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b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)
3M=1+1/3+1/3^2+1/3^3+1/3^4
3M-M=1-1/3^5
2M=242/243
M=242/243*1/2=121/243
\(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{12}{15}+\frac{22}{33}+\frac{48}{64}\)
\(=\frac{11}{33}+\frac{16}{64}+\frac{3}{15}+\frac{12}{15}+\frac{22}{33}+\frac{48}{64}\)
\(=\left(\frac{11}{33}+\frac{22}{33}\right)+\left(\frac{16}{64}+\frac{48}{64}\right)+\left(\frac{3}{15}+\frac{12}{15}\right)\)
\(\frac{33}{33}+\frac{64}{64}+\frac{15}{15}\)
\(=1+1+1\)
\(=3\)
1) \(\frac{4}{5}.\frac{8}{3}.\frac{x}{7}=\frac{96}{105}\)
\(\frac{32.x}{105}=\frac{96}{105}\)
\(32x=96\)
\(x=3\)
Bài 1: Tìm \(x\)
\(\frac45\times\frac83\times\) \(\frac{x}{7}\) = \(\frac{96}{105}\)
\(\frac{32}{15}\) x \(\frac{x}{7}\) = \(\frac{32}{35}\)
\(\frac{x}{7}\) = \(\frac{32}{35}\) : \(\frac{32}{15}\)
\(\frac{x}{7}\) = \(\frac{32}{35}\) x \(\frac{15}{32}\)
\(\frac{x}{7}\) = \(\frac37\)
\(x=\frac37\times7\)
\(x=3\)
b; \(\frac74\times\frac{3}{x}\times\) \(\frac{11}{5}\) = \(\frac{231}{200}\)
\(\frac74\) x \(\frac{3}{x}\) = \(\frac{231}{200}\) : \(\frac{11}{5}\)
\(\frac74\times\frac{3}{x}\) = \(\frac{231}{200}\) x \(\frac{5}{11}\)
\(\frac74\) x \(\frac{3}{x}\) = \(\frac{21}{40}\)
\(\frac{3}{x}\) = \(\frac{21}{40}\) : \(\frac74\)
\(\frac{3}{x}\) = \(\frac{21}{40}\) x \(\frac47\)
\(\frac{3}{x}\) = \(\frac{3}{10}\)
\(x=3:\frac{3}{10}\)
\(x=3\times\frac{3}{10}\)
\(x=10\)
3636/4545+x=4848/1515
x=4848/1515-3636/4545
x=14544/4545-3636/4545
x=10908/4545
3535/5050-x=8/25
x=3535/5050-1616/5050
x=1919/5050
2/5 = 4/10 = 8/20
4/12 = 2/6 = 1/3
dấu / chính là "phần " nha.
VD 1/4 : Một phần bốn
Đáp án lần lượt là: \(\frac{23}{36};\frac{31}{7};\frac{1}{6};\frac{3}{5}\)
#Hk_tốt
#Ken'z
\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)
\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)
\(=\frac{1}{24}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)
\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)
\(=\frac{1}{10}\)
a) \(\frac{3}{5}\times y+\frac{1}{2}:\frac{5}{3}-\frac{5}{4}=\frac{1}{2}\times\frac{1}{3}\)
\(\Rightarrow\frac{3}{5}\times y+\frac{3}{10}-\frac{5}{4}=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y+\left(-\frac{19}{20}\right)=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{67}{60}\)
\(\Rightarrow y=\frac{67}{36}\)
b) \(\frac{4}{5}:y+\frac{1}{4}\times\frac{1}{6}-\frac{1}{2}=\frac{1}{3}\times\frac{5}{2}\)
\(\Rightarrow\frac{4}{5}:y+\frac{1}{24}-\frac{1}{2}=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y+\left(-\frac{11}{24}\right)=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y=\frac{5}{6}+\frac{11}{24}=\frac{31}{24}\)
\(\Rightarrow y=\frac{4}{5}:\frac{31}{24}=\frac{96}{155}\)
c) \(\frac{3}{5}\times y-\frac{4}{5}:3+\frac{1}{12}=\frac{3}{2}+\frac{1}{5}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}+\frac{1}{12}=\frac{17}{10}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}=\frac{97}{60}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{113}{60}\)
\(\Rightarrow y=\frac{113}{36}\)
1/2,1/3,1/4,1/6
\(=\frac{6}{12}+\frac{4}{12}+\frac{3}{12}+\frac{2}{12}+\frac{1}{12}\)
\(=\frac{27}{12}=\frac{9}{4}\)