1.105. Вычислите:

Решение:

A) \(2\frac{3}{4}-0,6 = \frac{11}{4}-0,6 = 2,75-0,6 = 2,15\)

Б) \(121,2 : \frac{6}{25} = 121,2 \cdot \frac{25}{6} = 20,2 \cdot 25 = 505\)

B) \(5,18 \cdot \frac{5}{7} = \frac{518}{100} \cdot \frac{5}{7} = \frac{259}{50} \cdot \frac{5}{7} = \frac{259}{10 \cdot 7} = \frac{37}{10} = 3,7\)

Г) \(0,36 + \frac{1}{2} = 0,36 + 0,5 = 0,86\)

Д) \(5,8 - \frac{3}{4} = 5,8 - 0,75 = 5,05\)

E) \(\frac{2}{5} : 0,001 = 0,4 : 0,001 = 400\)

Ë) \(\frac{2}{3} + 0,6 = \frac{2}{3} + \frac{6}{10} = \frac{2}{3} + \frac{3}{5} = \frac{10+9}{15} = \frac{19}{15} = 1\frac{4}{15}\)

Ж) \(0,75^3 = \left(\frac{3}{4}\right)^3 = \frac{27}{64}\)

3) \(1\frac{1}{6} - 0,5 = \frac{7}{6} - \frac{1}{2} = \frac{7-3}{6} = \frac{4}{6} = \frac{2}{3}\)

И) \(0,3 - \frac{5}{9} = \frac{3}{10} - \frac{5}{9} = \frac{27-50}{90} = -\frac{23}{90}\)

Й) \(\frac{8}{11} : 0,4 = \frac{8}{11} : \frac{4}{10} = \frac{8}{11} \cdot \frac{10}{4} = \frac{2}{11} \cdot 10 = \frac{20}{11} = 1\frac{9}{11}\)

K) \(3\frac{4}{5} - 1,8 = \frac{19}{5} - 1,8 = 3,8 - 1,8 = 2\)

Л) \(0,84 \cdot \frac{3}{4} = \frac{84}{100} \cdot \frac{3}{4} = \frac{21}{25} \cdot \frac{3}{4} = \frac{63}{100} = 0,63\)

M) \(2,2 : \frac{11}{15} = \frac{22}{10} : \frac{11}{15} = \frac{11}{5} \cdot \frac{15}{11} = 3\)

H) \(3\frac{9}{10} + 1,68 = 3,9 + 1,68 = 5,58\)

O) \(4,2 : 3\frac{1}{2} = 4,2 : 3,5 = \frac{42}{10} : \frac{7}{2} = \frac{21}{5} \cdot \frac{2}{7} = \frac{3}{5} \cdot 2 = \frac{6}{5} = 1,2\)

П) \(1\frac{1}{5} - 20,08 = 1,2 - 20,08 = -18,88\)

P) \(5,384 - \frac{4}{20} = 5,384 - 0,2 = 5,184\)

C) \(1\frac{1}{3} + 2,5 = \frac{4}{3} + 2,5 = \frac{4}{3} + \frac{5}{2} = \frac{8+15}{6} = \frac{23}{6} = 3\frac{5}{6}\)

T) \(7\frac{3}{8} - 2,35 = 7,375 - 2,35 = 5,025\)

У) \(5,7 : 6\frac{1}{3} = 5,7 : \frac{19}{3} = \frac{57}{10} \cdot \frac{3}{19} = \frac{3}{10} \cdot 3 = \frac{9}{10} = 0,9\)

Ф) \(42,14 : \frac{1}{7} = 42,14 \cdot 7 = 294,98\)

X) \(1\frac{1}{5} + 3,2 = 1,2 + 3,2 = 4,4\)

Ц) \(3,6 : \frac{2}{9} = \frac{36}{10} \cdot \frac{9}{2} = \frac{18}{5} \cdot 9 = \frac{162}{5} = 32,4\)

Ч) \(7\frac{3}{5} - 3,059 = 7,6 - 3,059 = 4,541\)

Ш) \(\frac{1}{8} : 12,5 = 0,125 : 12,5 = 0,01\)

Щ) \(2\frac{3}{11} - 0,22 = \frac{25}{11} - 0,22 = \frac{25}{11} - \frac{22}{100} = \frac{25}{11} - \frac{11}{50} = \frac{1250-121}{550} = \frac{1129}{550} = 2\frac{29}{550}\)

) \(2,5 + 8\frac{4}{11} = 2,5 + \frac{92}{11} = \frac{5}{2} + \frac{92}{11} = \frac{55+184}{22} = \frac{239}{22} = 10\frac{19}{22}\)

Б) \(9\frac{7}{11} : 1,06 = \frac{106}{11} : \frac{106}{100} = \frac{106}{11} \cdot \frac{100}{106} = \frac{100}{11} = 9\frac{1}{11}\)

6) \(8,02 - 3\frac{1}{3} = 8,02 - \frac{10}{3} = \frac{802}{100} - \frac{10}{3} = \frac{401}{50} - \frac{10}{3} = \frac{1203-500}{150} = \frac{703}{150} = 4\frac{103}{150}\)

Ответ: см. решения выше.