\(\dfrac{2}{3}1+2\dfrac{3}{4}+3\dfrac{1}{3}+4\dfrac{1}{4}=\dfrac{5}{3}+\dfrac{11}{4}+\dfrac{10}{3}+\dfrac{17}{4}=\left(\dfrac{5}{3}+\dfrac{10}{3}\right)+\left(\dfrac{11}{4}+\dfrac{17}{4}\right)=\dfrac{15}{3}+\dfrac{28}{4}=\dfrac{5}{1}+\dfrac{7}{1}=5+7=12.\)
\(=\dfrac{5}{3}+\dfrac{11}{4}+\dfrac{10}{3}+\dfrac{17}{4}\\ =\dfrac{15}{3}+\dfrac{28}{4} =5+7 \\ =12\)
\(1\dfrac{2}{3}+2\dfrac{3}{4}+3\dfrac{1}{3}+4\dfrac{1}{4}\)
\(=\left(1+\dfrac{2}{3}\right)+\left(2+\dfrac{3}{4}\right)+\left(3+\dfrac{1}{3}\right)+\left(4+\dfrac{1}{4}\right)\)
\(=1+\dfrac{2}{3}+2+\dfrac{3}{4}+3+\dfrac{1}{3}+4+\dfrac{1}{4}\)
\(=\left(1+2+3+4\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)\)
\(=10+1+1\)
\(=12\)
