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\(A=\frac{1998.1996+1997.11+1985}{1997.1996-1995.1996}\)
\(A=\frac{1998.1996+\left(1996+1\right).11+1985}{1996.\left(1997-1995\right)}\)
\(A=\frac{1998.1996+1996.11+11+1985}{1996.2}\)
\(A=\frac{1998.1996+1996.11+1996}{1996.2}\)
\(A=\frac{1996.\left(1998+1+1\right)}{1996.2}\)
\(A=\frac{1996.2000}{1996.2}=1000\)
\(\frac{1998\times1996+1996\times11+1996}{1996\times2}\)\(=\frac{2010\times1996}{2\times1996}=1005\)
k nha
\(\dfrac{1988\:×\:1996\:+\:1997\:+\:1985}{1997\:×\:1996\:-\:1995\:×\:1996}\) (rút bỏ các phần tử, mẫu giống nhau)
= \(\dfrac{1988\:+\:1985}{1995\:×\:1996}\)
= (còn lại tự tính)
\(\frac{1998\times1996+1997+1995}{1996\times\left(1997-1995\right)}=\frac{1998\times1996+1996+1996}{1996\times2}=\frac{1996\times1999+1996}{1996\times2}\)
=\(\frac{1996\times2000}{1996.2}=\frac{2000}{2}=1000\)
Xét tử số ta có :
1998 . 1996 + 1997 . 11 + 1985
= 1998 . 1996 + (1996 + 1) . 11 + 1985 (Tách số)
= 1998 . 1996 + 1996 . 11 + 11 + 1985
= 1998 . 1996 + 1996 . 11 + 1996
= 1996 . (1998 + 11 + 1)
= 1996 . 2010
Vậy tử số là 1996 . 2010
Xét mẫu số ta có :
1997 . 1996 - 1995 . 1996
= 1996 . (1997 - 1995) = 1996 . 2
Vậy mẫu số là 1996 . 2
Vậy\(\frac{1998.1996+1997+1985}{1997.1996-1995.1996}=\frac{1996.2010}{1996.2}=\frac{2010}{2}=1005\)
a ) \(\frac{2016\cdot12+2003+2000\cdot2015+2015}{2015+2015\cdot502+504\cdot2015}\)
\(=\frac{\left(2015+1\right)\cdot12+2003+2000\cdot2015+2015}{2015\cdot\left(1+502+504\right)}\)
\(=\frac{2015\cdot12+12\cdot1+2003+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+\left(12\cdot1+2003\right)+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+2015+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot\left(12+1+2000+1\right)}{2015\cdot1007}\)
\(=\frac{2015\cdot2014}{2015\cdot1007}\)
\(=2\)
b ) \(\frac{1978\cdot1979+1980\cdot21+1958}{1980\cdot1979-1978\cdot1979}\)
\(=\frac{1978\cdot1979+\left(1979+1\right)\cdot21+1958}{\left(1980-1978\right)\cdot1979}\)
\(=\frac{1979\cdot1978+1979\cdot21+21\cdot1+1958}{2\cdot1979}\)
\(=\frac{1978\cdot1979+1979\cdot21+1979}{2\cdot1979}\)
\(=\frac{\left(1978+21+1\right)\cdot1979}{2\cdot1979}\)
\(=\frac{2000\cdot1979}{2\cdot1979}\)
\(=1000\)
\(B=\)\(\frac{3+33+333+3333+33333}{4+44+444+4444+44444}\)
\(B=\frac{3.1+3.11+3.111+3.1111+3.11111}{4.1+4.11+4.111+4.1111+4.11111}\)
\(B=\frac{3.\left(1+11+111+1111+11111\right)}{4.\left(1+11+111+1111+11111\right)}\)
\(B=\frac{3}{4}\)
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
\(A.2=\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\right).2\)
\(A.2=\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\)
=>\(A.2-A=\left(\frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}\right)-\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\right)\)
\(A=\frac{2}{3}-\frac{1}{192}\)
\(A=\frac{127}{192}\)
\(\frac{1995}{1997}.\frac{1990}{1993}.\frac{1997}{1994}.\frac{1993}{1995}.\frac{997}{995}\)
Đặt \(C=\frac{1995}{1997}.\frac{1990}{1993}.\frac{1997}{1994}.\frac{1993}{1995}.\frac{997}{995}\)
\(C=\frac{1995.1990.1997.1993.997}{1997.1993.1994.1995.995}\)
\(C=\frac{1990.997}{1994.995}\)
\(C=\frac{995.2+997}{997.2+995}=1\)
\(B=\frac{3+33+333+3333+ 33333}{4+44+444+4444+44444}\)
\(\Rightarrow B=\frac{3\left(1+11+111+1111+11111\right)}{4\left(1+11+111+1111+11111\right)}=\frac{3}{4}\)