Question

Rút gọn phân số:

a)\(\frac{2929-101}{2.1919+404}\)

b)\(\frac{-1997.1996+1}{-1995.\left(-1997\right)+1996}\)

c)\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}\)

d)\(\frac{3.7.13.37.39-10101}{505050-70707}\)

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

Answer 1

dễ quá đi. Nếu muốn mình giải hãy k trước đi

Answer 2

a) \(\frac{2929-101}{2.1919+404}\)\(=\frac{101.29-101}{2.1919+2.202}\)\(=\frac{101\left(29-1\right)}{2\left(1919+202\right)}\)\(=\frac{101.28}{2.2121}\)\(=\frac{2.101.7.2}{2.101.7.3}\)\(=\frac{2}{3}\)
b) \(\frac{-1997.1996+1}{-1995\left(-1997\right)+1996}\)\(=\frac{-1997.\left(1995+1\right)+1}{-1995\left(-1997\right)+1996}\)\(=\frac{-1997.1995-1997+1}{-1\left(-1997\right).1995+1996}\)\(=\frac{-1997.1995-1996}{1997.1995+1996}\)\(=\frac{-\left(1997.1995+1996\right)}{1997.1995+1996}\)\(=-1\)
c) \(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}\)\(=\frac{2.3+4.2.3+2.7.3.7}{3.5+2.3.2.5+3.7.5.7}\)\(=\frac{2.3\left(1+4+7.7\right)}{3.5\left(1+2.2+7.7\right)}\)\(=\frac{2\left(1+4+49\right)}{5\left(1+4+49\right)}\)\(=\frac{2}{5}\)
d) \(\frac{3.7.13.37.39-10101}{505050-70707}\)\(=\frac{3.7.13.37.39-3.7.13.37}{2.3.5.5.7.13.37-3.7.7.13.37}\)\(=\frac{3.7.13.37\left(39-1\right)}{3.7.13.37\left(2.5.5-7\right)}\)\(=\frac{38}{43}\)
e) \(\frac{18.34+\left(-18\right).124}{-36.17+9.\left(-52\right)}\)\(=\frac{18.2.17-18.2.62}{\left(-1\right).2.2.3.3.17+\left(-1\right)2.2.3.3.13}\)\(=\frac{18.2\left(17-62\right)}{\left(-1\right).2.2.3.3\left(17+13\right)}\)\(=\frac{\left(-1\right).2.2.3.3.45}{\left(-1\right).2.2.3.3.30}\)\(=\frac{45}{30}\)\(=\frac{3}{2}\)

Answer 3

a, \(\frac{29.101-101}{2.101.19+4.101}=\frac{101.\left(29-1\right)}{38.101+4.101}=\frac{101.28}{101.42}=\frac{28}{42}=\)\(\frac{2}{3}\)

b, \(\frac{-1997.1996+1}{-1995.\left(-1997\right)+1996}=\frac{-1997.\left(1995+1\right)+1}{1995.1997+1996}\)\(=\frac{-1997.1995+1997-1}{1995.1997+1996}=\frac{-1997.1995+1996}{1995.1997+1996}=-1\)

c,\(\frac{2.3+2\left(2.3\right)+7\left(2.3\right)}{3.5+2\left(3.5\right)+7\left(3.5\right)}=\frac{2.3\left(1+2+7\right)}{3.5\left(1+2+7\right)}=\frac{2.3}{3.5}=\frac{2}{5}\)

d,\(\frac{3.7.13.37.39-3.7.13.37}{2.3.5^2.7.13.37-3.7^2.13.37}=\frac{3.7.13.37.38}{3.7.13.37\left(2.5^2-7\right)}\)\(=\frac{3.7.13.37.38}{3.7.13.37.43}=\frac{38}{43}\)

e, \(\frac{18.34+18.\left(-124\right)}{9.\left(-4\right).17+9.\left(-52\right)}=\frac{18\left(-124+34\right)}{9.\left(-68\right)+9\left(-52\right)}\)\(=\frac{18\left(-90\right)}{9\left(-120\right)}=\frac{18.\left(-90\right)}{9.2\left(-60\right)}=\frac{18.\left(-90\right)}{18.\left(-60\right)}=\)\(\frac{-90}{-60}=\frac{3}{2}\)