$\frac{a}{b}$
при a = 2, b = 1:
$\frac{2}{1} = 2$
при a = −1, b = −3:
$\frac{-1}{-3} = \frac{1}{3}$
при $a = \frac{1}{2}$, b = 0,2:
$\frac{\frac{1}{2}}{0,2} = \frac{\frac{1}{2}}{\frac{1}{5}} = \frac{1}{2} * \frac{5}{1} = 2,5$
при a = 0,4, $b = -\frac{1}{3}$:
$\frac{0,4}{-\frac{1}{3}} = \frac{2}{5} * (-\frac{3}{1}) = -\frac{6}{5} = -1,2$
 
$a - \frac{1}{b}$
при a = 2, b = 1:
$2 - \frac{1}{1} = 2 - 1 = 2$
при a = −1, b = −3:
$-1 - \frac{1}{-3} = -1 + \frac{1}{3} = -\frac{2}{3}$
при $a = \frac{1}{2}$, b = 0,2:
$\frac{1}{2} - \frac{1}{0,2} = \frac{1}{2} - \frac{1}{\frac{1}{5}} = \frac{1}{2} - 5 = -4,5$
при a = 0,4, $b = -\frac{1}{3}$:
$0,4 - \frac{1}{-\frac{1}{3}} = 0,4 + 3 = 3,4$
 
$\frac{a + b}{a}$
при a = 2, b = 1:
$\frac{2 + 1}{2} = \frac{3}{2} = 1,5$
при a = −1, b = −3:
$\frac{-1 - 3}{-1} = \frac{-4}{-1} = 4$
при $a = \frac{1}{2}$, b = 0,2:
$\frac{\frac{1}{2} + 0,2}{\frac{1}{2}} = \frac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{2}} = \frac{\frac{5 + 2}{10}}{\frac{1}{2}} = \frac{7}{10} * 2 = \frac{7}{5} = 1,4$
при a = 0,4, $b = -\frac{1}{3}$:
$\frac{0,4 - \frac{1}{3}}{0,4} = \frac{\frac{2}{5} - \frac{1}{3}}{\frac{2}{5}} = \frac{\frac{6 - 5}{15}}{\frac{2}{5}} = \frac{1}{15} * \frac{5}{2} = \frac{1}{3} * \frac{1}{2} = \frac{1}{6}$
 
$\frac{a - b}{a + b}$
при a = 2, b = 1:
$\frac{2 - 1}{2 + 1} = \frac{1}{3}$
при a = −1, b = −3:
$\frac{-1 - (-3)}{-1 - 3} = \frac{-1 + 3}{-4} = -\frac{2}{4} = -0,5$
при $a = \frac{1}{2}$, b = 0,2:
$\frac{\frac{1}{2} - 0,2}{\frac{1}{2} + 0,2} = \frac{0,5 - 0,2}{0,5 + 0,2} = \frac{0,3}{0,7} = \frac{3}{10} * \frac{10}{7} = \frac{3}{7}$
при a = 0,4, $b = -\frac{1}{3}$:
$\frac{0,4 - (-\frac{1}{3})}{0,4 - \frac{1}{3}} = \frac{\frac{2}{5} + \frac{1}{3}}{\frac{2}{5} - \frac{1}{3}} = \frac{\frac{6 + 5}{15}}{\frac{6 - 5}{15}} = \frac{11}{15} * \frac{15}{1} = 11$
 
$\frac{a^2 - b^2}{a - 2b}$
при a = 2, b = 1:
$\frac{2^2 - 1^2}{2 - 2 * 1} = \frac{4 - 1}{0}$ − не имеет смысла
при a = −1, b = −3:
$\frac{(-1)^2 - (-3)^2}{-1 - 2 * (-3)} = \frac{1 - 9}{-1 + 6} = \frac{-8}{5} = -1,6$
при $a = \frac{1}{2}$, b = 0,2:
$\frac{(\frac{1}{2})^2 - 0,2^2}{\frac{1}{2} - 2 * 0,2} = \frac{\frac{1}{4} - 0,04}{0,5 - 0,4} = \frac{0,25 - 0,04}{0,1} = \frac{0,21}{0,1} = 2,1$
при a = 0,4, $b = -\frac{1}{3}$:
$\frac{0,4^2 - (-\frac{1}{3})^2}{0,4 - 2 * (-\frac{1}{3})} = \frac{0,16 - \frac{1}{9}}{0,4 + \frac{2}{3}} = \frac{\frac{4}{25} - \frac{1}{9}}{\frac{2}{5} + \frac{2}{3}} = \frac{\frac{36 - 25}{225}}{\frac{6 + 10}{15}} = \frac{11}{225} * \frac{15}{16} = \frac{11}{15} * \frac{1}{16} = \frac{11}{240}$