Спрости вираз і знайди його значення:
Розв'язок:
1) $2\frac{1}{3}a + 3\frac{5}{6}a - 7 = \frac{7}{3}a + \frac{23}{6}a - 7 =$
$= \frac{14}{6}a + \frac{23}{6}a - 7 = \frac{37}{6}a - 7 =$
$= 6\frac{1}{6}a - 7$
$6\frac{1}{6} \cdot 2\frac{2}{3} - 7 = \frac{37}{6} \cdot \frac{8}{3} - 7 =$
$= 16\frac{4}{9} - 7 = 15\frac{13}{9} - 7 = 9\frac{4}{9}$
$6\frac{1}{6} \cdot 16 - 7 = \frac{37}{6} \cdot 16 - 7 =$
$= 98\frac{2}{3} - 7 = 91\frac{2}{3}$
$6\frac{1}{6} \cdot 2\frac{2}{5} - 7 = \frac{37}{6} \cdot \frac{12}{5} - 7 =$
$= \frac{74}{5} - 7 = 14\frac{4}{5} - 7 = 7\frac{4}{5}$
2) $\frac{7}{8}x + 1\frac{9}{10}y - \frac{1}{6}x + \frac{13}{20}y =$
$= \left(\frac{7}{8}x - \frac{1}{6}x\right) + \left(1\frac{9}{10}y + \frac{13}{20}y\right) =$
$= \left(\frac{21}{24}x - \frac{4}{24}x\right) + \left(\frac{38}{20}y + \frac{13}{20}y\right) =$
$= \frac{17}{24}x + 2\frac{11}{20}y$
$\frac{17}{24} \cdot 1\frac{1}{2} + 2\frac{11}{20} \cdot \frac{5}{17} =$
$= \frac{17}{24} \cdot \frac{3}{2} + \frac{51}{20} \cdot \frac{5}{17} =$
$= \frac{17}{16} + \frac{3}{4} = \frac{17}{16} + \frac{12}{16} =$
$= \frac{29}{16} = 1\frac{13}{16}$