Tính: \(\dfrac{1987.1979+1980.21+1985}{1980.1979.1978.1979}\)
Những câu hỏi liên quan
a/\(\frac{1988\times1996+1997+1985}{1997\times1996-1995\times1996}\)
b/\(\frac{1978\times1979+1980.21+1985}{1980\times1979-1978\times1979}\)
c/\(\frac{2,43\times12300-24,3\times1230}{45\times20,1+55\times28,9+4,5+3,3-55\times5,37}\)
Giúp mk nha, giải ra đầy đủ thì mk sẽ like :-)))
1 tháng 5 2023 lúc 21:59
Tính nhanh:
\(\dfrac{1988\times1996+1997+1985}{1997\times1996-1995\times1996}\)
\(\dfrac{1988\:×\:1996\:+\:1997\:+\:1985}{1997\:×\:1996\:-\:1995\:×\:1996}\) (rút bỏ các phần tử, mẫu giống nhau)
= \(\dfrac{1988\:+\:1985}{1995\:×\:1996}\)
= (còn lại tự tính)
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Tính nhanh
\(\dfrac{1978.1979+1980.21+1958}{1980.1979-1978.1979}\)
\(\dfrac{1978.1979+1980.21+1958}{1980.1979-1978.1979}\)
\(=\dfrac{1978.1979+\left(1979+1\right).21+1958}{1979.\left(1980-1978\right)}\)
\(=\dfrac{1978.1979+1979.21+21+1958}{1979.2}\)
\(=\dfrac{1978.1979+1979.21+1979.1}{1979.2}\)
\(=\dfrac{1979.\left(1978+21 +1\right)}{1979.2}\)
\(=\dfrac{1978+21+1}{2}=\dfrac{2000}{2}=1000\)
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\(\dfrac{1978.1979+1980.21+1958}{1980.1979-1978.1979}\)
\(=\dfrac{1978.1979+1979.21+21+1958}{1980.1979-1978.1979}\)
\(=\dfrac{1979\left(1978+21\right)+21+1958}{1979\left(1980-1978\right)}\)
\(=\dfrac{1978+21+21+1958}{1980-1978}\)
\(=\dfrac{3978}{2}\)
\(=1989\)
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Anime là nhất:
(1979.1979+1980.21+1958):(1980.1979-1978.1979)
=(1979.1979+1980.21+1958):(1979.(1980-1878))
=(1979.1979+1980.21+1958):(1979.2)
=(1980.21+1958)+(1979.1979):(1979.2)
=1980.21+1958
=41580+1958
=43538
(1979.1979+1980.21+1958):(1980.1979-1978.1979)
=(1979.1979+1980.21+1958):(1979.(1980-1878))
=(1979.1979+1980.21+1958):(1979.2)
=(1980.21+1958)+(1979.1979):(1979.2)
=1980.21+1958
=41580+1958
=43538
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(1979.1979+1980.21+1958):(1980.1979-1978.1979)
=(1979.1979+1980.21+1958):(1979.(1980-1878))
=(1979.1979+1980.21+1958):(1979.2)
=(1980.21+1958)+(1979.1979):(1979.2)
=1980.21+1958
=41580+1958
=43538
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so sánh C và D biết C=\(\dfrac{1957}{2007}\) D= \(\dfrac{1935}{1985}\)
Giải:
Ta có:
C=1957/2007=1957+50-50/2007=2007-50/2007
=2007/2007-50/2007
=1-50/2007
Tương tự:
D=1935/1985=1935+50-50/1985=1985-50/1985
=1985/1985-50/1985
=1-50/1985
Vì 50/2007<50/1985 nên -50/2007>-50/1985
⇒C>D
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tính \(\frac{1978.1979+1980.21+1958}{1980.1979-1978.1979}\)
so sánh C và D biết C=\(\dfrac{1957}{2007}\) với D=\(\dfrac{1935}{1985}\)
\(C=\dfrac{1957}{2007}\) và \(D=\dfrac{1935}{1985}\)
\(\Rightarrow\left\{{}\begin{matrix}C=\dfrac{1957}{2007}\\D=\dfrac{1935}{1985}\end{matrix}\right.\\\Rightarrow\left\{{}\begin{matrix}C=1-\dfrac{50}{2007}\\D=1-\dfrac{50}{1985}\end{matrix}\right. \)
Vì \(\dfrac{50}{2007}<\dfrac{50}{1985}\)
\(\Rightarrow1-\dfrac{50}{2007}>1-\dfrac{50}{1985}\\\Rightarrow C>D\)
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Chứng minh rằng : \(\dfrac{1}{5}+\dfrac{1}{15}+\dfrac{1}{25}+...+\dfrac{1}{1985}< \dfrac{9}{20}\)
Chứng minh rằng: \(\dfrac{1}{5}+\dfrac{1}{15}+\dfrac{1}{25}+.....+\dfrac{1}{1985}< \dfrac{9}{20}\)
Ta có :
\(A=\dfrac{1}{5}+\dfrac{1}{15}+\dfrac{1}{25}+\dfrac{1}{35}+...+\dfrac{1}{1985}\)
\(A=\dfrac{1}{5}+\dfrac{1}{3.5}+\dfrac{1}{5.5}+\dfrac{1}{7.5}+...+\dfrac{1}{397.5}\)
\(\Rightarrow5A=1+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{397}\)
\(5A-1=\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{397}\)
\(5A-1=\dfrac{1}{3}+\left(\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{9}\right)+\left(\dfrac{1}{11}+\dfrac{1}{13}+...+\dfrac{1}{27}\right)+\)
\(\left(\dfrac{1}{29}+\dfrac{1}{31}+...+\dfrac{1}{81}\right)+\left(\dfrac{1}{83}+\dfrac{1}{85}+...+\dfrac{1}{243}\right)+...+\dfrac{1}{397}\)
\(\Rightarrow5A-1>\dfrac{1}{3}+\dfrac{1}{9}.3+\dfrac{1}{27}.9+\dfrac{1}{81}.27+\dfrac{1}{243}.81=\dfrac{1}{3}.5=\dfrac{5}{3}\)
\(\Rightarrow5A-1>\dfrac{5}{4}\Rightarrow5A>\dfrac{9}{4}\)
\(\Rightarrow A>\dfrac{9}{4}:5=\dfrac{9}{20}\Rightarrow\left(dpcm\right)\)
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