Tính :
a) \(\dfrac{17}{23}.\dfrac{8}{16}.\dfrac{23}{17}.\left(-80\right).\dfrac{3}{4}\)
b) \(\dfrac{5}{11}.\dfrac{18}{29}-\dfrac{5}{11}.\dfrac{8}{29}+\dfrac{5}{11}.\dfrac{19}{29}\)
c) \(\left(\dfrac{13}{23}+\dfrac{1313}{2323}-\dfrac{131313}{232323}\right).\left(\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{7}{12}\right)\)
d) \(\dfrac{1^2}{1.2}.\dfrac{2^{2^{ }}}{2.3}.\dfrac{3^2}{3.4}.\dfrac{4^2}{4.5}.\dfrac{5^2}{5.6}.\dfrac{6^2}{6.7}.\dfrac{7^2}{7.8}.\dfrac{8^2}{8.9}.\dfrac{9^2}{9.10}\)
e) \(\dfrac{2^2}{3}.\dfrac{3^2}{8}.\dfrac{4^2}{15}.\dfrac{5^2}{24}.\dfrac{6^2}{35}\dfrac{7^2}{48}.\dfrac{8^2}{63}.\dfrac{9^2}{80}\)
1. tìm x thuộc z biết \(\dfrac{x}{-12}\)=\(\dfrac{-3}{2}\)
2 tính
a,\(\dfrac{-7}{9}\times\dfrac{6}{11}+\dfrac{-2}{9}\)
b,\(\dfrac{-4}{7}:2=\)
c,115- (24-5\(\times\)3)
d,\(\dfrac{-3}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{-3}{7}+2\dfrac{3}{7}\)
e,\(\dfrac{1}{4\times5}+\dfrac{1}{6\times7}+......\dfrac{1}{79\times80}\)
*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)\(\dfrac{4}{9}:\left(\dfrac{-1}{7}\right)+6\dfrac{5}{9}:\left(\dfrac{-1}{7}\right)\)
Tính hợp lí
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)\(\dfrac{4}{9}:\left(-\dfrac{1}{7}\right)+6\dfrac{5}{9}:\left(-\dfrac{1}{7}\right)\)
Bài 1:
\(a)5\dfrac{1}{20}+\dfrac{8}{9}-\dfrac{15}{25}+\dfrac{75}{-18}\)
\(b)\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)
\(c)\dfrac{6}{7}+\dfrac{5}{7}:5-\dfrac{8}{9}.\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2\right)^2\)
Tính rồi tìm số nghịch đảo của :
\(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{6}{7}.\dfrac{8}{9}.\dfrac{10}{11}.\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}.\dfrac{7}{8}.\dfrac{9}{10}\)
Cho A=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{9^2}\)
Chứng tỏ \(\dfrac{8}{9}>A>\dfrac{2}{5}\)
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)\(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
a) Cho hai phân số \(\dfrac{1}{n}\)và \(\dfrac{1}{n+1}\)(n\(\in\)Z,n>0). Chứng tỏ rằng tích của hai phân số này bằng hiệu của chúng.
b) Áp dụng kết quả trên để tính biểu thức sau :
A=\(\dfrac{1}{2}.\dfrac{1}{3}+\dfrac{1}{3}.\dfrac{1}{4}+\dfrac{1}{4}.\dfrac{1}{5}+\dfrac{1}{5}.\dfrac{1}{6}+\dfrac{1}{6}.\dfrac{1}{7}+\dfrac{1}{7}.\dfrac{1}{8}+\dfrac{1}{8}.\dfrac{1}{9}\)
B=\(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}\)