a) \(\left(\dfrac{3}{29}-\dfrac{1}{5}\right)\cdot\dfrac{29}{3}\)

\(=\dfrac{3}{29}\cdot\dfrac{29}{3}-\dfrac{1}{5}\cdot\dfrac{29}{3}\)

\(=1-\dfrac{29}{15}\)

\(=\dfrac{15-29}{15}\)

\(=-\dfrac{14}{15}\) 

b) \(\dfrac{3}{4}\cdot\dfrac{7}{9}+\dfrac{1}{4}\cdot\dfrac{7}{9}\)

\(=\dfrac{7}{9}\cdot\left(\dfrac{1}{4}+\dfrac{3}{4}\right)\)

\(=\dfrac{7}{9}\cdot1\)

\(=\dfrac{7}{9}\)

c) \(\dfrac{1}{7}\cdot\dfrac{5}{9}+\dfrac{5}{9}\cdot\dfrac{1}{7}+\dfrac{5}{9}\cdot\dfrac{3}{7}\) 

\(=\dfrac{5}{9}\cdot\left(\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{3}{7}\right)\)

\(=\dfrac{5}{9}\cdot\dfrac{5}{7}\)

\(=\dfrac{25}{63}\)

d) \(4\cdot11\cdot\dfrac{3}{4}\cdot\dfrac{9}{121}\)

\(=\left(4\cdot\dfrac{3}{4}\right)\cdot\left(11\cdot\dfrac{9}{121}\right)\)

\(=3\cdot\dfrac{9}{11}\)

\(=\dfrac{27}{11}\)

D=5/3.5+5/5.7+5/7.9+5/9.11+...+5/27.29+5/29.31

2D=10/3.5+10/5.7+10/7.9+10/9.11+...+10/27.29+10/29.31

2D=5/3-5/5+5/5-5/7+5/7-5/9+5/9-5/11+...+5/27-5/29+5/29-5/31

2D=5/3-5/31

2D=155/93-15/93

2D=140/93

D=140/93:2

D=70/93

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3 : 4 = 6/8

 4: 9 = 8 /18

9 : 29 = 18/58

3/4= 6/8, 4: 9 = 8 /18, 9 : 29 = 18/58

 -29.(85-47)-85.(47-29)

=-29.38-85.18

=-1102-1503

=-2605

-15.(23-29)+23-(15-29)

=-15.(-6)+23-(-14)

=90+23+14

=113+14

=127

 -13.(55-29)+23.(15-29)

=-13.26+23.(-14)

=-338+(-322)

=-660

-10.(2+4)-5.(4-3)

=-10.6-5.1

=-60-5

=-65

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a) 19 + (29 - 9*37) - (63*9 - 29*99)

= 19 + 29 - 9*37 - 63*9 + 29*99

= 19 + 29(1 + 99) - 9(37 + 63)

= 19 + 29*100 - 9*100

= 19 + 100(29 - 9)

= 19 + 100*20

= 19 + 2000 = 2019

b) \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

= \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)

= \(\frac{2^6+2^5+2^4+2^3+2^2+2+1}{2^7}\)

= \(\frac{64+32+16+8+4+2+1}{128}\) = \(\frac{127}{128}\)

\(\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{29}\cdot9^{10}-7\cdot2^{29}\cdot27^6}\)

\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^2\cdot2^{27}\cdot3^{20}}{5\cdot2^{29}\cdot3^{20}-7\cdot2^{29}\cdot3^{18}}\)

\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot3^2-7\right)}\)

\(=\dfrac{10-9}{5\cdot9-7}=\dfrac{1}{38}\)

\(\frac{9}{8}-\frac{-11}{8}=\frac{9-\left(-11\right)}{8}=\frac{9+11}{8}=\frac{20}{8}=\frac{5}{2}\)

\(-\frac{1}{2}-\frac{5}{2}=\frac{-1-5}{2}=\frac{-6}{2}=-3\)

\(\frac{4}{3}-\frac{7}{3}=\frac{4-7}{3}=\frac{11}{3}\)

\(\frac{3}{-5}-\frac{-8}{10}=\frac{6}{-10}-\frac{-8}{10}=\frac{-6}{10}-\frac{-8}{10}=\frac{-6-\left(-8\right)}{10}=\frac{-6+8}{10}=\frac{2}{10}=\frac{1}{5}\)

\(\frac{5}{7}-\frac{-3}{21}=\frac{5}{7}-\frac{-1}{7}=\frac{5-\left(-1\right)}{7}=\frac{5+1}{7}=\frac{6}{7}\)

\(\frac{4}{-3}-\frac{9}{27}=\frac{4}{-3}-\frac{1}{3}=\frac{-4}{3}-\frac{1}{3}=\frac{-4-1}{3}=\frac{-5}{3}\)

\(\frac{7}{29}-\frac{9}{29}=\frac{7-9}{29}=\frac{2}{29}\)

\(\frac{-7}{22}-\frac{9}{22}=\frac{-7-9}{22}=\frac{-16}{22}=\frac{-8}{11}\)

\(\frac{-23}{7}-\frac{31}{7}=\frac{-23-31}{7}=\frac{-54}{7}\)