Đáp án:

Giải thích các bước giải:

Câu 7)

$\frac{-5}{9} + \frac{8}{15} + \frac{-2}{11} + \frac{4}{-9} + \frac{7}{15}$

$= \left( \frac{-5}{9} + \frac{-4}{9} \right) + \left( \frac{8}{15} + \frac{7}{15} \right) + \frac{-2}{11}$

$= \frac{-9}{9} + \frac{15}{15} + \frac{-2}{11}$

$= -1 + 1 + \frac{-2}{11}$

$= 0 + \frac{-2}{11} = \mathbf{\frac{-2}{11}}$

Câu 8)

$\frac{-8}{17} + \frac{8}{23} - \frac{9}{17} + \frac{15}{23} + \frac{2014}{2015}$

$= \left( \frac{-8}{17} - \frac{9}{17} \right) + \left( \frac{8}{23} + \frac{15}{23} \right) + \frac{2014}{2015}$

$= \frac{-17}{17} + \frac{23}{23} + \frac{2014}{2015}$

$= -1 + 1 + \frac{2014}{2015} = \mathbf{\frac{2014}{2015}}$

Câu 9)

$\frac{2018}{2019} \cdot \frac{7}{18} - \frac{2018}{2019} \cdot \frac{11}{-18}$

$= \frac{2018}{2019} \cdot \frac{7}{18} + \frac{2018}{2019} \cdot \frac{11}{18}$ (Đổi dấu âm dưới mẫu)

$= \frac{2018}{2019} \cdot \left( \frac{7}{18} + \frac{11}{18} \right)$

$= \frac{2018}{2019} \cdot \frac{18}{18}$

$= \frac{2018}{2019} \cdot 1 = \mathbf{\frac{2018}{2019}}$

Bài 3: Thực hiện phép tính

Câu 1)

$\frac{3}{4} + \frac{1}{4} : \left( 1,25 - \frac{3}{4} \right) : \frac{5}{8}$

$= \frac{3}{4} + \frac{1}{4} : \left( \frac{5}{4} - \frac{3}{4} \right) : \frac{5}{8}$

$= \frac{3}{4} + \frac{1}{4} : \frac{2}{4} : \frac{5}{8}$

$= \frac{3}{4} + \frac{1}{4} \cdot \frac{4}{2} \cdot \frac{8}{5}$

$= \frac{3}{4} + \frac{1}{2} \cdot \frac{8}{5} = \frac{3}{4} + \frac{4}{5}$

$= \frac{15}{20} + \frac{16}{20} = \mathbf{\frac{31}{20}}$

Câu 2)

$1\frac{1}{3} \cdot 0,75 - 4\frac{1}{2} : \left( -1\frac{4}{5} \right) + (-0,5)$

$= \frac{4}{3} \cdot \frac{3}{4} - \frac{9}{2} : \left( -\frac{9}{5} \right) - \frac{1}{2}$

$= 1 - \left( \frac{9}{2} \cdot \frac{-5}{9} \right) - \frac{1}{2}$

$= 1 - \left( \frac{-5}{2} \right) - \frac{1}{2}$

$= 1 + \frac{5}{2} - \frac{1}{2} = 1 + \frac{4}{2} = 1 + 2 = \mathbf{3}$

Câu 3)

$\left( \frac{3}{8} + \frac{-3}{4} + \frac{7}{12} \right) : \frac{5}{6} + \frac{1}{2}$

$= \left( \frac{9}{24} + \frac{-18}{24} + \frac{14}{24} \right) \cdot \frac{6}{5} + \frac{1}{2}$

$= \frac{5}{24} \cdot \frac{6}{5} + \frac{1}{2}$

$= \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \mathbf{\frac{3}{4}}$

Câu 4)

$1\frac{1}{3} \cdot (0,5) + \left( \frac{8}{15} - \frac{19}{30} \right) : \frac{6}{15}$

$= \frac{4}{3} \cdot \frac{1}{2} + \left( \frac{16}{30} - \frac{19}{30} \right) \cdot \frac{15}{6}$

$= \frac{2}{3} + \left( \frac{-3}{30} \right) \cdot \frac{15}{6}$

$= \frac{2}{3} + \left( \frac{-1}{10} \right) \cdot \frac{5}{2}$

$= \frac{2}{3} - \frac{1}{4} = \frac{8}{12} - \frac{3}{12} = \mathbf{\frac{5}{12}}$