Вычислите (4.111-4.113). 4.111/1) 4/7:0,4+0,3. 5/6 2) 0,7+3/14:0,5 3) 14,4:1 1/8+5 3/7. 4) 11 1/9-18,9-4,2:5/6 4.112. 1) 1,8-(2+1 1/3) 3) 0,64:(5/8-1 5/32) 2) 7,5:(2 4/15+4/5) 4) 3,6:(5-1 3/4/9) 4.113. 1) (4/5)^2:(0,5)^3 3) (1,2)^2:(3/5)^3 2) (0.8)^2:(3/4)^3 4) (2,4)^2:(1 1/5)^3

Задание 4.111

1. \[\frac{4}{7} : 0.4 + 0.3 \cdot \frac{5}{6} = \frac{4}{7} : \frac{4}{10} + \frac{3}{10} \cdot \frac{5}{6} = \frac{4}{7} \cdot \frac{10}{4} + \frac{1}{2} \cdot \frac{1}{2} = \frac{10}{7} + \frac{1}{4} = \frac{40+7}{28} = \frac{47}{28} = 1\frac{19}{28}\]
2. \[0.7 + \frac{3}{14} : 0.5 = \frac{7}{10} + \frac{3}{14} : \frac{5}{10} = \frac{7}{10} + \frac{3}{14} \cdot \frac{10}{5} = \frac{7}{10} + \frac{3}{7} \cdot \frac{1}{1} = \frac{7}{10} + \frac{3}{7} = \frac{49+30}{70} = \frac{79}{70} = 1\frac{9}{70}\]
3. \[14.4 : 1\frac{1}{8} + 5\frac{3}{7} = 14.4 : \frac{9}{8} + \frac{38}{7} = \frac{144}{10} \cdot \frac{8}{9} + \frac{38}{7} = \frac{16}{5} \cdot \frac{8}{1} + \frac{38}{7} = \frac{128}{5} + \frac{38}{7} = \frac{896+190}{35} = \frac{1086}{35} = 30\frac{36}{35} = 30\frac{26}{35}\]
4. \[11\frac{1}{9} - 18.9 - 4.2 : \frac{5}{6} = \frac{100}{9} - \frac{189}{10} - \frac{42}{10} : \frac{5}{6} = \frac{100}{9} - \frac{189}{10} - \frac{42}{10} \cdot \frac{6}{5} = \frac{100}{9} - \frac{189}{10} - \frac{21}{5} \cdot \frac{6}{5} = \frac{100}{9} - \frac{189}{10} - \frac{126}{25} = \frac{25000 - 42525 - 22680}{2250} = -\frac{40205}{2250} = -17\frac{205}{2250} = -17\frac{41}{450}\]

Ответ: 1) 1 19/28; 2) 1 9/70; 3) 30 26/35; 4) -17 41/450

Задание 4.112

1. \[1.8 - (2 + 1\frac{1}{3}) = 1.8 - (2 + \frac{4}{3}) = 1.8 - \frac{10}{3} = \frac{18}{10} - \frac{10}{3} = \frac{9}{5} - \frac{10}{3} = \frac{27 - 50}{15} = -\frac{23}{15} = -1\frac{8}{15}\]
2. \[7.5 : (2\frac{4}{15} + \frac{4}{5}) = 7.5 : (\frac{34}{15} + \frac{12}{15}) = \frac{75}{10} : \frac{46}{15} = \frac{15}{2} \cdot \frac{15}{46} = \frac{225}{92} = 2\frac{41}{92}\]
3. \[0.64 : (\frac{5}{8} - 1\frac{5}{32}) = 0.64 : (\frac{5}{8} - \frac{37}{32}) = \frac{64}{100} : (\frac{20}{32} - \frac{37}{32}) = \frac{16}{25} : (-\frac{17}{32}) = \frac{16}{25} \cdot (-\frac{32}{17}) = -\frac{512}{425} = -1\frac{87}{425}\]
4. \[3.6 : (5 - 1\frac{3}{4} : \frac{3}{5}) = 3.6 : (5 - \frac{7}{4} : \frac{3}{5}) = \frac{36}{10} : (5 - \frac{7}{4} \cdot \frac{5}{3}) = \frac{18}{5} : (5 - \frac{35}{12}) = \frac{18}{5} : (\frac{60 - 35}{12}) = \frac{18}{5} : \frac{25}{12} = \frac{18}{5} \cdot \frac{12}{25} = \frac{216}{125} = 1\frac{91}{125}\]

Ответ: 1) -1 8/15; 2) 2 41/92; 3) -1 87/425; 4) 1 91/125

Задание 4.113

1. \[(\frac{4}{5})^2 : (0.5)^3 = \frac{16}{25} : (\frac{1}{2})^3 = \frac{16}{25} : \frac{1}{8} = \frac{16}{25} \cdot 8 = \frac{128}{25} = 5\frac{3}{25}\]
2. \[(0.8)^2 : (\frac{3}{4})^3 = (\frac{8}{10})^2 : \frac{27}{64} = (\frac{4}{5})^2 : \frac{27}{64} = \frac{16}{25} : \frac{27}{64} = \frac{16}{25} \cdot \frac{64}{27} = \frac{1024}{675} = 1\frac{349}{675}\]
3. \[(1.2)^2 : (\frac{3}{5})^3 = (\frac{12}{10})^2 : \frac{27}{125} = (\frac{6}{5})^2 : \frac{27}{125} = \frac{36}{25} : \frac{27}{125} = \frac{36}{25} \cdot \frac{125}{27} = \frac{4}{1} \cdot \frac{5}{3} = \frac{20}{3} = 6\frac{2}{3}\]
4. \[(2.4)^2 : (1\frac{1}{5})^3 = (\frac{24}{10})^2 : (\frac{6}{5})^3 = (\frac{12}{5})^2 : \frac{216}{125} = \frac{144}{25} : \frac{216}{125} = \frac{144}{25} \cdot \frac{125}{216} = \frac{2}{1} \cdot \frac{5}{3} = \frac{10}{3} = 3\frac{1}{3}\]

Ответ: 1) 5 3/25; 2) 1 349/675; 3) 6 2/3; 4) 3 1/3

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