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\(\frac{6}{7}.\frac{11}{5}+\frac{11}{5}.\frac{4}{7}-\frac{2}{3}\)
=\(\left(\frac{6}{7}+\frac{4}{7}\right).\frac{11}{5}-\frac{2}{3}\)
=\(\frac{10}{7}.\frac{11}{5}-\frac{2}{3}\)
=\(\frac{52}{21}\)
`#25080409`
\(\dfrac{6}{11}\times\dfrac{3}{7}+\dfrac{3}{7}\times\dfrac{5}{11}?\)
`=`\(\left(\dfrac{6}{11}+\dfrac{5}{11}\right)\times\dfrac{3}{7}\)
`=`\(\dfrac{11}{11}\times\dfrac{3}{7}=1\times\dfrac{3}{7}=\dfrac{3}{7}\)
A = ( 6 : 3/5 - 7/6 x 6/7 ) : ( 21/58 x 10/11 + 57/11 )
A = 9 : .....
A = .......
\(1,\frac{5}{7}+\frac{3}{14}=\frac{10}{14}+\frac{3}{14}=\frac{13}{14}\)
\(2,\frac{11}{12}-\frac{5}{6}=\frac{11}{12}-\frac{10}{12}=\frac{1}{12}\)
\(3,6.\frac{5}{8}=\frac{30}{8}=\frac{15}{4}\)
\(4,\frac{4}{5}:\frac{3}{7}=\frac{4.7}{5.3}=\frac{28}{15}\)
5/7+3/14=13/14
11/12-5/6=1/12
6*5/8=30/8
4/5:3/7=28/15
\(\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{16}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)\)
= 1 + 2 + 2
= 5
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
=\(1-\frac{1}{7}\)
=\(\frac{6}{7}\)
\(M=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+....+\frac{5}{46.51}\)
\(M=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+...+\frac{51-46}{46.51}\)
\(M=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+....+\frac{1}{46}-\frac{1}{51}\)
\(M=1-\frac{1}{51}=\frac{50}{51}\)
\(N=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{199\cdot201}\)
\(N=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{199}-\frac{1}{201}\right)\)
\(N=\frac{1}{2}\cdot\left(1-\frac{1}{201}\right)\)
\(N=\frac{1}{2}\cdot\frac{200}{201}=\frac{100}{201}\)
`5/11 \times 7/6 + 7/6 \times 6/11 + 5/6`
`= 7/6 \times (5/11 + 6/11) + 5/6`
`= 7/6 \times 11/11 + 5/6`
`= 7/6 \times 1 + 5/6`
`= 7/6 + 5/6`
`= 12/6`
`= 2`
`5/11 \times 7/6 + 7/6 \times 6/11 + 5/6`
`= (5/11 + 6/11) \times 7/6 + 5/6`
`= 11/11 \times 7/6 + 5/6`
`= 1 \times 7/6 + 5/6`
`= 7/6 + 5/6`
`= 12/6`
`= 2`