Answer :
Answer:
[tex]\large\boxed{\large\boxed{\dfrac{35}{459}}}[/tex]
Explanation:
Fractions:
[tex]\bigg(\dfrac{1}{12}+\dfrac{1}{24}-\dfrac{1}{36}\bigg):\bigg(\dfrac{1}{4}+\dfrac{3}{5}\bigg)\times \dfrac{2}{3}[/tex]
1. Solve the first parenthesis:
[tex]\dfrac{1}{12}+\dfrac{1}{24}-\dfrac{1}{36}=\dfrac{6+3-2}{72}=\dfrac{7}{72}[/tex]
2. Solve the second parenthesis:
[tex]\dfrac{1}{4}+\dfrac{3}{5}=\dfrac{5+12}{20}=\dfrac{17}{20}[/tex]
3. Solve the division:
[tex]\dfrac{7}{72}:\dfrac{17}{20}=\dfrac{7}{72}\times \dfrac{20}{17}=\\ \\ \\ =\dfrac{7\times 20}{72\times 17}=\dfrac{7\times 5}{18\times 17}=\dfrac{35}{306}[/tex]
4. Multiply by the last fraction:
[tex]\dfrac{35}{306}\times \dfrac{2}{3}=\dfrac{35}{153\times 3}=\dfrac{35}{459}[/tex]