a: 78/42-4/7=13/7-4/7=9/7

100/110-56/88=10/11-7/11=3/11

75/35-11/7+21/49=15/7-11/7+3/7=7/7=1

99/72-15/40-1212/1616=11/8-3/8-3/4=1-3/4=1/4

\(=\dfrac{11}{8}-\dfrac{3}{8}-\dfrac{3}{4}=1-\dfrac{3}{4}=\dfrac{1}{4}\)

=11/8−3/8−3/4=1−3/4=1/4

1/4

hơi lệch

\(1,A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\\ 2A=\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{99}-\dfrac{1}{103}\\ 2A=\dfrac{1}{3}-\dfrac{1}{103}=\dfrac{100}{309}\\ A=\dfrac{100}{309}\cdot\dfrac{1}{2}=\dfrac{50}{309}\)

\(2,A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\\ A=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{9\cdot10}\right)\\ A=7\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ A=7\left(1-\dfrac{1}{10}\right)=7\cdot\dfrac{9}{10}=\dfrac{63}{10}\)

Bài 1: 

Ta có: \(A=\dfrac{2}{3\cdot7}+\dfrac{2}{7\cdot11}+\dfrac{2}{11\cdot15}+...+\dfrac{2}{99\cdot103}\)

\(=\dfrac{1}{2}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{99\cdot103}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{103}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{100}{309}=\dfrac{50}{309}\)

Bài 2: 

Ta có: \(A=\dfrac{7}{2}+\dfrac{7}{6}+\dfrac{7}{12}+\dfrac{7}{20}+\dfrac{7}{30}+\dfrac{7}{42}+\dfrac{7}{56}+\dfrac{7}{72}+\dfrac{7}{90}\)

\(=7\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\)

\(=7\left(1-\dfrac{1}{10}\right)\)

\(=\dfrac{63}{10}\)

5/7>6/21

18/24>15/25

12/13=1212/1313

\(\dfrac{5}{7}\)>\(\dfrac{6}{21}\)

\(\dfrac{18}{24}\)>\(\dfrac{15}{25}\)

\(\dfrac{12}{13}\)=\(\dfrac{1212}{1313}\)

\(\dfrac{15}{35}+\dfrac{7}{10}=\dfrac{3}{7}+\dfrac{7}{10}=\dfrac{30}{70}+\dfrac{49}{70}=\dfrac{79}{70}\)

\(\dfrac{27}{72}+\dfrac{11}{24}=\dfrac{3}{8}+\dfrac{11}{24}=\dfrac{9}{24}+\dfrac{11}{24}=\dfrac{20}{24}=\dfrac{5}{6}\)

\(\dfrac{6}{12}+\dfrac{7}{6}=\dfrac{1}{2}+\dfrac{7}{6}=\dfrac{3}{6}+\dfrac{7}{6}=\dfrac{10}{6}=\dfrac{5}{3}\)

`2/5 + 9/15= 2/5 + 3/5=5/5=1`

`15/45 + 25/30= 1/3 + 5/6= 2/6+5/6=7/6`

`28/32 + 45/72=7/8+ 5/8=12/8=3/2`

`8/28 + 5/30= 2/7 + 1/6= 12/42 + 7/42= 19/42`

\(\frac{28}{35}\times\frac{15}{72}\times1\frac{7}{49}=\frac{4}{5}\times\frac{5}{24}\times\frac{8}{7}=\frac{160}{840}=\frac{4}{21}\)

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