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a) MC: 20
\(\frac{3}{4}\)=\(\frac{3x5}{4x5}\)=\(\frac{15}{20}\)
\(\frac{2}{5}\)=\(\frac{2x4}{5x4}\)=\(\frac{8}{20}\)
b) MC: 36
\(\frac{5}{12}\)=\(\frac{5x3}{12x3}\)=\(\frac{15}{36}\)
\(\frac{11}{36}\)giữ nguyên
c) MC: 60
\(\frac{2}{3}\)=\(\frac{2x20}{3x20}\)=\(\frac{40}{60}\)
\(\frac{3}{4}\)=\(\frac{3x15}{4x15}\)=\(\frac{45}{60}\)
\(\frac{4}{5}\)=\(\frac{4x12}{5x12}\)=\(\frac{48}{60}\)
a ) Ta có :
\(\frac{3}{4}=\frac{3.5}{4.5}=\frac{15}{20}\)
\(\frac{2}{5}=\frac{2.4}{5.4}=\frac{8}{20}\)
a) \(\dfrac{2}{3}+\dfrac{3}{5}=\dfrac{10}{15}+\dfrac{9}{15}=\dfrac{19}{15}\)
a) \(\dfrac{7}{12}-\dfrac{2}{7}+\dfrac{1}{12}=\dfrac{2}{3}-\dfrac{2}{7}=\dfrac{14}{21}-\dfrac{6}{21}=\dfrac{8}{21}\)
TL:
\(\frac{12}{100}\)= 0,12
\(\frac{5}{100}\)= 0,05
\(\frac{306}{1000}\)= 0,306
-HT-
=13/12x14/13x15/14x16/15x...x2006/2005x2007/2006x2008/2007
=2008/12
=502/3
A = 1\(\dfrac{1}{12}\) \(\times\) 1\(\dfrac{1}{13}\) \(\times\) 1\(\dfrac{1}{14}\) \(\times\) 1\(\dfrac{1}{15}\) \(\times\) ... \(\times\) 1\(\dfrac{1}{2005}\) \(\times\) 1\(\dfrac{1}{2006}\) \(\times\) 1\(\dfrac{1}{2007}\)
A = ( 1 + \(\dfrac{1}{12}\)) \(\times\) ( 1 + \(\dfrac{1}{13}\)) \(\times\) ( 1 + \(\dfrac{1}{14}\)) \(\times\)...\(\times\) ( 1 + \(\dfrac{1}{2006}\))\(\times\)(1+\(\dfrac{1}{2007}\))
A = \(\dfrac{13}{12}\) \(\times\) \(\dfrac{14}{13}\) \(\times\) \(\dfrac{15}{14}\) \(\times\) ...\(\times\) \(\dfrac{2007}{2006}\) \(\times\) \(\dfrac{2008}{2007}\)
A = \(\dfrac{13\times14\times15\times...\times2007}{13\times14\times15\times...\times2007}\) \(\times\) \(\dfrac{2008}{12}\)
A = 1 \(\times\) \(\dfrac{502}{3}\)
A = \(\dfrac{502}{3}\)
B1:
\(\dfrac{3}{4}=\dfrac{3\times10}{4\times10}=\dfrac{30}{40}=\dfrac{75}{100};\dfrac{4}{5}=\dfrac{4\times8}{5\times8}=\dfrac{32}{40}=\dfrac{80}{100}\\ Vì:\dfrac{30}{40}< \dfrac{31}{40}< \dfrac{32}{40}.Nên:\dfrac{3}{4}< \dfrac{31}{40}< \dfrac{4}{5}\\ Và:\dfrac{75}{100}< \dfrac{77}{100}< \dfrac{79}{100}< \dfrac{80}{100}.Nên:\dfrac{3}{4}< \dfrac{77}{100}< \dfrac{79}{100}< \dfrac{4}{5}\)
3 phân số nằm giữa 2 phân số \(\dfrac{3}{4}\) và \(\dfrac{4}{5}\) là: \(\dfrac{31}{40};\dfrac{77}{100};\dfrac{79}{100}\)
B2:
\(\dfrac{3}{5}=\dfrac{3\times2}{5\times2}=\dfrac{6}{10};\dfrac{4}{5}=\dfrac{4\times2}{5\times2}=\dfrac{8}{10}\)
Vì: 6<7<8. Nên phân số có mẫu số bằng 10, lớn hơn \(\dfrac{3}{5}\) và nhỏ hơn \(\dfrac{4}{5}\) là \(\dfrac{7}{10}\)
Ta có công thức tổng quát:
\(\dfrac{k}{n\cdot\left(n+k\right)}=\dfrac{1}{n}-\dfrac{1}{n+k}\)
\(a,A=\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}\\ =\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\left(\dfrac{1}{5}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\dfrac{x-2}{5\left(x+3\right)}\\ =\dfrac{x-2}{15\left(x+3\right)}\)
Theo đề bài ta có:
\(A=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{15\left(x+3\right)}=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{303}{308}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{305-2}{305+3}\\ \Rightarrow x=305\)
\(\dfrac{13+x}{20}\) = \(\dfrac{3}{4}\)
13 + \(x\) = 20 \(\times\) \(\dfrac{3}{4}\)
13 + \(x\) = 15
\(x\) = 15 - 13
\(x\) = 2
Cách khác :
\(\dfrac{13+x}{20}=\dfrac{3}{4}\)
\(\dfrac{13+x}{20}=\dfrac{15}{20}\)
\(13+x=15\)
\(x=15-13\)
\(x=2\)
a) \(\dfrac{3}{4}=\dfrac{3\cdot5}{4\cdot5}=\dfrac{15}{20}\\ \dfrac{2}{5}=\dfrac{2\cdot4}{5\cdot4}=\dfrac{8}{20}\)
b) \(\dfrac{5}{12}=\dfrac{5\cdot3}{12\cdot3}=\dfrac{15}{36}\\ \dfrac{11}{36}=\dfrac{11}{36}\)
c) \(\dfrac{2}{3}=\dfrac{2\cdot4\cdot5}{3\cdot4\cdot5}=\dfrac{40}{60}\\ \dfrac{3}{4}=\dfrac{3\cdot3\cdot5}{4\cdot3\cdot5}=\dfrac{45}{60}\\ \dfrac{4}{5}=\dfrac{4\cdot3\cdot4}{5\cdot3\cdot4}=\dfrac{48}{60}\)
a) \(\dfrac{3}{4}\) và \(\dfrac{2}{5}\)
Mẫu số chung: 20
\(\dfrac{3}{4}=\dfrac{3.5}{4.5}=\dfrac{15}{20}\)
\(\dfrac{2}{5}=\dfrac{2.4}{5.4}=\dfrac{8}{20}\)
b) \(\dfrac{5}{12}\) và \(\dfrac{11}{36}\)
Mẫu số chung: 36
\(\dfrac{5}{12}=\dfrac{5.3}{12.3}=\dfrac{15}{36}\)
c) \(\dfrac{2}{3};\dfrac{3}{4}\) và \(\dfrac{4}{5}\)
Mẫu số chung: 60
\(\dfrac{2}{3}=\dfrac{2.20}{3.20}=\dfrac{40}{60}\\ \dfrac{3}{4}=\dfrac{3.15}{4.15}=\dfrac{45}{60}\\ \dfrac{4}{5}=\dfrac{4.12}{5.12}=\dfrac{48}{60}\)