$$\begin{gathered} \mathrm{x}-\frac{1}{6}=\frac{7}{30} \\ \mathrm{x}=\frac{7}{30}+\frac{1}{6} \\ \mathrm{x}=\frac{7}{30}+\frac{5}{30} \\ \mathrm{x}=\frac{12}{30}=\frac{2}{5} \end{gathered}$$

$$\begin{gathered} \frac{15}{34}+\frac{7}{21}+\frac{19}{34}-1\frac{15}{17}+\frac{2}{3} \\ =\frac{15}{34}+\frac{1}{3}+\frac{19}{34}-\frac{32}{17}+\frac{2}{3} \\ =\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{1}{3}+\frac{2}{3}\right)-\frac{32}{17} \\ =1+1-\frac{32}{17} \\ =2-\frac{32}{17} \\ =\frac{34}{17}-\frac{32}{17} \\ =\frac{2}{17} \end{gathered}$$

$$\begin{gathered} \mathrm{x}-\frac{1}{3}=-\frac{3}{4} \\ \mathrm{x}=-\frac{3}{4}+\frac{1}{3} \\ \mathrm{x}=-\frac{9}{12}+\frac{4}{12} \\ \mathrm{x}=-\frac{5}{12} \end{gathered}$$

Ta có:

$$\begin{gathered} \frac{1}{2}-\frac{1}{3}-\frac{1}{4} \\ =\frac{6}{12}-\frac{4}{12}-\frac{3}{12} \\ =\frac{2}{12}-\frac{3}{12} \\ =\frac{-1}{12} \end{gathered}$$

$$\begin{gathered} \frac{1}{48}-\frac{1}{16}+\frac{1}{6} \\ =\frac{1}{48}-\frac{3}{48}+\frac{8}{48} \\ =\frac{-2}{48}+\frac{8}{48} \\ =\frac{6}{48}=\frac{1}{8} \end{gathered}$$

Do đó ta có: $\frac{-1}{12}<\boxed{}<\frac{1}{8}$ hay $\frac{-2}{24}<\boxed{}<\frac{3}{24}$.

Vậy số nguyên thích hợp cần điền vào ô trống là: $\frac{0}{24}=0$

$$\begin{gathered} 0,7+\frac{-2}{3}=\frac{7}{10}+\frac{-2}{3} \\ =\frac{21}{30}+\frac{-20}{30}=\frac{1}{30} \end{gathered}$$

$\frac{1}{3}+\frac{1}{3}-\frac{7}{3}=\frac{2}{3}-\frac{7}{3}=\frac{-5}{3}$

$\frac{2}{3}+\frac{4}{5}=\frac{10}{15}+\frac{12}{15}=\frac{22}{15}$

$$\begin{gathered} \frac{1}{3}-\left(-0,4\right) \\ =\frac{1}{3}+\frac{4}{10}=\frac{1}{3}+\frac{2}{5} \\ =\frac{5}{15}+\frac{6}{15}=\frac{11}{15} \end{gathered}$$

Do đó A đúng.

$$\begin{gathered} \frac{2}{7}+75\% \\ =\frac{2}{7}+\frac{75}{100}=\frac{2}{7}+\frac{3}{4} \\ =\frac{8}{28}+\frac{21}{28}=\frac{29}{28} \end{gathered}$$

Do đó B đúng.

$$\begin{gathered} \frac{-2}{3}+\frac{6}{7} \\ =\frac{-14}{21}+\frac{18}{21}=\frac{4}{21} \end{gathered}$$

Do đó C đúng.

$$\begin{gathered} 3,5-\left(-\frac{2}{7}\right) \\ =\frac{35}{10}+\frac{2}{7}=\frac{7}{2}+\frac{2}{7} \\ =\frac{49}{14}+\frac{4}{14}=\frac{53}{14} \end{gathered}$$

Do đó D sai.

$\frac{5}{12}+\frac{-7}{24}=\frac{10}{24}-\frac{7}{24}=\frac{3}{24}=\frac{1}{8}>0$

Vậy kết quả của phép tính đã cho là một số hữu tỉ dương.

$$\begin{gathered} \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1999.2000} \\ =\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{1999}-\frac{1}{2000} \\ =\frac{1}{1}-\frac{1}{2000} \\ =\frac{2000}{2000}-\frac{1}{2000}=\frac{1999}{2000} \end{gathered}$$

Chọn B.

$$\begin{gathered} \frac{17}{6}-\left(\mathrm{x}-\frac{7}{6}\right)=\frac{7}{4} \\ \mathrm{x}-\frac{7}{6}=\frac{17}{6}-\frac{7}{4} \\ \mathrm{x}-\frac{7}{6}=\frac{34}{12}-\frac{21}{12} \\ \mathrm{x}-\frac{7}{6}=\frac{13}{12} \\ \mathrm{x}=\frac{13}{12}+\frac{7}{6} \\ \mathrm{x}=\frac{13}{12}+\frac{14}{12} \\ \mathrm{x}=\frac{27}{12}=\frac{9}{4} \end{gathered}$$

Ta có: $\frac{1}{4}+\frac{8}{9}=\frac{9}{36}+\frac{32}{36}=\frac{41}{36}$

$$\begin{gathered} 1-\left(\frac{5}{9}-\frac{3}{4}\right) \\ =1-\left(\frac{20}{36}-\frac{27}{36}\right) \\ =\frac{36}{36}+\frac{7}{36}=\frac{43}{36} \end{gathered}$$

Suy ra: $\frac{41}{36}\le \frac{\mathrm{x}}{36}<\frac{43}{36}$ hay $41\le \mathrm{x}<43$

Mà x là số nguyên nên x = 41, x = 42.

Có hai giá trị nguyên của x thỏa mãn yêu cầu đầu bài

Ta có:

$\frac{7}{3}-\frac{23}{5}=\frac{35}{15}-\frac{69}{15}=\frac{-34}{15}$

Do đó A sai.

$\frac{5}{3}-\frac{3}{5}=\frac{25}{15}-\frac{9}{15}=\frac{16}{25}$

Do đó B đúng.

$$\begin{gathered} 2\mathrm{x}-3=\mathrm{x}+\frac{1}{2} \\ 2\mathrm{x}-\mathrm{x}=3+\frac{1}{2} \\ \mathrm{x}=\frac{7}{2} \end{gathered}$$

$$\begin{gathered} \frac{1}{2}+\left(\frac{16}{21}+\frac{27}{13}\right)-\left(\frac{14}{13}-\frac{5}{21}\right) \\ =\frac{1}{2}+\frac{16}{21}+\frac{27}{13}-\frac{14}{13}+\frac{5}{21} \\ =\frac{1}{2}+\left(\frac{16}{21}+\frac{5}{21}\right)+\left(\frac{27}{13}-\frac{14}{13}\right) \\ =\frac{1}{2}+1+1 \\ =\frac{5}{2} \end{gathered}$$