Giải thích các bước giải: image

Đáp án:

 $1) 0\\ 2) \dfrac{77}{30}\\ 3) \dfrac{11}{20}\\ 4) 5\\ 5) \dfrac{50}{7}\\ 6) -8\\ 7) 12\\ 8) \dfrac{11}{20}\\ 9) \dfrac{109}{27}\\ 10) \dfrac{7}{18}\\ 11) \dfrac{-3}{4}$

Giải thích các bước giải:

 $1) \dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{20}{15}\\ =\dfrac{15}{34}+\dfrac{19}{34}+\dfrac{1}{3}-\dfrac{4}{3}\\ =\dfrac{34}{34}+\dfrac{-3}{3}\\ =1-1=0\\ 2) 2\dfrac{5}{6}+\dfrac{1}{6}:\dfrac{-5}{8}\\ =\dfrac{17}{6}+\dfrac{1}{6}.\dfrac{-8}{5}\\ =\dfrac{17}{6}-\dfrac{4}{15}\\ =\dfrac{85}{30}-\dfrac{8}{30}\\ =\dfrac{77}{30}\\ 3) 3-\dfrac{3}{2}+\dfrac{1}{4}-1\dfrac{1}{5}\\ =\dfrac{60}{20}-\dfrac{30}{20}+\dfrac{5}{20}-\dfrac{6}{5}\\ =\dfrac{35}{20}-\dfrac{24}{30}\\ =\dfrac{11}{20}\\ 4) 5^3:125+2^4:4\\ =5^3:5^3+2^4:2^2\\ =1+2^2\\ =5\\ 5) 23\dfrac{1}{4}:\dfrac{7}{5}-13\dfrac{1}{4}:\dfrac{7}{5}\\ =23\dfrac{1}{4}.\dfrac{5}{7}-13\dfrac{1}{4}.\dfrac{5}{7}\\ =\left ( 23\dfrac{1}{4}-13\dfrac{1}{4} \right ).\dfrac{5}{7}\\ =\left ( 23-13+\dfrac{1}{4}-\dfrac{1}{4} \right ).\dfrac{5}{7}\\ =10.\dfrac{5}{7}\\ =\dfrac{50}{7}\\ 6) 12\dfrac{1}{5}.\dfrac{4}{5}-22\dfrac{1}{5}.\dfrac{4}{5}\\ =\dfrac{4}{5}.\left ( 12\dfrac{1}{5}-22\dfrac{1}{5} \right )\\ =\dfrac{4}{5}.\left ( 12-22+\dfrac{1}{5}-\dfrac{1}{5} \right )\\ =\dfrac{4}{5}.(-10)\\ =-8\\ 7) (-2)^2+\sqrt{49}-\sqrt{16}+\sqrt{25}\\ =4+7-4+5\\ =12\\ 8) \dfrac{4}{5}-\left ( \dfrac{-1}{2} \right )^2\\ =\dfrac{4}{5}-\dfrac{1}{4}\\ =\dfrac{16}{20}-\dfrac{5}{20}\\ =\dfrac{11}{20}\\ 9) 5-\left ( -\dfrac{5}{7} \right )^0+\left ( \dfrac{1}{3} \right )^2:3\\ =5-1+\left (\dfrac{1}{3}  \right )^2.\dfrac{1}{3}\\ =4+\left (\dfrac{1}{3}  \right )^3\\ =4+\dfrac{1}{27}\\ =\dfrac{108}{27}+\dfrac{1}{27}\\ =\dfrac{109}{27}\\ 10) \dfrac{2}{9}.\left ( \dfrac{5}{2}-\dfrac{3}{4} \right )\\ =\dfrac{2}{9}.\left ( \dfrac{10}{4}-\dfrac{3}{4} \right )\\ =\dfrac{2}{9}.\dfrac{7}{4}\\ =\dfrac{7}{18}\\ 11) 16.\left ( -\dfrac{1}{4} \right )^3-\dfrac{1}{2}\\ =16.\dfrac{-1}{64}-\dfrac{1}{2}\\ =\dfrac{-1}{4}-\dfrac{1}{2}\\ =\dfrac{-1}{4}-\dfrac{2}{4}\\ =\dfrac{-3}{4}$