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a) 1/7 . 5/6 + 1/7 . 1/6 + -8/7
= 1/7 . ( 5/6 + 1/6 ) + -8/7
= 1/7 . 1 + -8/7
= 1/7 + -8/7 = -1
b) 3/5 . -4/9 . 5/3 . 18/7
= ( 3/5 . 5/3 ) . ( -4/9 . 18/7 )
= 1 . -8/7 = -8/7
c) 1/2 + -3/4 . 16/9
= 1/2 + -4/3 = -5/6
d) ( 1/7 + 5/14 ) . -28/3
= 1/2 . -28/3 = -14/3
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\(\frac{5}{7}\times\frac{8}{9}+\frac{-1}{7}\times\frac{5}{9}+3\frac{4}{9}\\ =\frac{5}{9}\times\frac{8}{7}+\frac{-1}{7}\times\frac{5}{9}+3\frac{4}{9}\\ =\left(\frac{8}{7}+\frac{-1}{7}\right)\times\frac{5}{9}+3\frac{4}{9}=1\times\frac{5}{9}+3\frac{4}{9}\\ =\frac{5}{9}+3\frac{4}{9}=4\)
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c: Ta có: \(\dfrac{5}{3}+\dfrac{5}{3\cdot5}+\dfrac{5}{5\cdot7}+...+\dfrac{5}{101\cdot103}\)
\(=\dfrac{5}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{101\cdot103}\right)\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{103}\right)\)
\(=\dfrac{5}{2}\cdot\dfrac{102}{103}\)
\(=\dfrac{255}{103}\)
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= (11+19)+(12+18)+(13+17)+(14+16)+15
=(30+30+30+30)+15
=120+15
=135
A = \(\dfrac{5}{9}\cdot\left(\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{3}{7}\right)\)
=\(\dfrac{5}{9}\cdot\dfrac{5}{7}=\dfrac{25}{63}\)
=(1/7+1/7+3/7).5/9
=5/7.5/9
=25/63