\(1,15\dfrac{1}{7}\cdot\left(\dfrac{3}{11}+\dfrac{-5}{9}\right)+15\dfrac{1}{7}\cdot\left(\dfrac{-4}{9}+\dfrac{8}{11}\right)\)
\(=15\dfrac{1}{7}\cdot\left[\left(\dfrac{3}{11}+\dfrac{-5}{9}\right)+\left(\dfrac{-4}{9}+\dfrac{8}{11}\right)\right]\)
\(=15\dfrac{1}{7}\cdot\left[\dfrac{3}{11}+\dfrac{-5}{9}+\dfrac{-4}{9}+\dfrac{8}{11}\right]\)
\(=15\dfrac{1}{7}\cdot\left[\left(\dfrac{3}{11}+\dfrac{8}{11}\right)+\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)\right]\)
\(=\dfrac{106}{7}\cdot\left[1+\left(-1\right)\right]\)
\(=\dfrac{106}{7}\cdot0\)
`= 0`
\(2)7,5:\left(\dfrac{-5}{3}\right)+\dfrac{1}{2}:\left(\dfrac{-5}{3}\right)\)
\(=\dfrac{15}{2}:\left(\dfrac{-5}{3}\right)+\dfrac{1}{2}:\left(\dfrac{-5}{3}\right)\)
\(=\dfrac{15}{2}\cdot\left(\dfrac{-3}{5}\right)+\dfrac{1}{2}\cdot\left(\dfrac{-3}{5}\right)\)
\(=\left(\dfrac{15}{2}+\dfrac{1}{2}\right)\cdot\left(\dfrac{-3}{5}\right)\)
\(=8\cdot\left(\dfrac{-3}{5}\right)\)
\(=\left(\dfrac{-24}{5}\right)\)
\(2)\dfrac{2}{3}\cdot\left(\dfrac{1}{4}+\dfrac{4}{5}\right)-\dfrac{2}{3}\cdot\left(\dfrac{1}{4}-\dfrac{1}{5}\right)\)
\(=\dfrac{2}{3}\cdot\left[\left(\dfrac{1}{4}+\dfrac{4}{5}\right)-\left(\dfrac{1}{4}-\dfrac{1}{5}\right)\right]\)
\(=\dfrac{2}{3}\cdot\left[\dfrac{1}{4}+\dfrac{4}{5}-\dfrac{1}{4}+\dfrac{1}{5}\right]\)
\(=\dfrac{2}{3}\cdot\left[\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+\left(\dfrac{4}{5}+\dfrac{1}{5}\right)\right]\)
\(=\dfrac{2}{3}\cdot\left[0+1\right]\)
\(=\dfrac{2}{3}\cdot1\)
\(=\dfrac{2}{3}\)
\(4,\dfrac{5}{7}:\left(\dfrac{15}{8}-\dfrac{1}{4}\right)-\dfrac{5}{7}:\left(\dfrac{1}{4}-\dfrac{1}{2}\right)\)
\(=\dfrac{5}{7}:\left[\left(\dfrac{15}{8}-\dfrac{1}{4}\right)-\left(\dfrac{1}{4}-\dfrac{1}{2}\right)\right]\)
\(=\dfrac{5}{7}:\left[\dfrac{15}{8}-\dfrac{1}{4}-\dfrac{1}{4}+\dfrac{1}{2}\right]\)
\(=\dfrac{5}{7}:\left[\left(\dfrac{15}{8}+\dfrac{1}{2}\right)-\left(\dfrac{1}{4}+\dfrac{1}{4}\right)\right]\)
\(=\dfrac{5}{7}:\left[\dfrac{19}{8}-\dfrac{1}{2}\right]\)
\(=\dfrac{5}{7}:\dfrac{15}{8}\)
\(=\dfrac{5}{7}\cdot\dfrac{8}{15}\)
\(=\dfrac{1}{7}\cdot\dfrac{8}{3}\)
\(=\dfrac{8}{21}\)
\(5,\dfrac{3}{5}:\left(\dfrac{1}{15}+\dfrac{1}{6}\right)+\dfrac{3}{5}:\left(\dfrac{1}{3}+1\dfrac{1}{15}\right)\)
\(=\dfrac{3}{5}:\left[\left(\dfrac{1}{15}+\dfrac{1}{6}\right)+\left(\dfrac{1}{3}+1\dfrac{1}{15}\right)\right]\)
\(=\dfrac{3}{5}:\left[\dfrac{1}{15}+\dfrac{1}{6}+\dfrac{1}{3}+\dfrac{16}{15}\right]\)
\(=\dfrac{3}{5}:\left[\left(\dfrac{1}{15}+\dfrac{16}{15}\right)+\left(\dfrac{1}{6}+\dfrac{1}{3}\right)\right]\)
\(=\dfrac{3}{5}:\left[\dfrac{17}{15}+\dfrac{1}{2}\right]\)
\(=\dfrac{3}{5}:\left[\dfrac{34}{30}+\dfrac{15}{30}\right]\)
\(=\dfrac{3}{5}:\dfrac{49}{30}\)
\(=\dfrac{3}{5}\cdot\dfrac{30}{49}\)
\(=3\cdot\dfrac{6}{49}\)
\(=\dfrac{18}{49}\)
\(6,\left(-\dfrac{3}{4}+\dfrac{2}{5}\right):\dfrac{3}{7}+\left(\dfrac{3}{5}+\dfrac{-1}{4}\right):\dfrac{3}{7}\)
\(=\left[\left(-\dfrac{3}{4}+\dfrac{2}{5}\right)+\left(\dfrac{3}{5}+\dfrac{-1}{4}\right)\right]:\dfrac{3}{7}\)
\(=\left[-\dfrac{3}{4}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{-1}{4}\right]:\dfrac{3}{7}\)
\(=\left[\left(-\dfrac{3}{4}+\dfrac{-1}{4}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)\right]:\dfrac{3}{7}\)
\(=\left[\left(-1\right)+1\right]:\dfrac{3}{7}\)
\(=0:\dfrac{3}{7}\)
`=0`
\(7,\left[\left(-\dfrac{5}{7}\right)+\dfrac{3}{5}\right]:\dfrac{2023}{2024}+\left(\dfrac{2}{5}-\dfrac{2}{7}\right):\dfrac{2023}{2024}\)
\(=\left\{\left[\left(-\dfrac{5}{7}\right)+\dfrac{3}{5}\right]+\left(\dfrac{2}{5}-\dfrac{2}{7}\right)\right\}:\dfrac{2023}{2024}\)
\(=\left\{-\dfrac{5}{7}+\dfrac{3}{5}+\dfrac{2}{5}-\dfrac{2}{7}\right\}:\dfrac{2023}{2024}\)
\(=\left\{\left(-\dfrac{5}{7}-\dfrac{2}{7}\right)+\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\right\}:\dfrac{2023}{2024}\)
\(=\left\{\left(-1\right)+1\right\}:\dfrac{2023}{2024}\)
\(=0:\dfrac{2023}{2024}\)
`=0`
\(8,\dfrac{3}{8}:\left(\dfrac{7}{22}-\dfrac{2}{11}\right)+\dfrac{3}{8}:\left(\dfrac{2}{5}-\dfrac{1}{10}\right)\)
\(=\dfrac{3}{8}:\left[\left(\dfrac{7}{22}-\dfrac{2}{11}\right)+\left(\dfrac{2}{5}-\dfrac{1}{10}\right)\right]\)
\(=\dfrac{3}{8}:\left[\dfrac{3}{22}+\dfrac{3}{10}\right]\)
\(=\dfrac{3}{8}:\left[\dfrac{30}{220}+\dfrac{66}{220}\right]\)
\(=\dfrac{3}{8}:\dfrac{24}{55}\)
\(=\dfrac{3}{8}\cdot\dfrac{55}{24}\)
\(=\dfrac{1}{8}\cdot\dfrac{55}{8}\)
`= 55/64`
\(9,\left[\dfrac{3}{5}+\left(\dfrac{-1}{4}\right)\right]:\dfrac{3}{7}+\left[\left(\dfrac{-3}{4}\right)+\dfrac{2}{5}\right]:\dfrac{3}{7}\)
\(=\left\{\left[\dfrac{3}{5}+\left(\dfrac{-1}{4}\right)\right]+\left[\left(\dfrac{-3}{4}\right)+\dfrac{2}{5}\right]\right\}:\dfrac{3}{7}\)
\(=\left\{\dfrac{3}{5}-\dfrac{1}{4}-\dfrac{3}{4}+\dfrac{2}{5}\right\}:\dfrac{3}{7}\)
\(=\left\{\left(\dfrac{3}{5}+\dfrac{2}{5}\right)-\left(\dfrac{1}{4}+\dfrac{3}{4}\right)\right\}:\dfrac{3}{7}\)
\(=\left\{1-1\right\}:\dfrac{3}{7}\)
`= 0 : 3/7`
`= 0`
\(10,\dfrac{7}{8}:\left(\dfrac{2}{9}-\dfrac{1}{18}\right)+\dfrac{7}{8}:\left(\dfrac{1}{36}-\dfrac{5}{12}\right)\)
`= 7/8 : 1/6 + 7/8 : (-7/18)`
`= 7/8 : [1/6 + (-7/18)]`
`= 7/8 : [3/18 + (-7/18)]`
`= 7/8 : -2/9`
`= 7/8 * -9/2`
`=-63/16`
