Question

[doan trang]

1.Tính tổng: \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{99.101}\)

2.Rút gọn phân số:

a)\(\frac{2929-101}{2.1919+404}\)                                    b)\(\frac{6.9-2.17}{63.3-119}\)              

c)\(\frac{3.13-13.18}{15.40-80}\)                                    d)\(\frac{\left(-5\right)^3.40.4^3}{135.\left(-2\right)^{14}.\left(-100\right)^0}\)

e)\(\frac{-1997.1996+1}{-1995.\left(-1997\right)+1996}\)                    f)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}\)                      

f)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}\)                              g)\(\frac{3.7.13.37.39-10101}{505050-70707}\) 

 h)\(\frac{18.34+\left(-18\right).124}{-36.17+9.\left(-52\right)}\)     

Answer 1

[Le Thi Khanh Huyen]

Bài 1:

Coi \(A=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{99.101}\)

\(2A=\left(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{99.101}\right).2\)

\(=5.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{99.101}\right)\)

\(=5.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=5.\left(1-\frac{1}{101}\right)\)

\(=5.\frac{100}{101}\)

\(=\frac{500}{101}\Rightarrow A=\frac{500}{101}:2=\frac{250}{101}\)

Answer 2

[thien ty tfboys]

\(\left(\frac{5}{1}-\frac{5}{3}+\frac{5}{3}-\frac{5}{5}....+\frac{5}{99}-\frac{5}{101}\right):\frac{1}{5}\)

\(\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}.....+\frac{1}{99}-\frac{1}{101}\right).5\)

\(\left(\frac{1}{1}-\frac{1}{101}\right).5\)

\(\frac{100}{101}.5\)

\(\frac{500}{101}\)

2,a,\(\frac{2929-101}{3838+404}\)\(=\frac{2828}{4242}=\frac{2}{3}\)

\(b,\frac{54-34}{189-119}=\frac{20}{70}=\frac{2}{7}\)

\(c,d,e,f,f,g,h\)\(tuong\) \(tu\)