BT2: Tính nhanh
7) \(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{71}-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
8)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
BT2: Tính nhanh
9) (\(\left(5+\dfrac{1}{5}-\dfrac{2}{9}\right)-\left(2-\dfrac{1}{23}-2\dfrac{3}{35}+\dfrac{5}{6}\right)-\left(8+\dfrac{2}{7}-\dfrac{1}{18}\right)\)
10)\(\dfrac{1}{3}-\dfrac{3}{4}-\left(-\dfrac{3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)
Tính:
\(\left(\dfrac{1}{2}-1\right):\left(\dfrac{1}{3}-1\right):\left(\dfrac{1}{4}-1\right):\) ... : \(\left(\dfrac{1}{50}-1\right)\)
Chứng minh rằng:
\(\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{50}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+...+\dfrac{1}{100}+\dfrac{1}{102}\right)=\dfrac{1}{52}+\dfrac{1}{53}+...+\dfrac{1}{100}+\dfrac{1}{101}+\dfrac{1}{102}\)
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=\(10101.\left(\dfrac{5}{111111}+\dfrac{5}{222222}-\dfrac{4}{3.7.11.13.37}\right)\)
1 Thực hiện phép tính:
A=\(\dfrac{1}{15.16}+\dfrac{1}{16.17}+...+\dfrac{1}{2016.2017}\)
B=\(\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{4}\right)+\left(1-\dfrac{1}{8}\right)+...+\left(1-\dfrac{1}{1024}\right)\)
C=\(\dfrac{1}{5.8}+\dfrac{1}{8.11}+...+\dfrac{1}{101.104}\)
D=\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+...+\dfrac{2}{101.104}\)
E=\(\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+...+\dfrac{5^2}{101.106}\)
tìm x biết
\(\left(3\dfrac{1}{2}+2x\right).2\dfrac{2}{3}=5\dfrac{1}{3}\)
\(\dfrac{3}{4}-2.\left|2x-\dfrac{2}{3}\right|=2\)
\(\left(0.6-\dfrac{1}{2}\right).\dfrac{3}{4}-\left(-1\right)=\dfrac{1}{3}\)
\(\left(3x-1\right).\left(-\dfrac{1}{2}x+5\right)=0\)
\(\dfrac{1}{4}+\dfrac{1}{3}:\left(2x-1\right)=-5\)
\(\left(2x+\dfrac{3}{5}\right)^2-\dfrac{9}{25}=0\)
\(-5.\left(x+\dfrac{1}{5}\right)-\dfrac{1}{2}.\left(x-\dfrac{2}{3}\right)=\dfrac{3}{2}x-\dfrac{5}{6}\)
BT2: Tính nhanh
13) \(\dfrac{4}{9}:\left(-\dfrac{1}{7}\right)+6\dfrac{5}{9}:\left(-\dfrac{1}{7}\right)\)
14) \(\left(-\dfrac{3}{4}+\dfrac{5}{13}\right):\dfrac{2}{7}-\left(2\dfrac{1}{4}+\dfrac{8}{13}\right):\dfrac{2}{7}\)
*Phép chia
a)\(11\dfrac{1}{4}-\left(2\dfrac{5}{7}+5\dfrac{1}{4}\right)\)
b)\(\left(8\dfrac{5}{11}+3\dfrac{5}{8}\right)-3\dfrac{5}{11}\)
c)\(\dfrac{-1}{4}.13\dfrac{9}{11}-0,25.6\dfrac{2}{11}\)
d)\(\dfrac{4}{9}:\left(\dfrac{-1}{7}\right)+6\dfrac{5}{9}:\left(\dfrac{-1}{7}\right)\)
BT2: Tính nhanh
15) \(\left(\dfrac{1}{2}-\dfrac{13}{14}\right):\dfrac{5}{7}-\left(-\dfrac{2}{21}+\dfrac{1}{7}\right):\dfrac{5}{7}\)
16)\(\dfrac{3}{5}:\left(\dfrac{-1}{15}-\dfrac{1}{6}\right)+\dfrac{3}{5}:\left(\dfrac{-1}{3}-1\dfrac{1}{15}\right)\)
