Áp dụng công thức \(\dfrac{a}{b}< 1\Leftrightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\) \(\left(a;b;m\in N\right)\)
Ta có : \(A=\dfrac{5^{12}+1}{5^{13}+1}< 1\)
\(\Leftrightarrow A=\dfrac{5^{12}+1}{5^{13}+1}< \dfrac{5^{12}+1+4}{5^{13}+1+4}=\dfrac{5^{12}+5}{5^{13}+5}=\dfrac{5\left(5^{11}+1\right)}{5\left(5^{12}+1\right)}=B\)
\(\Leftrightarrow A< B\)
BT2: Tính nhanh
11) \(-\dfrac{5}{7}-\left(-\dfrac{5}{67}\right)+\dfrac{13}{30}+\dfrac{1}{2}+\left(-1\dfrac{5}{6}\right)+1\dfrac{3}{14}-\left(-\dfrac{2}{5}\right)\)
12) \(\dfrac{-1}{4}.13\dfrac{9}{11}-0.25.6\dfrac{2}{11}\)
a)\(\dfrac{2}{7}+\dfrac{-3}{8}+\dfrac{11}{7}+\dfrac{1}{7}_{ }+\dfrac{5}{-8}\)
b)\(\dfrac{3}{17}+\dfrac{-5}{13}+\dfrac{-18}{35}+\dfrac{14}{17}+\dfrac{17}{-35}_{ }+\dfrac{-8}{13}\)
c)\(\dfrac{-3}{8}+\dfrac{12}{25}+\dfrac{5}{-8}+\dfrac{2}{-5}+\dfrac{13}{25}\)
d)\(\dfrac{-5}{21}+\left(\dfrac{-16}{21}+1\right)\)
e)\(\dfrac{-3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)\)
f)\(\left(\dfrac{-1}{6}+\dfrac{5}{-12}\right)+\dfrac{7}{12}\)
1.So Sánh
a) A=\(\dfrac{11}{2017}+\dfrac{4}{2019}và\) B=\(\dfrac{10}{2017}+\dfrac{10}{2019}\)
b) M=\(\dfrac{1}{5}+\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{30}+\dfrac{1}{61}+\dfrac{1}{62}và\dfrac{1}{2}\)
c) E=\(\dfrac{4116-14}{10290-35}và\) K=\(\dfrac{2929-101}{2.1919+404}\)
So sánh
a) \(\dfrac{21}{52}\) và \(\dfrac{213}{523}\)
b) \(\dfrac{n}{n+1}\)và \(\dfrac{n+2}{n+3}\)
c) \(\dfrac{n}{n+3}\)và \(\dfrac{n-1}{n+4}\)
d) \(A=\dfrac{2^{2012}-1}{2^{2013}-1}\) và \(B=\dfrac{2^{2013}-1}{2^{2014}-1}\)
e) \(D=\dfrac{5^{12}+1}{5^{13}+1}\)và \(E=\dfrac{5^{11}+1}{5^{12}+1}\)
Bài 1: Thực hiện phép tính:
a, \(\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right)\)
b, \(\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\)
c, \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)
Tính:
\(A=\dfrac{\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}}{\dfrac{5}{12}+1-\dfrac{7}{11}}\)
Thực hiện phép tính:
( \(\dfrac{3}{8}+\dfrac{-3}{4}+\dfrac{7}{12}\)).\(\dfrac{5}{6}+\dfrac{1}{2}\)
b) 1\(\dfrac{13}{15}.0,75-\left(\dfrac{11}{20}+25\%\right):\dfrac{7}{5}\)
Bài 1: Thực hiện phép tính
a) \(\left(\dfrac{3}{8}+\dfrac{-3}{4}+\dfrac{7}{12}\right):\dfrac{5}{6}+\dfrac{1}{2}\)
b) \(\dfrac{1}{2}+\dfrac{3}{4}-\left(\dfrac{3}{4}-\dfrac{4}{5}\right)\)
c) \(6\dfrac{5}{12}:2\dfrac{3}{4}+11\dfrac{1}{4}.\left(\dfrac{1}{3}\dfrac{1}{5}\right)\)
d)\(\left(\dfrac{7}{8}-\dfrac{3}{4}\right).1\dfrac{1}{3}-\dfrac{2}{7}.\left(3,5\right)^2\)
e)\(\left(\dfrac{3}{5}+0,415-\dfrac{3}{200}\right).2\dfrac{2}{3}.0,25\)
f)\(\dfrac{5}{16}:0,125-\left(2\dfrac{1}{4}-0,6\right).\dfrac{10}{11}\)
g) \(0,25:\left(10,3-9,8\right)-\dfrac{3}{4}\)
h)\(1\dfrac{13}{15}.0,75-\left(\dfrac{11}{20}+20\%\right):\dfrac{7}{3}\)
i)\(\dfrac{\left(\dfrac{1}{2-0,75}\right).\left(0,2-\dfrac{2}{5}\right)}{\dfrac{5}{9}-1\dfrac{1}{12}}\)
k)\(\dfrac{\dfrac{2}{3}+\dfrac{2}{7}-\dfrac{1}{14}}{-1-\dfrac{3}{7}+\dfrac{3}{28}}\)
Bài 2: Tính bằng cánh hợp lí
A=\(0,7.2\dfrac{2}{3}.20.0,375.\dfrac{5}{28}\)
B=\(\left(9\dfrac{30303}{80808}+7\dfrac{303030}{484848}\right)+4,03\)
C=\(\left(9,75.21\dfrac{3}{7}+\dfrac{39}{4}.18\dfrac{4}{7}\right).\dfrac{15}{78}\)
D=\(10101.\left(\dfrac{5}{111111}+\dfrac{5}{222222}-\dfrac{4}{3.7.11.13.37}\right)\)
tìm x
\([\dfrac{6:\dfrac{3}{5}-1\dfrac{1}{16}.\dfrac{16}{7}}{4\dfrac{1}{5}-\dfrac{10}{11}+5\dfrac{2}{11}}-\dfrac{\left(\dfrac{3}{20}+\dfrac{1}{2}-\dfrac{1}{5}\right).\dfrac{12}{49}}{3\dfrac{1}{3}+\dfrac{2}{9}}].x=2\dfrac{23}{96}\)
