a: =9+7=16

b: =11+3/13-2-4/7-5-3/13

=4-4/7

=28/7-4/7=24/7

c: =2/7(5+1/4-3-1/4)=2/7x2=4/7

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

= 4/9 x 1

=4/9

b) ( 312 + 325 - 247 ) : 13

= 390 : 13

= 30

a)4/9 x 3/5 + 4/9 x 8/5 - 4/9 x 2/10 

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

= 4/9x1

=4/9

b,312 : 13 + 325 : 13 - 247 : 13

=(312+325-247) : 13

=         390 : 3

= 130

a: =27/45-20/45=7/45

b: \(=\dfrac{3}{5}+\dfrac{30}{40}=\dfrac{3}{5}+\dfrac{3}{4}=\dfrac{12}{20}+\dfrac{15}{20}=\dfrac{27}{20}\)

c: \(=\dfrac{8}{13}\left(\dfrac{7}{2}-\dfrac{5}{2}+1\right)=\dfrac{8}{13}\cdot2=\dfrac{16}{13}\)

d: \(=\dfrac{9}{23}\left(\dfrac{5}{17}-\dfrac{22}{17}\right)+11+\dfrac{9}{23}=11\)

a) \(\dfrac{3}{5}+\dfrac{-4}{9}=\dfrac{27}{45}+\dfrac{-20}{45}=\dfrac{7}{45}\)

b) \(\dfrac{3}{5}+\dfrac{2}{5}.\dfrac{15}{8}=1.\dfrac{15}{8}=\dfrac{15}{8}\)

c) \(\dfrac{7}{2}.\dfrac{8}{13}+\dfrac{8}{13}.\dfrac{-5}{2}+\dfrac{8}{13}=\dfrac{8}{13}.\left(\dfrac{7}{2}+\dfrac{-5}{2}\right)=\dfrac{8}{13}.1=\dfrac{8}{13}\)

d) \(\dfrac{-5}{17}.\dfrac{-9}{23}+\dfrac{9}{23}.\dfrac{-22}{17}+11\dfrac{9}{23}=\dfrac{9}{23}.\left(\dfrac{-5}{17}+\dfrac{-22}{17}\right)=\dfrac{-243}{391}\)

a) \(\left(\dfrac{2}{3}\right)^3-\left(\dfrac{3}{4}\right)^2.\left(-1\right)^5\)

\(=\dfrac{8}{27}-\dfrac{9}{16}.\left(-1\right)\)

\(=\dfrac{8}{27}-\left(-\dfrac{9}{16}\right)\)

\(=\dfrac{8}{27}+\dfrac{9}{16}\)

\(=\dfrac{128}{432}+\dfrac{243}{432}\)

\(=\dfrac{371}{432}\)

b) \(12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2\)

\(=12:\left(\dfrac{9}{12}-\dfrac{10}{12}\right)^2\)

\(=12:\left(\dfrac{-1}{12}\right)^2\)

\(=12:\dfrac{1}{144}\)

\(=12.144\)

\(=1728\)

c) \(\dfrac{7}{22}:\dfrac{3}{11}+\dfrac{7}{22}:\dfrac{4}{11}\)

\(=\dfrac{7}{22}:\left(\dfrac{3}{11}+\dfrac{4}{11}\right)\)

\(=\dfrac{7}{22}:\dfrac{7}{11}\)

\(=\dfrac{7}{22}.\dfrac{11}{7}\)

\(=\dfrac{1}{2}\)

d) \(\dfrac{12}{35}.\left(\dfrac{7}{4}+\dfrac{13}{4}\right)-\dfrac{1}{3}\)

\(=\dfrac{12}{35}.5-\dfrac{1}{3}\)

\(=\dfrac{12}{7}-\dfrac{1}{3}\)

\(=\dfrac{36}{21}-\dfrac{7}{21}\)

\(=\dfrac{29}{21}\)

`6/11+2/5+16/11+19/13+3/5+7/13`

`=(6/11+16/11)+(2/5+3/5)+(19/13+7/13)`

`=22/11+5/5+26/13`

`=2+1+2=5`

\(=\left(\dfrac{6}{11}+\dfrac{16}{11}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)+\left(\dfrac{19}{13}+\dfrac{7}{13}\right)\)

\(=2+1+2\)

\(=5\)

a \(\dfrac{6}{15}+\dfrac{11}{15}=\dfrac{17}{15}\)

b \(\dfrac{22}{77}-\dfrac{14}{77}=\dfrac{8}{77}\)

c \(\dfrac{11}{13}\times\dfrac{26}{31}=11\times\dfrac{2}{31}=\dfrac{22}{31}\)

d \(\dfrac{1}{2}\times3\times\dfrac{2}{5}=\dfrac{3}{5}\)

a, 2/5 + 11/15 = 6/15 + 11/15 = 17/15

b,2/7 - 2/11 = 22/77 - 14/77 = 8/77

c, 11/13 x 26/31= 11 x 2/31 =22/31

d, 1/2 : 1/3 x 2/5

=  ( 1/2 x 2/5 ) : 1/3

=     1/5        : 1/3

=         3/5