\(19\frac{1}{3}.\frac{3}{7}-33\frac{1}{3}=\frac{58}{3}.\frac{3}{7}-\frac{100}{3}=\frac{58}{7}-\frac{100}{3}=\frac{174}{21}-\frac{700}{21}=\frac{-526}{21}\)
Tính nhanh nếu có thể:
3/7 * 19\(\frac{1}{3}\) - 3/7 * 33\(\frac{1}{3}\)
9 *(\(^{-\frac{1}{3}^3}\)) +1/3
15\(\frac{1}{4}\) : (-5/7) -25\(\frac{1}{4}\) : (-5/7)
CHỖ NÀO KHÔNG RÕ CỨ ẤN CTRL VỚI "+" NHÉ
\(\frac{2\cdot a+13\cdot b}{3\cdot a-7\cdot b}=\frac{2\cdot c+13\cdot d}{3\cdot c-7\cdot d}\)
CMR \(\frac{a}{b}=\frac{c}{d}\)
Tính \(E=\left[\frac{1\frac{11}{31}.4\frac{3}{7}-\left(15-6\frac{1}{3}.\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}.\left(-1\frac{14}{93}\right)\right].\frac{31}{50}\)
Thực hiện phép tính:
a,\(\frac{15}{33}+\frac{7}{20}+\frac{18}{33}+\frac{13}{20}\)
b, \(2\frac{1}{2}+\frac{4}{7}:\left(\frac{-8}{21}\right)\)
c, \(\left(\frac{-1}{2}\right)^3+\frac{1}{2}:5\)
D=\(\frac{3}{1^2\cdot2^2}+\frac{5}{2^2\cdot3^2}+\frac{7}{3^2\cdot4^2}+...+\frac{19}{9^2\cdot10^2}\)
Chứng minh D<1
Bài 1:Thực hiện các phép tính
a)A=\(1-\frac{1}{1+\frac{2}{1-\frac{3}{1-4}}}\)
b)B=\(-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}-\frac{1}{100000}-\frac{1}{1000000}\)
Bài 2:Thực hiện các phép tính sau 1 cách hợp lý
a)A=\(\frac{\frac{3}{7}-\frac{3}{17}+\frac{3}{37}}{\frac{5}{7}-\frac{5}{17}+\frac{5}{37}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{7}{5}-\frac{7}{4}+\frac{7}{3}-\frac{7}{2}}\)
b)B=\(\frac{\frac{2}{39}-\frac{1}{15}-\frac{2}{153}}{\frac{1}{34}+\frac{3}{20}-\frac{3}{26}}:\frac{1+\frac{2}{71}-\frac{5}{121}}{\frac{65}{121}-\frac{26}{71}-13}\)
c)C=\(\left(\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\right):\left(-\frac{5}{9.13}-\frac{7}{9.25}-\frac{13}{19.25}-\frac{31}{19.69}\right)\)
d)D=\(\frac{2.2016}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+2016}}\)
e)E=\(-1-\frac{1}{3}-\frac{1}{6}-\frac{1}{10}-\frac{1}{15}-...-\frac{1}{1225}\)
CMR:\(\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+\frac{7}{\left(3.4\right)^2}+...+\frac{19}{\left(9.10\right)^2}< 1\)
\(\frac{7}{4}+\left(\frac{33}{42}+\frac{3333}{2020}+\frac{333333}{303030}+\frac{33333333}{42424242}\right)\)
\(\left[\left(\frac{2}{193}-\frac{3}{386}\right).\frac{193}{17}+\frac{33}{34}\right]:\left[\left(\frac{7}{1931}+\frac{11}{3862}\right).\frac{1931}{25}+\frac{9}{2}\right]\)
cho S=\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{60}\) c/m \(\frac{3}{5}< S< \frac{4}{5}\)
