=5/18+3/8*5/3

=5/18+5/8

=65/72

\(\dfrac{5}{6}\cdot\dfrac{1}{3}+\dfrac{1}{2}\cdot\dfrac{3}{4}\cdot\dfrac{5}{3}\)

\(=\dfrac{5\cdot1}{6\cdot3}+\dfrac{1}{2}\cdot\dfrac{3\cdot5}{4\cdot3}\)

\(=\dfrac{5}{18}+\dfrac{1}{2}\cdot\dfrac{15}{12}\)

\(=\dfrac{5}{18}+\dfrac{1}{2}\cdot\dfrac{5}{4}\)

\(=\dfrac{5}{18}+\dfrac{1\cdot5}{2\cdot8}\)

\(=\dfrac{5}{18}+\dfrac{5}{8}\)

\(=\dfrac{65}{72}\)

\(\dfrac{5}{6}.\dfrac{1}{3}+\dfrac{5}{6}+\dfrac{3}{4}\)

\(=\dfrac{5}{6}.\left(\dfrac{1}{3}+\dfrac{3}{4}\right)=\dfrac{5}{6}.\dfrac{7}{12}=\dfrac{35}{72}\)

\(\frac{3-\frac{1}{2}+\frac{1}{4}}{\frac{2}{3}-\frac{5}{6}-\frac{3}{4}}=\frac{\left(3-\frac{1}{2}+\frac{1}{4}\right)\left(3.4\right)}{\left(\frac{2}{3}-\frac{5}{6}-\frac{3}{4}\right)\left(3.4\right)}=\frac{36-6+3}{8-10-9}=\frac{33}{-11}=-3\)

= (2/5 + 3/5) + (6/9 + 1/3) + (7/4 + 1/4)

= 1 + (6/9 + 3/9) + 2 = 1 + 1 + 2 = 4

\(\dfrac{2}{5}+\dfrac{6}{9}+\dfrac{7}{4}+\dfrac{3}{5}+\dfrac{1}{3}+\dfrac{1}{4}\\ =\left(\dfrac{2}{5}+\dfrac{3}{5}\right)+\left(\dfrac{7}{4}+\dfrac{1}{4}\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\\ =1+2+1=4\)

\(240:\left(5^3-5^3:5^2\right)-3^6:3^4+15\cdot11\cdot\left(13-9\right)\)

\(=240:\left(5^3-5\right)-3^{6-4}+15\cdot11\cdot4\)

\(=240\cdot\left(125-5\right)-3^2+60\cdot11\)

\(=240:120-9+60\cdot\left(10+1\right)\)

\(=2-9+600+60\)

\(=653\)

= -5 / 7 x ( 2 / 11 + 9 / 11) + 12/7

= -5/7 x 1 + 12/7

= -5/7 + 12/7

= 1

b, = ( 9/4 x 105 - 9/4 x 101) : 3/2 - 64 x ( 1/4 - 3/4)

  =  [ 9/4 x ( 105 - 101)] : 3/2 -64 x -1/2

= 9/4 x 4 : 3 /2 - (-32)

= 9 : 3/2 + 32

= 18/3 +32

= 

a: \(B=\frac12-\left\lbrack\frac38+\left(-\frac74\right)\right\rbrack\)

\(=\frac12-\frac38+\frac74\)

\(=\frac48-\frac38+\frac{14}{8}=\frac{15}{8}\)

b: \(-\frac{4}{12}-\left(-\frac{13}{39}-0,25\right)+0,75\)

\(=-\frac13+\frac13+0,25+0,75\)

=0,25+0,75

=1

c: \(\frac12-\frac13+\frac{1}{23}+\frac16\)

\(=\left(\frac12-\frac13+\frac16\right)+\frac{1}{23}\)

\(=\left(\frac16+\frac16\right)+\frac{1}{23}=\frac13+\frac{1}{23}=\frac{26}{69}\)

d: \(\left(-\frac{13}{7}-\frac49\right)-\left(-\frac{10}{7}-\frac49\right)\)

\(=-\frac{13}{7}-\frac49+\frac{10}{7}+\frac49\)

\(=-\frac{13}{7}+\frac{10}{7}=-\frac37\)

e: \(\left(\frac78-\frac52+\frac47\right)-\left(-\frac37+1-\frac{13}{8}\right)\)

\(=\frac78-\frac52+\frac47+\frac37-1+\frac{13}{8}\)

\(=\frac{20}{8}-\frac52=0\)

f: \(-\frac37+\left(3-\frac34\right)-\left(2,25-\frac{10}{7}\right)\)

\(=-\frac37+3-\frac34-2,25+\frac{10}{7}\)

\(=\frac77+0,75-\frac34\)

=1
g: \(\left(\frac53-\frac37+9\right)-\left(2+\frac57-\frac23\right)+\left(\frac87-\frac43-10\right)\)

\(=\frac53-\frac37+9-2-\frac57+\frac23+\frac87-\frac43-10\)

\(=\left(\frac53+\frac23-\frac43\right)+\left(-\frac37-\frac57+\frac87\right)+\left(9-2-10\right)\)

\(=\frac33+7-10=1-3=-2\)

\(A=\left(\frac{5}{3}-\frac{3}{7}+9\right)-\left(2+\frac{5}{7}-\frac{2}{3}\right)+\left(\frac{8}{7}-\frac{4}{3}-10\right)\)

\(=\frac{5}{3}-\frac{3}{7}+9-2-\frac{5}{7}+\frac{2}{3}+\frac{8}{7}-\frac{4}{3}-10\)

\(=\left(\frac{5}{3}+\frac{2}{3}-\frac{4}{3}\right)-\left(\frac{3}{7}+\frac{5}{7}-\frac{8}{7}\right)+\left(9-2-10\right)\)

\(=1-0-3\)

\(=-2\)

5/3-3/7+9-2-5/7+2/3+8/7-4/3-10

(5/3-4/3+2/3)+(8/7-3/7-5/7)+(9-2-10)

1+0-3=-2