a)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\)
\(=\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{41}\)
\(=\left(\dfrac{12}{67}-\dfrac{79}{67}\right)+\left(\dfrac{13}{41}+\dfrac{28}{41}\right)+\dfrac{1}{3}\)
\(=-1+1+\dfrac{1}{3}\)
\(=0+\dfrac{1}{3}\)
\(=\dfrac{1}{3}\)
c)
\(139\dfrac{5}{7}:\dfrac{2}{3}-138\dfrac{2}{7}:\sqrt{\dfrac{4}{9}}\)
\(=\dfrac{978}{7}:\dfrac{2}{3}-\dfrac{968}{7}:\dfrac{2}{3}\)
\(=\dfrac{978}{7}\times\dfrac{3}{2}-\dfrac{968}{7}\times\dfrac{3}{2}\)
\(=\dfrac{3}{2}\times\left(\dfrac{978}{7}-\dfrac{968}{7}\right)\)
\(=\dfrac{3}{2}\times\dfrac{10}{7}\)
\(=\dfrac{15}{7}\)
\(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\)
\(=\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{41}\)
\(=\dfrac{1}{3}+\left(\dfrac{12}{69}-\dfrac{79}{67}\right)+\left(\dfrac{13}{41}+\dfrac{28}{41}\right)\)
\(=\dfrac{1}{3}+\left(-1\right)+1=\dfrac{1}{3}+0=\dfrac{1}{3}\)
