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42 + y/76 = 153/171
y/76=153/171 - 42
y/76 = 781/19
y = 3124
\(3\times\frac{7}{10}+5\times\frac{7}{10}+2\times\frac{7}{10}\)
\(=\frac{7}{10}\times\left(3+5+2\right)\)
\(=\frac{7}{10}\times10\)
\(=7\)
#)Giải :
Bài 1 :
\(A=\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+...+\frac{1}{1280}\)
\(\Rightarrow A\times2=\frac{2}{5}-\left(\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+...+\frac{1}{1280}\right)-\frac{1}{1280}\)
\(\Rightarrow A\times2=\frac{2}{5}-A-\frac{1}{1280}\)
\(\Rightarrow A\times2+A=\frac{2}{5}-\frac{1}{1280}\)
\(\Rightarrow A=\frac{2}{5}-\frac{1}{1280}\)
\(\Rightarrow A=\frac{511}{1280}\)
#)Giải :
Bài 2 :
\(B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+...+\frac{1}{59049}\)
\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{10}}\)
\(3B=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^9}\)
\(3B-B=\left(1+\frac{1}{3}+\frac{1}{3^2}...+\frac{1}{3^9}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{10}}\right)\)
\(2B=1-\frac{1}{3^{10}}\)
\(B=\frac{1-\frac{1}{3^{10}}}{2}\)
\(1-\dfrac{89}{90}=\dfrac{1}{90}\)
\(1-\dfrac{171}{172}=\dfrac{1}{172}\)
Vì \(\dfrac{1}{90}>\dfrac{1}{172}\Rightarrow\dfrac{89}{90}< \dfrac{171}{172}\)
a) 4 x 9120 x 25
= 25 x 4 x 9120
= 100 x 9120
= 912000
b) 15 800 + 4 200 + 7 260 + 2 740
= (15800 + 4200) + (7260 + 2740)
= 20000 + 10000
= 30000
a) 4 x 9120 x 25
= 25 x 4 x 9120
= 100 x 9120
= 912000
b) 15 800 + 4 200 + 7 260 + 2 740
= (15800 + 4200) + (7260 + 2740)
= 20000 + 10000
= 30000
\(\frac{1}{8}:\frac{1}{5}=\frac{1}{8}\)x\(\frac{5}{1}=\frac{5}{8}\)
\(\frac{5}{6}\)x \(\frac{10}{10}=\frac{5}{6}\)x \(1=\frac{5}{6}\)
\(\frac{171}{260}-\frac{10}{200}=\frac{171}{260}-\frac{1}{20}=\frac{79}{130}\)
\(\frac{171}{260}-\frac{10}{200}=\frac{171}{260}-\frac{1}{20}=\frac{171}{260}-\frac{13}{260}=\frac{158}{260}=\frac{79}{130}\)