1. Найдите сумму или разность: 1) a) 1/5 + 4/15; 2) a) 3/8 - 1/9; 3) a) 7/30 - 31/45; 1) б) 2/3 - 5/12; 2) б) 5/6 + 3/11; 3) б) 2 1/20 - 6 9/40; 1) в) 5 1/7 + 7 13/21; 2) в) 9 1/29 - 1 3/4; 3) в) 5/18 - 2 23/30

Решение:

1. 1. Найдите сумму или разность:
   1. 1) a)\[ \frac{1}{5} + \frac{4}{15} = \frac{3}{15} + \frac{4}{15} = \frac{7}{15} \]
   2. 2) a)\[ \frac{3}{8} - \frac{1}{9} = \frac{27}{72} - \frac{8}{72} = \frac{19}{72} \]
   3. 3) a)\[ \frac{7}{30} - \frac{31}{45} = \frac{21}{90} - \frac{62}{90} = -\frac{41}{90} \]
   4. 1) б)\[ \frac{2}{3} - \frac{5}{12} = \frac{8}{12} - \frac{5}{12} = \frac{3}{12} = \frac{1}{4} \]
   5. 2) б)\[ \frac{5}{6} + \frac{3}{11} = \frac{55}{66} + \frac{18}{66} = \frac{73}{66} = 1 \frac{7}{66} \]
   6. 3) б)\[ 2 \frac{1}{20} - 6 \frac{9}{40} = \frac{41}{20} - \frac{249}{40} = \frac{82}{40} - \frac{249}{40} = -\frac{167}{40} = -4 \frac{7}{40} \]
   7. 1) в)\[ 5 \frac{1}{7} + 7 \frac{13}{21} = 5 \frac{3}{21} + 7 \frac{13}{21} = 12 \frac{16}{21} \]
   8. 2) в)\[ 9 \frac{1}{29} - 1 \frac{3}{4} = \frac{262}{29} - \frac{7}{4} = \frac{1048}{116} - \frac{203}{116} = \frac{845}{116} = 7 \frac{43}{116} \]
   9. 3) в)\[ \frac{5}{18} - 2 \frac{23}{30} = \frac{5}{18} - \frac{83}{30} = \frac{25}{90} - \frac{249}{90} = -\frac{224}{90} = -\frac{112}{45} = -2 \frac{22}{45} \]
2. 2. Найдите значение выражения:
   1. 1) a)\[ 13 + 27,13 + 40 + 50,07 = 40,13 + 40 + 50,07 = 80,13 + 50,07 = 130,2 \]
   2. 2) a)\[ 5,47 - (8,32 - 5,311) = 5,47 - 3,009 = 2,461 \]
   3. 1) б)\[ 71,35 + 30,6 + 7,07 + 0,06 = 101,95 + 7,13 = 109,08 \]
   4. 2) б)\[ 7,83 - (5,31 + 6,69) = 7,83 - 12 = -4,17 \]
3. 3. Найдите произведение или частное:
   1. 1) a)\[ \frac{9}{13} \cdot \frac{26}{27} = \frac{9 \cdot 26}{13 \cdot 27} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3} \]
   2. 2) a)\[ 1 \frac{2}{3} \cdot 1 \frac{1}{5} = \frac{5}{3} \cdot \frac{6}{5} = \frac{5 \cdot 6}{3 \cdot 5} = 2 \]
   3. 3) a)\[ \frac{1}{2} : \left( -\frac{1}{32} \right) = \frac{1}{2} \cdot \left( -32 \right) = -16 \]
   4. 4) a)\[ \frac{3}{8} \cdot (-8) = -3 \]
   5. 5) a)\[ 7,4 \cdot 3,5 = 25,9 \]
   6. 6) a)\[ 0,72 : 0,008 = 90 \]
   7. 1) б)\[ -\frac{5}{14} \cdot \frac{42}{75} = -\frac{5 \cdot 42}{14 \cdot 75} = -\frac{1 \cdot 3}{1 \cdot 15} = -\frac{1}{5} \]
   8. 2) б)\[ -3 \frac{1}{5} \cdot 1 \frac{1}{4} = -\frac{16}{5} \cdot \frac{5}{4} = -4 \]
   9. 3) б)\[ -\frac{5}{7} : \left( -1 \frac{4}{21} \right) = \frac{5}{7} : \frac{25}{21} = \frac{5}{7} \cdot \frac{21}{25} = \frac{1 \cdot 3}{1 \cdot 5} = \frac{3}{5} \]
   10. 4) б)\[ -\frac{3}{4} : 8 = -\frac{3}{4} \cdot \frac{1}{8} = -\frac{3}{32} \]
   11. 5) б)\[ -3,7 \cdot 5,5 = -20,35 \]
   12. 6) б)\[ 0,1616 : 0,04 = 40,4 \]
   13. 1) в)\[ \frac{17}{24} \cdot \left( -\frac{48}{51} \right) = -\frac{17 \cdot 48}{24 \cdot 51} = -\frac{1 \cdot 2}{1 \cdot 3} = -\frac{2}{3} \]
   14. 2) в)\[ -4 \frac{1}{6} \cdot \left( -2 \frac{2}{5} \right) = \frac{25}{6} \cdot \frac{12}{5} = 10 \]
   15. 3) в)\[ 5 \frac{1}{3} : 2 \frac{2}{9} = \frac{16}{3} : \frac{20}{9} = \frac{16}{3} \cdot \frac{9}{20} = \frac{4 \cdot 3}{1 \cdot 5} = \frac{12}{5} = 2,4 \]
   16. 4) в)\[ -5 : \left( -1 \frac{2}{3} \right) = 5 : \frac{5}{3} = 5 \cdot \frac{3}{5} = 3 \]
   17. 5) в)\[ -8,3 \cdot (-1,4) = 11,62 \]
   18. 6) в)\[ 0,289 : 0,17 = 1,7 \]
4. 4. Вычислите:
   1. 1) a)\[ 13^3 = 13 \cdot 13 \cdot 13 = 169 \cdot 13 = 2197 \]
   2. 6)\[ 32^2 = 32 \cdot 32 = 1024 \]
   3. в)\[ 320^2 = 320 \cdot 320 = 102400 \]
   4. г)\[ 1300^3 = 1300 \cdot 1300 \cdot 1300 = 1690000 \cdot 1300 = 2197000000 \]
   5. 1) б)\[ (-7)^3 = (-7) \cdot (-7) \cdot (-7) = 49 \cdot (-7) = -343 \]
   6. 6)\[ (-11)^2 = (-11) \cdot (-11) = 121 \]
   7. в)\[ (-0,7)^3 = (-0,7) \cdot (-0,7) \cdot (-0,7) = 0,49 \cdot (-0,7) = -0,343 \]
   8. г)\[ (-0,11)^2 = (-0,11) \cdot (-0,11) = 0,0121 \]

Ответ:

1. а) 7/15, б) 1/4, в) 12 16/21; а) 19/72, б) 1 7/66, в) 7 43/116; а) -41/90, б) -4 7/40, в) -2 22/45.

2. а) 130,2, б) 2,461; а) 109,08, б) -4,17.

3. а) 2/3, 2, -16, -3, 25,9, 90; б) -1/5, -4, 3/5, -3/32, -20,35, 40,4; в) -2/3, 10, 2,4, 3, 11,62, 1,7.

4. а) 2197, б) 1024, в) 102400, г) 2197000000; а) -343, б) 121, в) -0,343, г) 0,0121.