Зариант 1 1. Найдите значение выражения: а) 13 – 11,2 : 9 ; б) 3,6+4,8. (8-7). 5 3 5 6

1. Найдите значение выражения:

a) $$13\frac{2}{5}-11,2:9\frac{1}{3};$$

$$13\frac{2}{5} = \frac{13 \cdot 5 + 2}{5} = \frac{65+2}{5} = \frac{67}{5};$$

$$9\frac{1}{3} = \frac{9 \cdot 3 + 1}{3} = \frac{27+1}{3} = \frac{28}{3};$$

$$11,2:9\frac{1}{3} = 11,2 : \frac{28}{3} = \frac{112}{10} : \frac{28}{3} = \frac{112}{10} \cdot \frac{3}{28} = \frac{4 \cdot 3}{10} = \frac{12}{10} = 1,2;$$

$$13\frac{2}{5}-11,2:9\frac{1}{3} = \frac{67}{5} - 1,2 = \frac{67}{5} - \frac{12}{10} = \frac{67 \cdot 2}{5 \cdot 2} - \frac{12}{10} = \frac{134}{10} - \frac{12}{10} = \frac{134-12}{10} = \frac{122}{10} = 12,2.$$

б) $$3,6+4,8 \cdot (8\frac{3}{4}-7\frac{5}{6}).$$

$$8\frac{3}{4} = \frac{8 \cdot 4 + 3}{4} = \frac{32+3}{4} = \frac{35}{4};$$

$$7\frac{5}{6} = \frac{7 \cdot 6 + 5}{6} = \frac{42+5}{6} = \frac{47}{6};$$

$$8\frac{3}{4}-7\frac{5}{6} = \frac{35}{4} - \frac{47}{6} = \frac{35 \cdot 3}{4 \cdot 3} - \frac{47 \cdot 2}{6 \cdot 2} = \frac{105}{12} - \frac{94}{12} = \frac{105-94}{12} = \frac{11}{12};$$

$$3,6+4,8 \cdot (8\frac{3}{4}-7\frac{5}{6}) = 3,6 + 4,8 \cdot \frac{11}{12} = 3,6 + \frac{48}{10} \cdot \frac{11}{12} = 3,6 + \frac{4 \cdot 11}{10} = 3,6 + \frac{44}{10} = 3,6 + 4,4 = 8.$$

Ответ: а) 12,2; б) 8.