\(\frac{7}{4}\) of 2
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Dịch sang tiếng việt rồi giải1. fractionfrac{6}{35}can be written as the product of two fractions of which the numerator and the denominator are one-digit postitve intergersFor instance: frac{6}{35}frac{2}{3}.frac{5}{7}Look for different writtings.2. Puzzle: there are a pairs of fractions that when we multiply or add them together, we recive the same resultsFor instance: the pair of fractions frac{7}{3}andfrac{7}{4}has: frac{7}{3}.frac{7}{4}frac{7.7}{3.4}frac{49}{12} frac{7}{3}+frac{7}{4}frac{7....
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Dịch sang tiếng việt rồi giải
1. fraction\(\frac{6}{35}\)can be written as the product of two fractions of which the numerator and the denominator are one-digit postitve intergers
For instance: \(\frac{6}{35}=\frac{2}{3}.\frac{5}{7}\)
Look for different writtings.
2. Puzzle: there are a pairs of fractions that when we multiply or add them together, we recive the same results
For instance: the pair of fractions \(\frac{7}{3}\)and\(\frac{7}{4}\)has:
\(\frac{7}{3}.\frac{7}{4}=\frac{7.7}{3.4}=\frac{49}{12}\)
\(\frac{7}{3}+\frac{7}{4}=\frac{7.4+7.3}{12}=\frac{49}{12}\)
We ask you a riddle to find another pair of fractions having that property
\(\frac{1+\frac{1}{7}+\frac{1}{7^2}-\frac{1}{7^3}}{4+\frac{4}{7}+\frac{4}{7^2}-\frac{4}{7^3}}.\frac{858585}{313131}.\left(-1\frac{14}{17}\right)\)
\(\frac{1+\frac{1}{7}+\frac{1}{7^2}-\frac{1}{7^3}}{4+\frac{4}{7}+\frac{4}{7^2}-\frac{4}{7^3}}.\frac{858585}{313131}.\left(-1\frac{14}{17}\right)\)\
\(=\frac{1+\frac{1}{7}+\frac{1}{7^2}-\frac{1}{7^3}}{4.\left(1+\frac{1}{7}+\frac{1}{7^2}-\frac{1}{7^3}\right)}.\frac{85}{31}.\left(-\frac{31}{17}\right)\)
\(=\frac{1}{4}.\frac{85}{31}.\left(-\frac{31}{17}\right)\)
\(=-\frac{5}{4}\)
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\(=\frac{1+\frac{1}{7}+\frac{1}{7^2}-\frac{1}{7^3}}{4\left(1+\frac{1}{7}+\frac{1}{7^2}-\frac{1}{7^3}\right)}.\frac{85.10101}{31.10101}.\left(-\frac{31}{17}\right).\)
\(=\frac{1}{4}.\frac{3.17}{31}.\left(-\frac{31}{17}\right)=-\frac{3}{4}\)
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Tính giá trị biểu thức
a, A= \(\frac{-5}{7}+\frac{7}{-5}+\frac{4}{7}+\frac{7}{4}\)
b, B=\(\frac{-5}{7}+\frac{2}{-7}+\frac{4}{-9}+\frac{4}{9}\)
c, C=\(\left(3-\frac{3}{4}+\frac{2}{3}\right)-\left(2-\frac{4}{3}-\frac{3}{2}\right)-\left(1-\frac{7}{3}-\frac{9}{2}\right)\)
So sánh:frac{frac{frac{1}{2}}{frac{3}{4}}}{frac{frac{5}{6}}{frac{7}{8}}}+frac{frac{frac{8}{7}}{frac{6}{5}}}{frac{frac{4}{3}}{frac{2}{1}}} vàfrac{frac{frac{1}{2}}{frac{3}{4}}+frac{frac{8}{7}}{frac{6}{5}}}{frac{frac{5}{6}}{frac{7}{8}}+frac{frac{4}{3}}{frac{2}{1}}}và frac{frac{frac{1}{2}+frac{8}{7}}{frac{3}{4}+frac{6}{5}}}{frac{frac{5}{6}+frac{4}{3}}{frac{7}{8}+frac{2}{1}}}vàfrac{frac{frac{1+8}{2+7}}{frac{3+6}{4+5}}}{frac{5+4}{frac{6+3}{2+1}}}
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So sánh:\(\frac{\frac{\frac{1}{2}}{\frac{3}{4}}}{\frac{\frac{5}{6}}{\frac{7}{8}}}+\frac{\frac{\frac{8}{7}}{\frac{6}{5}}}{\frac{\frac{4}{3}}{\frac{2}{1}}}\) và\(\frac{\frac{\frac{1}{2}}{\frac{3}{4}}+\frac{\frac{8}{7}}{\frac{6}{5}}}{\frac{\frac{5}{6}}{\frac{7}{8}}+\frac{\frac{4}{3}}{\frac{2}{1}}}\)và \(\frac{\frac{\frac{1}{2}+\frac{8}{7}}{\frac{3}{4}+\frac{6}{5}}}{\frac{\frac{5}{6}+\frac{4}{3}}{\frac{7}{8}+\frac{2}{1}}}\)và\(\frac{\frac{\frac{1+8}{2+7}}{\frac{3+6}{4+5}}}{\frac{5+4}{\frac{6+3}{2+1}}}\)
thực hiện phép tính :a, frac{0,4-frac{2}{9}+frac{2}{11}}{1,4-frac{7}{9}+frac{7}{11}}-frac{frac{1}{3}-0,25+frac{1}{5}}{frac{7}{6}-58+5+0,7}b, frac{frac{1}{9}-frac{1}{7}-frac{1}{11}}{frac{4}{9}-frac{4}{7}-frac{4}{11}}+frac{frac{3}{5}-frac{3}{25}-frac{3}{125}-frac{3}{625}}{frac{4}{5}-frac{4}{25}-frac{4}{125}-frac{4}{625}}c, frac{frac{3}{7}-frac{3}{17}+frac{3}{37}}{frac{5}{7}-frac{5}{17}+frac{5}{37}}+frac{frac{1}{2}-frac{1}{3}+frac{1}{4}-frac{1}{5}}{frac{7}{5}-frac{7}{4}+frac{7}{3}-frac{7}{2}}M...
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thực hiện phép tính :
a, \(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{\frac{7}{6}-58+5+0,7}\)
b, \(\frac{\frac{1}{9}-\frac{1}{7}-\frac{1}{11}}{\frac{4}{9}-\frac{4}{7}-\frac{4}{11}}+\frac{\frac{3}{5}-\frac{3}{25}-\frac{3}{125}-\frac{3}{625}}{\frac{4}{5}-\frac{4}{25}-\frac{4}{125}-\frac{4}{625}}\)
c, \(\frac{\frac{3}{7}-\frac{3}{17}+\frac{3}{37}}{\frac{5}{7}-\frac{5}{17}+\frac{5}{37}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{7}{5}-\frac{7}{4}+\frac{7}{3}-\frac{7}{2}}\)
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Rút gọn
1.\(\frac{7}{19}.\frac{8}{11}+\frac{7}{19}.\frac{3}{11}+\frac{12}{19}\)
2.\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(1\)) \(\frac{7}{19}.\frac{8}{11}+\frac{7}{19}.\frac{3}{11}+\frac{12}{19}\)
\(=\frac{7}{19}\left(\frac{8}{11}+\frac{3}{11}\right)+\frac{12}{19}\)
\(=\frac{7}{19}+\frac{12}{19}\)
\(=1\)
\(2\)) \(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(=\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{2\left(\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}\right)}\)
\(=\frac{1}{2}\)
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1. \(\frac{7}{19}\times\frac{8}{11}+\frac{7}{19}\times\frac{3}{11}+\frac{12}{19}\)
\(=\frac{7}{19}\left(\frac{8}{11}+\frac{3}{11}\right)+\frac{12}{19}\)
\(=\frac{7}{19}\times1+\frac{12}{19}=\frac{19}{19}=1\)
2. \(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(=\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{2\left(\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}\right)}=\frac{1}{2}\)
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So sánh:
A=\(\frac{4}{7}+5+\frac{3}{7^2}+\frac{5}{7^3}+\frac{6}{7^4}\) và B=\(\frac{5}{7^4}+5+\frac{6}{7^2}+\frac{4}{7}+\frac{5}{7^3}\)
cách này mình tự nghĩ
\(\hept{\begin{cases}A=\frac{4}{7}+5+\frac{3}{7^2}+\frac{5}{7^3}+\frac{6}{7^4}\\B=\frac{5}{7^4}+5+\frac{6}{7^2}+\frac{4}{7}+\frac{5}{7^3}\end{cases}}\)
\(\Rightarrow A-B=\left(\frac{4}{7}-\frac{4}{7}\right)+\left(\frac{5}{7^3}-\frac{5}{7^3}\right)+\left(5-5\right)+\left(\frac{3}{7^2}-\frac{6}{7^2}\right)+\left(\frac{6}{7^4}-\frac{5}{7^4}\right)\)
\(\Rightarrow A-B=-\frac{3}{7^2}+\frac{1}{7^4}\)
\(\Rightarrow A-B=\frac{-3\times7^2}{7^4}+\frac{1}{7^4}\)
mà \(-3\times7^2< 1\Rightarrow\frac{1}{7^4}>\frac{-3\times7^2}{7^4}\Rightarrow B>A\)
\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}-\left(\frac{-5}{6}\right)-\frac{6}{7}-\frac{-7}{8}+\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
\(\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}-\left(-\frac{5}{6}\right)-\frac{-7}{8}+\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
\(=\frac{1}{2}-\frac{2}{3}+\frac{3}{4}-\frac{4}{5}+\frac{5}{6}+\frac{7}{8}+\frac{6}{7}-\frac{5}{6}+\frac{4}{5}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
\(=\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{2}{3}-\frac{2}{3}\right)+\left(\frac{3}{4}-\frac{3}{4}\right)+\left(\frac{4}{5}-\frac{4}{5}\right)+\left(\frac{5}{6}-\frac{5}{6}\right)+\frac{7}{8}+\frac{6}{7}\)
\(=\frac{7}{8}+\frac{6}{7}=\frac{49}{56}+\frac{48}{56}=\frac{49+48}{56}=\frac{97}{56}\)
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Cho A= \(\frac{4+\frac{4}{2012}-\frac{4}{2013}+\frac{4}{2014}-\frac{4}{2015}}{\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}+7}\)
Và B= \(\frac{1+2+2^2+...+2^{2013}}{2^{2015}-2}\)
Tính A - B
p/S: LM ƠN GIÚP TỚ VS :
\(TA-CO':\)
\(A=\frac{4+\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}}{7+\frac{7}{2014}-\frac{7}{2015}+\frac{7}{2012}-\frac{7}{2013}}\)
\(A=\frac{4\left(\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2012}-\frac{1}{2013}\right)}{7\left(\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2012}-\frac{1}{2013}\right)}\)
\(A=\frac{4}{7}\)
\(B=\frac{1+2+...+2^{2013}}{2^{2015}-2}\)
ĐẶT \(C=1+2+...+2^{2013}\)
\(\Rightarrow2C=2+2^2+...+2^{2014}\)
\(\Rightarrow2C-C=\left(2+2^2+...+2^{2014}\right)-\left(1+2+...+2^{2013}\right)\)
\(\Rightarrow C=2^{2014}-2\)
\(\Rightarrow B=\frac{2^{2014}-1}{2^{2015}-2}\)
\(B=\frac{2^{2014}-1}{2\left(2^{2014}-1\right)}\)
\(B=\frac{1}{2}\)
\(\Rightarrow A-B=\frac{3}{7}-\frac{1}{2}=\frac{6}{14}-\frac{7}{14}\)
\(A-B=\frac{6-7}{14}=\frac{-1}{14}\)
VẬY, \(A-B=\frac{-1}{14}\)
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