Đáp án:

Bài 2 :

$1. \frac{2}{11} > \frac{-3}{11}$

$2. \frac{-13}{12} = -1\frac{1}{12}$

$3. 0,75 < \frac{5}{4}$

$4. -0,125 = \frac{-1}{8}$

$5. \frac{-2}{3} < \frac{-9}{15}$

$6. \frac{-1}{5} < \frac{-1}{10}$

Bài 3 :

$1. \frac{-17}{13}$

$2. 0$

$3. \frac{-9}{10}$

$4. \frac{-7}{12}$

$5. \frac{-2}{3}$

$6. \frac{-5}{7}$

Bài 4 :

$1. x = \frac{17}{14}$

$2. x = \frac{-4}{7}$

$3. x = \frac{-5}{21}$

$4. x = -4$

$5. x = \frac{-11}{4}$

$6. x = \frac{-3}{2}$

Giải thích các bước giải:

Bài 2 :

$1. \frac{2}{11} > 0 , \frac{-3}{11} < 0$

⇒ $\frac{2}{11} > 0 > \frac{-3}{11}$

⇔ $\frac{2}{11} > \frac{-3}{11}$

$2. -1\frac{1}{12} = - \frac{1×12+1}{12} = \frac{-13}{12}$

⇒ $\frac{-13}{12} = -1\frac{1}{12}$

$3. 0,75 = \frac{75}{100} = \frac{3×25}{4×25} = \frac{3}{4}$

Nhận xét : $\frac{3}{4} < \frac{5}{4}$

hay $0,75 < \frac{5}{4}$

$4. -0,125 = \frac{-125}{1000} = \frac{-125}{125×8} = \frac{-1}{8}$

⇒ $-0,125 = \frac{-1}{8}$

$5.\frac{-2}{3} = \frac{-2×5}{3×5} = \frac{-10}{15}$

Nhận xét : $\frac{10}{15} > \frac{9}{15}$

⇒ $\frac{-10}{15} < \frac{-9}{15}$

hay $\frac{-2}{3} < \frac{-9}{15}$

$6. \frac{-1}{5} = \frac{-1×2}{5×2} = \frac{-2}{10}$

Nhận xét : $\frac{2}{10} > \frac{1}{10}$

⇒ $\frac{-2}{10} < \frac{-1}{10}$

hay $\frac{-1}{5} < \frac{-1}{10}$

Bài 3 :

$1. \frac{-2}{13} - \frac{15}{13} = \frac{-2-15}{13} = \frac{-17}{13}$

$2. \frac{-5}{6} + \frac{5}{6} = \frac{-5+5}{6} = 0$

$3. \frac{13}{5} - \frac{7}{2} = \frac{13×2-7×5}{5×2} = \frac{26-35}{10} = \frac{-9}{10}$

$4. \frac{-1}{3} + \frac{-1}{4} = \frac{-1×4-1×3}{3×4} = \frac{-4-3}{12} = \frac{-7}{12}$

$5. \frac{17}{18} - \frac{11}{6} + \frac{2}{9}$

$= \frac{17}{18} - \frac{11×3}{6×3} + \frac{2×2}{9×2}$

$= \frac{17}{18} - \frac{33}{18} + \frac{4}{18}$

$= \frac{-12}{18} = \frac{-2×6}{3×6}$

$= \frac{-2}{3}$

$6. \frac{21}{28} - ( \frac{5}{7} + \frac{3}{4} )$

$= \frac{3×7}{4×7} - \frac{5}{7} - \frac{3}{4}$

$= \frac{3}{4} - \frac{5}{7} - \frac{3}{4}$

$= ( \frac{3}{4} - \frac{3}{4} ) - \frac{5}{7}$

$= \frac{-5}{7}$

Bài 4 :

$1. x - \frac{1}{2} = \frac{5}{7}$

⇔ $x = \frac{5}{7} + \frac{1}{2}$

⇔ $x = \frac{5×2+1×7}{7×2}$

⇔ $x = \frac{10+7}{14}$

⇔ $x = \frac{17}{14}$

$2. x - \frac{2}{7} = \frac{-6}{7}$

⇔ $x = \frac{-6}{7} + \frac{2}{7}$

⇔ $x = \frac{-4}{7}$

$3. \frac{4}{7} + x = \frac{1}{3}$

⇔ $x = \frac{1}{3} - \frac{4}{7}$

⇔ $x = \frac{1×7-4×3}{3×7}$

⇔ $x = \frac{7-12}{21}$

⇔ $x = \frac{-5}{21}$

$4. x + \frac{5}{2} = \frac{-3}{2}$

⇔ $x = \frac{-3}{2} - \frac{5}{2}$

⇔ $x = \frac{-8}{2}$

⇔ $x = -4$

$5. \frac{-5}{4} - x = 1\frac{1}{2}$

⇔ $\frac{-5}{4} - x = \frac{1×2+1}{2}$

⇔ $\frac{-5}{4} - x = \frac{3}{2}$

⇔ $x = \frac{-5}{4} - \frac{3}{2}$

⇔ $x = \frac{-5}{4} - \frac{6}{4}$

⇔ $x = \frac{-11}{4}$

$6. \frac{7}{2} - x = 5$

⇔ $x = \frac{7}{2} - 5$

⇔ $x = \frac{7}{2} - \frac{10}{2}$

⇔ $x = \frac{-3}{2}$