a) \(\dfrac{4}{7}< \dfrac{6}{7}\)

\(\dfrac{15}{23}>\dfrac{12}{23}\)

\(\dfrac{45}{60}=\dfrac{3}{4}\)

b) \(\dfrac{8}{9}>\dfrac{11}{18}\)

\(\dfrac{13}{18}>\dfrac{2}{3}\)

\(\dfrac{27}{25}>1\)

\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{5\times4\times13}{13\times5\times3}=\dfrac{4}{3}\\ b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\dfrac{3}{7}\times\dfrac{7}{5}+\dfrac{5}{2}\times\dfrac{7}{5}=\dfrac{3}{5}+\dfrac{7}{2}=\dfrac{6}{10}+\dfrac{35}{10}=\dfrac{41}{10}\\ c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)

a, 4/3  b, 41/10   c,22/45

a: =13/26*9/18*2/3=2/3*1/4=2/12=1/6

b: =44/22*5/15*3/2=2*1/3*3/2=2*1/2=1

1) \(\dfrac{1}{2}+\dfrac{13}{19}-\dfrac{4}{9}+\dfrac{6}{19}+\dfrac{5}{18}\)

\(=\dfrac{1}{2}+\left(\dfrac{13}{19}+\dfrac{6}{19}\right)-\dfrac{4}{9}+\dfrac{5}{18}\)

\(=\dfrac{3}{2}-\dfrac{4}{9}+\dfrac{5}{18}\)

\(=\dfrac{19}{18}+\dfrac{5}{18}\)

\(=\dfrac{24}{18}\)

\(=\dfrac{4}{3}\)

2) \(\dfrac{-20}{23}+\dfrac{2}{3}-\dfrac{3}{23}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=\left(-\dfrac{20}{23}-\dfrac{3}{23}\right)+\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=-1+\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=-\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=\dfrac{1}{15}+\dfrac{7}{15}\)

\(=\dfrac{8}{15}\)

3) \(\dfrac{4}{3}+\dfrac{-11}{31}+\dfrac{3}{10}-\dfrac{20}{31}-\dfrac{2}{5}\)

\(=\left(\dfrac{-11}{31}-\dfrac{20}{31}\right)+\dfrac{4}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=-1+\dfrac{4}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=\dfrac{1}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=\dfrac{1}{3}-\dfrac{1}{10}\)

\(=\dfrac{7}{30}\)

4) \(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\)

\(=\dfrac{5}{7}.\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\)

\(=\dfrac{5}{7}.-\dfrac{7}{11}\)

\(=-\dfrac{35}{77}\)

\(=-\dfrac{5}{11}\)

\(\left(\dfrac{18}{37}+\dfrac{19}{37}\right)+\left(\dfrac{8}{24}-\dfrac{47}{24}\right)+\dfrac{2}{3}=\dfrac{37}{37}-\dfrac{13}{8}+\dfrac{2}{3}=\dfrac{1}{24}\)

`@` `\text {Ans}`

`\downarrow`

`j)`

`-3/4 + 2/7 + (-1)/4 + 3/5 + 5/7`

`= (-3/4 - 1/4) + (2/7 + 5/7) + 3/5`

`= -1 + 1 + 3/5`

`= 3/5`

`k)`

`-2/17 + 15/23 + (-15)/17 + 4/19 + 8/23`

`= (-2/17 - 15/17) + (15/23 + 8/23) + 4/19`

`= -1 + 1 + 4/19`

`= 4/19`

$#KDN040510$

j: =-3/4-1/4+2/7+5/7+3/5

=-1+1+3/5

=3/5

k: =-2/17-15/17+15/23+8/23+4/19

=-1+1+4/19

=4/19

\(j)\dfrac{-3}{4}+\dfrac{2}{7}+\dfrac{-1}{4}+\dfrac{3}{5}+\dfrac{5}{7}\\ =\left(\dfrac{-3}{4}+\dfrac{-1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\dfrac{3}{5}\\ =\dfrac{-4}{4}+\dfrac{7}{7}+\dfrac{3}{5}\\ =-1+1+\dfrac{3}{5}\\ =0+\dfrac{3}{5}\\ =\dfrac{3}{5}\\ k)\dfrac{-2}{17}+\dfrac{15}{23}+\dfrac{-15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\\ =\left(\dfrac{-2}{17}+\dfrac{-15}{17}\right)+\left(\dfrac{15}{23}+\dfrac{8}{23}\right)+\dfrac{4}{19}\\ =\dfrac{-17}{17}+\dfrac{23}{23}+\dfrac{4}{19}\\ =-1+1+\dfrac{4}{9}\\ =0+\dfrac{4}{19}\\ =\dfrac{4}{19}\)

1301

=1301

1301

f)\(-\dfrac{2}{17}+\dfrac{15}{23}+-\dfrac{15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\)
\(=\left(-\dfrac{2}{17}+-\dfrac{15}{17}\right)+\left(\dfrac{15}{23}+\dfrac{8}{23}\right)+\dfrac{4}{19}\)
\(=-1+1+\dfrac{4}{19}\)
\(=0+\dfrac{4}{19}=\dfrac{4}{19}\)
g)\(-\dfrac{1}{2}+\dfrac{3}{21}+-\dfrac{2}{6}+-\dfrac{5}{30}\)
\(=-\dfrac{1}{2}+\dfrac{1}{7}+-\dfrac{1}{3}+-\dfrac{1}{6}\)
\(=\left(-\dfrac{1}{2}+-\dfrac{1}{3}+-\dfrac{1}{6}\right)+\dfrac{1}{7}\)
\(=-\dfrac{3+2+1}{6}+\dfrac{1}{7}\)
\(=\dfrac{1}{7}-1\)
\(=\dfrac{1}{7}-\dfrac{7}{7}=-\dfrac{6}{7}\)

`f)(-2)/17 + 15/23 + (-15)/17 + 4/19 + 8/23`

`= (-2/17+ -15/17)+(15/23+8/23)+4/19`

`= -1+1+4/19`

`= 0 +4/19`

`= 0`

`g)(-1)/2 + 3/21 + (-2)/6 + (-5)/30`

`= (-1)/2 + 1/7 + (-1)/3 + (-1)/6`

`= (-21)/42 + 6/42 + (-14)/42 + (-7)/42`

`=(-36)/42`

`=(-6)/7`

\(f,-\dfrac{2}{17}+\dfrac{15}{23}-\dfrac{15}{17}+\dfrac{4}{19}+\dfrac{8}{23}\)

\(=-\dfrac{2}{17}-\dfrac{15}{17}+\dfrac{15}{23}+\dfrac{8}{23}+\dfrac{4}{19}\)

\(=-1+1+\dfrac{4}{19}\)

\(=\dfrac{4}{19}\)

\(g,-\dfrac{1}{2}+\dfrac{3}{21}-\dfrac{2}{6}-\dfrac{5}{30}\)

\(=-\dfrac{5}{14}-\dfrac{1}{2}\)

\(=-\dfrac{5}{14}-\dfrac{7}{14}\)

\(=-\dfrac{6}{7}\)