Đáp án + Giải thích các bước giải:

$\textbf{A} = -\dfrac{5}{18} +\dfrac{32}{45} - \dfrac{9}{10}$

$= -\dfrac{25}{90} + \dfrac{64}{90} - \dfrac{81}{90}$

$= -\dfrac{42}{90}$

$= -\dfrac{7}{15}$

$\textbf{B} = \bigg(-\dfrac{1}{4} + \dfrac{7}{33} - \dfrac{5}{3}\bigg) - \bigg(-\dfrac{15}{12} + \dfrac{6}{11} - \dfrac{48}{49}\bigg)$

$= -\dfrac{1}{4} + \dfrac{7}{33} - \dfrac{5}{3} + \dfrac{15}{12} - \dfrac{6}{11} + \dfrac{48}{49}$

$= -\dfrac{1}{4} + \dfrac{7}{33} - \dfrac{5}{3} + \dfrac{5}{4} - \dfrac{18}{33} + \dfrac{48}{49}$

$= \bigg(-\dfrac{1}{4} + \dfrac{5}{4} - \dfrac{5}{3}\bigg) + \bigg(\dfrac{7}{33} - \dfrac{18}{33}\bigg) + \dfrac{48}{49}$

$= \bigg(1 - \dfrac{5}{3}\bigg) - \dfrac{11}{33} + \dfrac{48}{49}$

$= -\dfrac{2}{3} - \dfrac{1}{3} + \dfrac{48}{49}$

$= -1 + \dfrac{48}{49}$

$= -\dfrac{1}{49}$

$\textbf{C} = \dfrac{11}{125} - \dfrac{17}{18} - \dfrac{5}{7} + \dfrac{4}{9} + \dfrac{17}{14}$

$= \dfrac{11}{125} + \bigg(\dfrac{4}{9} - \dfrac{17}{18}\bigg) + \bigg(\dfrac{17}{14} - \dfrac{5}{7}\bigg)$

$= \dfrac{11}{125} + \bigg(\dfrac{8}{18} - \dfrac{17}{18}\bigg) + \bigg(\dfrac{17}{14} - \dfrac{10}{14}\bigg)$

$= \dfrac{11}{125} - \dfrac{9}{18} + \dfrac{7}{14}$

$= \dfrac{11}{125} -\dfrac{1}{2} + \dfrac{1}{2}$

$= \dfrac{11}{125}$

$\textbf{D} = 1 - \dfrac{1}{2} + 2 - \dfrac{2}{3} + 3 - \dfrac{3}{4} + 4 - \dfrac{1}{4} - 3 - \dfrac{1}{3} - 2 - \dfrac{1}{2} - 1$

$= (1 + 2 + 3 + 4 - 3 - 2 - 1) - \dfrac{1}{2} - \dfrac{2}{3} - \dfrac{3}{4} - \dfrac{1}{4} - \dfrac{1}{3} - \dfrac{1}{2}$

$= 4 - \dfrac{1}{2} - \dfrac{1}{2} - \dfrac{2}{3} - \dfrac{1}{3} - \dfrac{3}{4} - \dfrac{1}{4}$

$= 4 - \bigg(\dfrac{1}{2} + \dfrac{1}{2}\bigg) - \bigg(\dfrac{2}{3} + \dfrac{1}{3}\bigg) - \bigg(\dfrac{3}{4} +\dfrac{1}{4}\bigg)$

$= 4 - 1 - 1 - 1$

$= 1$