36}=- \frac{2*36+29}{36}=-( \frac{2*36}{36}+ \frac{29}{36})= -( \frac{2*36}{1*36}+ \frac{29}{36})= -( \frac{2}{1}+ \frac{29}{36})=[/latex] [latex]=-(2+ \frac{29}{36})=-(2\frac{29}{36})=-2\frac{29}{36}[/latex]