Tính bằng cách nhanh nhất: \(\dfrac{7}{8}+\dfrac{4}{11}.\dfrac{1}{8}+\dfrac{1}{8}.\dfrac{7}{11}\) \(1\) \(\dfrac{11}{8}\) \(\dfrac{9}{8}\) \(\dfrac{3}{2}\) Hướng dẫn giải: \(\dfrac{7}{8}+\dfrac{4}{11}.\dfrac{1}{8}+\dfrac{1}{8}.\dfrac{7}{11}\) \(=\dfrac{7}{8}+\dfrac{1}{8}.\left(\dfrac{4}{11}+\dfrac{7}{11}\right)\) \(=\dfrac{7}{8}+\dfrac{1}{8}.1\) \(=1\)
Thực hiện phép tính \(\dfrac{7}{8}.\dfrac{13}{3}-\dfrac{7}{3}.\dfrac{-11}{8}\) \(7\) \(\dfrac{7}{3}\) \(\dfrac{7}{6}\) \(21\) Hướng dẫn giải: \(\dfrac{7}{8}.\dfrac{13}{3}-\dfrac{7}{3}.\dfrac{-11}{8}\) \(=\dfrac{7}{3}.\dfrac{13}{8}-\dfrac{7}{3}.\dfrac{-11}{8}\) \(=\dfrac{7}{3}.\left(\dfrac{13}{8}-\dfrac{-11}{8}\right)\) \(=\dfrac{7}{3}.\dfrac{24}{8}\) \(=7\)
Thực hiện phép tính: \(\dfrac{11}{9}.\dfrac{17}{5}.\dfrac{9}{11}.\dfrac{15}{51}.6\) \(6\) \(3\) \(2\) \(1\) Hướng dẫn giải: \(\dfrac{11}{9}.\dfrac{17}{5}.\dfrac{9}{11}.\dfrac{15}{51}.6\) \(=\dfrac{11}{9}.\dfrac{9}{11}.\dfrac{17}{5}.\dfrac{15}{51}.6\) \(=1.\dfrac{1.3}{1.3}.6=6\)
Thực hiện phép tính: \(\dfrac{5}{8}.\dfrac{8}{17}-\dfrac{5}{8}.\dfrac{19}{17}+\dfrac{5}{8}.\dfrac{-6}{17}\) \(-\dfrac{5}{8}\) \(-\dfrac{1}{2}\) \(\dfrac{5}{8}\) \(-\dfrac{7}{8}\) Hướng dẫn giải: \(\dfrac{5}{8}.\dfrac{8}{17}-\dfrac{5}{8}.\dfrac{19}{17}+\dfrac{5}{8}.\dfrac{-6}{17}\) \(=\dfrac{5}{8}.\left(\dfrac{8}{17}-\dfrac{19}{17}+\dfrac{-6}{17}\right)\) \(=\dfrac{5}{8}.\dfrac{8+\left(-19\right)+\left(-6\right)}{17}\) \(=\dfrac{5}{8}.\dfrac{-17}{17}=-\dfrac{5}{8}\)
Thực hiện phép tính: \(\left(\dfrac{1}{111}+\dfrac{1}{1111}+\dfrac{1}{11111}\right).\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{5}{6}\right)\) \(0\) \(\dfrac{2}{111}\) \(2\) \(\dfrac{5}{111}\) Hướng dẫn giải: \(\left(\dfrac{1}{111}+\dfrac{1}{1111}+\dfrac{1}{11111}\right).\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{5}{6}\right)\) \(=\left(\dfrac{1}{111}+\dfrac{1}{1111}+\dfrac{1}{11111}\right).\left(\dfrac{3}{6}+\dfrac{2}{6}-\dfrac{5}{6}\right)\) \(=\left(\dfrac{1}{111}+\dfrac{1}{1111}+\dfrac{1}{11111}\right).0\) \(=0\)
Rút gọn biểu thức \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)........\left(1-\dfrac{1}{100}\right)\) \(\dfrac{1}{100}\) \(\dfrac{1}{99}\) \(\dfrac{99}{100}\) \(\dfrac{1}{98}\) Hướng dẫn giải: \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)........\left(1-\dfrac{1}{100}\right)\) \(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\left(\dfrac{4}{4}-\dfrac{1}{4}\right).......\left(\dfrac{100}{100}-\dfrac{1}{100}\right)\) \(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.......\dfrac{98}{99}.\dfrac{99}{100}\) \(=\dfrac{1}{100}\)
Tính tổng: \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.........+\dfrac{1}{97.99}\) \(\dfrac{49}{99}\) \(\dfrac{98}{99}\) \(\dfrac{50}{99}\) \(\dfrac{1}{2}\) Hướng dẫn giải: \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.........+\dfrac{1}{97.99}\) \(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...........+\dfrac{2}{97.99}\right)\) \(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+........+\dfrac{1}{97}-\dfrac{1}{99}\right)\) \(=\dfrac{1}{2}\left(1-\dfrac{1}{99}\right)\) \(=\dfrac{1}{2}\left(\dfrac{99}{99}-\dfrac{1}{99}\right)\) \(=\dfrac{1}{2}.\dfrac{98}{99}=\dfrac{49}{99}\)
Tìm số nghịch đảo của số \(-\dfrac{9}{8}\) \(-\dfrac{8}{9}\) \(\dfrac{8}{9}\) \(\dfrac{1}{9}\) \(\dfrac{1}{8}\)
Tìm số nghịch đảo của \(A=\dfrac{2}{3}.\dfrac{9}{4}-1\) \(2\) \(\dfrac{1}{2}\) \(-2\) \(-\dfrac{1}{4}\) Hướng dẫn giải: \(A=\dfrac{2}{3}.\dfrac{9}{4}-1=\dfrac{1.3}{1.2}-1=\dfrac{1}{2}\). Vậy số nghịch đảo của \(A=\dfrac{1}{2}\) là \(1:\dfrac{1}{2}=2\).
Tìm x biết \(-\dfrac{2}{3}x=\dfrac{5}{6}\). \(x=-\dfrac{5}{4}\) \(x=-\dfrac{5}{9}\) \(x=\dfrac{1}{6}\) \(x=\dfrac{5}{4}\)
