`#\text{nn}`
`a)`
`1/5 \times 2/3 + 2/6 \times 1/5`
`= 1/5 \times (2/3 + 1/3)`
`= 1/5 \times 3/3`
`= 1/5 \times 1`
`= 1/5`
`b)`
\(\dfrac{4}{5}+\dfrac{1}{5}\times\left(-\dfrac{5}{5}\right)+\dfrac{9}{5}\times\dfrac{1}{5}\\ =\dfrac{3}{5}+\dfrac{1}{5}\times\left(1-1+\dfrac{9}{5}\right)\\ =\dfrac{3}{5}+\dfrac{1}{5}\times\dfrac{9}{5}\\ =\dfrac{3}{5}+\dfrac{9}{25}\\ =\dfrac{24}{25}\)
`c)`
\(\dfrac{34}{15}\div\dfrac{3}{2}-\dfrac{4}{15}\div\dfrac{3}{2}\\ =\dfrac{34}{15}\cdot\dfrac{2}{3}-\dfrac{4}{15}\cdot\dfrac{2}{3}\\ =\dfrac{2}{3}\cdot\left(\dfrac{34}{15}-\dfrac{4}{15}\right)\\ =\dfrac{2}{3}\cdot\dfrac{30}{15}\\ =\dfrac{2}{3}\cdot2=3\)
`d)`
\(\dfrac{5}{17}+\dfrac{12}{5}\cdot\dfrac{4}{17}+\dfrac{12}{17}\cdot\dfrac{1}{5}\\ =\dfrac{5}{17}+\dfrac{12}{17}\cdot\dfrac{4}{5}+\dfrac{12}{17}\cdot\dfrac{1}{5}\\ =\dfrac{5}{17}+\dfrac{12}{17}\cdot\left(\dfrac{4}{5}+\dfrac{1}{5}\right)\\ =\dfrac{5}{17}+\dfrac{12}{17}\cdot\dfrac{5}{5}\\ =\dfrac{5}{17}+\dfrac{12}{17}\cdot1\\ =\dfrac{5}{17}+\dfrac{12}{17}\\ =\dfrac{17}{17}=1\)