Danh mục bài soạn

$A = 1\frac{13}{15}\times (0,5)^2 \times 3+(\frac{8}{15} - 1\frac{19}{60}) : 1\frac{23}{24} = \frac{28}{15}\times (\frac{1}{2})^2 \times 3+(\frac{8}{15} - \frac{79}{60}) : \frac{47}{24} = \frac{28}{15}\times \frac{1}{4} \times 3+(\frac{32}{60} - \frac{79}{60}) \times \frac{24}{47} = \frac{28\times 1\times 3+}{15\times 4} - \frac{47}{60}\times \frac{24}{47} = \frac{4 \times 7\times 1\times 3}{3\times 5\times 4} - \frac{24}{60} = \frac{7}{5} - \frac{2}{5} = \frac{5}{5} = 1$.

$B = \frac{(\frac{11^2}{200}+0,415) : 0.01}{\frac{1}{12} - 37,25 + 3\frac{1}{6}} = \frac{(\frac{121}{200}+\frac{415}{1000}) : \frac{1}{100}}{\frac{1}{12} - \frac{3725}{100} + \frac{19}{6}} = \frac{(\frac{121}{200}+\frac{83}{200}) \times 100}{\frac{1}{12} - \frac{149}{4} + \frac{19}{6}} = \frac{\frac{204}{200}\times 100}{\frac{1}{12} - \frac{447}{12} + \frac{38}{12}} = \frac{\frac{102}{100}\times 100}{\frac{1 - 447 + 38}{12}} = \frac{102}{\frac{-408}{12}} = \frac{102}{-34} = -3$.

$\frac{-9}{46} - 4\frac{1}{23} : (3\frac{1}{4} - x : \frac{3}{5}) + 2\frac{8}{23} = 1$;

$\Leftrightarrow \frac{-9}{46} - \frac{93}{23} : (\frac{13}{4} - x \times \frac{5}{3}) + \frac{54}{23} = 1$

$\Leftrightarrow \frac{-9}{46} + \frac{54}{23} - \frac{93}{23} : (\frac{39}{12} - x \times \frac{20}{12}) = 1$

$\Leftrightarrow \frac{-9}{46} + \frac{108}{46} - \frac{93}{23} : (\frac{39 - x \times 20}{12}) = 1$

$\Leftrightarrow \frac{99}{46} - \frac{93}{23} \times \frac{12}{39 - x\times 20} = 1$

$\Leftrightarrow \frac{99}{46} - 1 = \frac{93}{23} \times \frac{12}{39 - x\times 20}$

$\Leftrightarrow \frac{53}{46} = \frac{93}{23} \times \frac{12}{39 - x\times 20}$

$\Leftrightarrow \frac{53}{2} = 93 \times \frac{12}{39 - x\times 20}$

$\Leftrightarrow \frac{53}{2} = \frac{1116}{39 - x\times 20}$

$\Leftrightarrow 53\times (39 - x\times 20) = 1116\times 2$

$\Leftrightarrow 2067 - x\times 1060 = 2232$

$\Leftrightarrow x\times 1060 = -165$

$\Leftrightarrow x = \frac{-165}{1060} = \frac{-33}{212}$

$(6\frac{2}{7}\times x + \frac{3}{7}) : 2\frac{1}{5} - \frac{3}{7} = -1$;

$\Leftrightarrow (\frac{44}{7}\times x + \frac{3}{7}) \times \frac{5}{11} = -1 + \frac{3}{7} $

$\Leftrightarrow (\frac{44}{7}\times x + \frac{3}{7}) \times \frac{5}{11}= \frac{-4}{7}$

$\Leftrightarrow \frac{44}{7}\times x + \frac{3}{7} = \frac{-4}{7} \times \frac{11}{5}$

$\Leftrightarrow \frac{44}{7}\times x + \frac{3}{7} = \frac{-44}{35}$

$\Leftrightarrow \frac{44x}{7} = -\frac{3}{7} + \frac{-44}{35}$

$\Leftrightarrow \frac{44x}{7} = -\frac{59}{35}$

$\Leftrightarrow 44x = -\frac{59}{5}$

$\Leftrightarrow x = -\frac{-59}{220}$

$5\frac{8}{17} : x + (-\frac{1}{17}) : x + 3\frac{1}{17} : 17\frac{1}{3} = \frac{4}{17}$;

$\Leftrightarrow \frac{93}{17} \times \frac{1}{x} - \frac{1}{17}\times \frac{1}{x} + \frac{52}{17} : \frac{52}{3} = \frac{4}{17}$

$\Leftrightarrow \frac{92}{17} \times \frac{1}{x} + \frac{52}{17} \times \frac{3}{52} = \frac{4}{17}$

$\Leftrightarrow \frac{92}{17} \times \frac{1}{x} + \frac{3}{17} = \frac{4}{17}$

$\Leftrightarrow \frac{92}{17} \times \frac{1}{x} = \frac{4}{17} - \frac{3}{17}$

$\Leftrightarrow \frac{92}{17} \times \frac{1}{x} = \frac{1}{17}$

$\Leftrightarrow \frac{92}{x} = 1$

$\Leftrightarrow x = 92$

$\frac{1}{1\times 4} + \frac{1}{4\times 7} + \frac{1}{7\times 10} + ........ + \frac{1}{x\times (x + 3)} = \frac{6}{19}$.

$\Leftrightarrow \frac{1}{3}\times (\frac{1}{1} - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{10} + ... +\frac{1}{x} - \frac{1}{x + 3}) = \frac{6}{19}$

$\Leftrightarrow \frac{1}{3}\times (\frac{1}{1} - \frac{1}{x + 3}) = \frac{6}{19}$

$\Leftrightarrow (\frac{1}{1} - \frac{1}{x + 3}) = \frac{18}{19}$

$\Leftrightarrow \frac{1}{x + 3} = \frac{1}{1} - \frac{18}{19}$

$\Leftrightarrow \frac{1}{x + 3} = \frac{1}{19}$

$\Leftrightarrow x + 3 = 19$

$\Leftrightarrow x = 16$.

c) Đổi: 3 giờ 30 phút = $3\frac{30}{60} = \frac{7}{2}$; 2 giờ 20 phút = $2\frac{20}{60} = \frac{7}{3}$;

Trong 1 giờ, vòi A chảy được: $\frac{1}{3} : \frac{7}{2} = \frac{2}{21}$ (bể).

Trong 1 giờ, vòi B chảy được: $\frac{1}{3} : \frac{7}{3} = \frac{1}{7}$ (bể).

Trong một giờ, hai vòi chảy được: $\frac{2}{21} + \frac{1}{7} = \frac{5}{21}$ bể.

Vậy thời gian để cả hai vòi chảy đầy bể là: $1 : \frac{5}{21} = \frac{21}{5}$ (giờ).

Ta có: $B = \frac{2012 + 2013}{2013 + 2014} = \frac{2012}{2013 + 2014} + \frac{2013}{2014 + 2014}$.