№ 1 Найдите значение выражений: a)-0,8+(-\frac{1}{9}); 6)-\frac{7}{15}-(-2,175); в)-\frac{3}{50} -0,39; г) 0,45-1\frac{1}{12}; д) -2,4⋅(-5\frac{1}{3}); е) 2\frac{2}{5}: (-0,36); ж)|-\frac{5}{12}|:|-2,5|; з) |-6,5|⋅|2\frac{2}{9}|. № 2 Найдите неизвестный член пропорции: a) x : 1 \frac{5}{7} = 2,4:2 \frac{2}{35} № 3 Решите уравнение: a) 0,6(y - 3) - 0,5(y − 1) = 1,5; б) 8x-62,4+5х; в) 1,2х-0,6 = 0,8x-27. г) -3x+1,9 = 2x + 8,4. д)\frac{3,6-2,4y}{1,2} = \frac{3y+5}{-2} 6) \frac{11}{8} = \frac{x-1}{2x-3}. № 4. Упростите выражения: a) 4m-6m-3m+7+m; 6)-8(k-3)+4(k-2)-2(3k+1);

Ответ:

№1 Найдите значение выражений:

• а) \[ -0.8 + \left(-\frac{1}{9}\right) = -\frac{8}{10} - \frac{1}{9} = -\frac{4}{5} - \frac{1}{9} = -\frac{36}{45} - \frac{5}{45} = -\frac{41}{45} \]
• б) \[ -\frac{7}{15} - (-2.175) = -\frac{7}{15} + 2.175 = -\frac{7}{15} + \frac{2175}{1000} = -\frac{7}{15} + \frac{87}{40} = -\frac{56}{120} + \frac{261}{120} = \frac{205}{120} = \frac{41}{24} = 1\frac{17}{24} \]
• в) \[ -\frac{3}{50} - 0.39 = -\frac{3}{50} - \frac{39}{100} = -\frac{6}{100} - \frac{39}{100} = -\frac{45}{100} = -0.45 \]
• г) \[ 0.45 - 1\frac{1}{12} = \frac{45}{100} - \frac{13}{12} = \frac{9}{20} - \frac{13}{12} = \frac{27}{60} - \frac{65}{60} = -\frac{38}{60} = -\frac{19}{30} \]
• д) \[ -2.4 \cdot \left(-5\frac{1}{3}\right) = -\frac{24}{10} \cdot \left(-\frac{16}{3}\right) = \frac{12}{5} \cdot \frac{16}{3} = \frac{4}{5} \cdot 16 = \frac{64}{5} = 12.8 \]
• е) \[ 2\frac{2}{5} : (-0.36) = \frac{12}{5} : \left(-\frac{36}{100}\right) = \frac{12}{5} : \left(-\frac{9}{25}\right) = \frac{12}{5} \cdot \left(-\frac{25}{9}\right) = \frac{4}{1} \cdot \left(-\frac{5}{3}\right) = -\frac{20}{3} = -6\frac{2}{3} \]
• ж) \[ \left|-\frac{5}{12}\right| : |-2.5| = \frac{5}{12} : \frac{25}{10} = \frac{5}{12} : \frac{5}{2} = \frac{5}{12} \cdot \frac{2}{5} = \frac{1}{6} \]
• з) \[ |-6.5| \cdot \left|2\frac{2}{9}\right| = 6.5 \cdot \frac{20}{9} = \frac{65}{10} \cdot \frac{20}{9} = \frac{13}{1} \cdot \frac{2}{9} = \frac{26}{9} = 2\frac{8}{9} \]

№2 Найдите неизвестный член пропорции:

• a) \[ x : 1\frac{5}{7} = 2.4 : 2\frac{2}{35}\\ x : \frac{12}{7} = \frac{24}{10} : \frac{72}{35}\\ x : \frac{12}{7} = \frac{12}{5} : \frac{72}{35}\\ x = \frac{12}{5} : \frac{72}{35} \cdot \frac{12}{7}\\ x = \frac{12}{5} \cdot \frac{35}{72} \cdot \frac{12}{7}\\ x = \frac{1}{1} \cdot \frac{7}{6} \cdot \frac{12}{7}\\ x = \frac{1}{1} \cdot \frac{1}{1} \cdot \frac{2}{1}\\ x = 2 \]

№3 Решите уравнение:

• a) \[ 0.6(y - 3) - 0.5(y - 1) = 1.5\\\ 0.6y - 1.8 - 0.5y + 0.5 = 1.5\\\ 0.1y - 1.3 = 1.5\\\ 0.1y = 2.8\\\ y = 28 \]
• б) \[ 8x = -62.4 + 5x\\\ 8x - 5x = -62.4\\\ 3x = -62.4\\\ x = -20.8 \]
• в) \[ 1.2x - 0.6 = 0.8x - 27\\\ 1.2x - 0.8x = -27 + 0.6\\\ 0.4x = -26.4\\\ x = -66 \]
• г) \[ -3x + 1.9 = 2x + 8.4\\\ -3x - 2x = 8.4 - 1.9\\\ -5x = 6.5\\\ x = -1.3 \]
• д) \[ \frac{3.6 - 2.4y}{1.2} = \frac{3y + 5}{-2}\\ -2(3.6 - 2.4y) = 1.2(3y + 5)\\ -7.2 + 4.8y = 3.6y + 6\\\ 4.8y - 3.6y = 6 + 7.2\\\ 1.2y = 13.2\\\ y = 11 \]
• 6) \[ \frac{11}{8} = \frac{x - 1}{2x - 3}\\ 11(2x - 3) = 8(x - 1)\\ 22x - 33 = 8x - 8\\\ 22x - 8x = -8 + 33\\\ 14x = 25\\\ x = \frac{25}{14} = 1\frac{11}{14} \]

№4 Упростите выражения:

• a) \[ 4m - 6m - 3m + 7 + m = (4 - 6 - 3 + 1)m + 7 = -4m + 7 \]
• б) \[ -8(k - 3) + 4(k - 2) - 2(3k + 1) = -8k + 24 + 4k - 8 - 6k - 2 = -10k + 14 \]

Ответ: