Question

[Nguyen Phan Minh Hieu]

Tớ có cái này đố các cậu

a)\(\frac{53}{101}.\frac{-13}{97}+\frac{53}{101}.\frac{-84}{97}\)

b)\(\left(\frac{1}{57}-\frac{1}{5757}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)

c)\(\frac{-3^3}{25}.\frac{75}{-21}.\frac{50}{35}\)

d)\(\frac{25.48-25.18}{20.5^3}\)

e)\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)+\left(1+\frac{1}{4}\right)+...+\left(1+\frac{1}{2003}\right)\)

f)\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)+\left(1-\frac{1}{4}\right)+...+\left(1-\frac{1}{200}\right)\)

Chúc các cậu may mắn!!

Answer 1

[Kiệt Nguyễn]

a) \(\frac{53}{101}.\frac{-13}{97}+\frac{53}{101}.\frac{-84}{97}\)

\(=\frac{53}{101}\left(\frac{-13}{97}+\frac{-84}{97}\right)\)

\(=\frac{53}{101}.\frac{-97}{97}\)

\(=\frac{53}{101}.\left(-1\right)\)

\(=\frac{-53}{101}\)

b) \(\left(\frac{1}{57}-\frac{1}{5757}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)

\(=\left(\frac{1}{57}-\frac{1}{5757}\right)\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)

\(=\left(\frac{1}{57}-\frac{1}{5757}\right).0\)

\(=0\)

Answer 2

[Kiệt Nguyễn]

c) \(\frac{3^2}{25}.\frac{75}{-21}.\frac{50}{35}\)

\(=\frac{3^2.75.50}{25.\left(-21\right).35}\)

\(=\frac{3.3.25.3.5.5.2}{25.3.\left(-7\right).5.7}\)

\(=\frac{3.3.5.2}{\left(-7\right).7}\)

\(=\frac{90}{-49}\)

d) \(\frac{25.48-25.18}{20.5^3}\)

\(=\frac{25\left(48-18\right)}{10.2.125}\)

\(=\frac{25.10.3}{10.2.25.5}\)

\(=\frac{3}{10}\)