a: \(\dfrac{2}{5}+\dfrac{6}{5}=\dfrac{2+6}{5}=\dfrac{8}{5}\)

b: \(\dfrac{4}{9}+\dfrac{7}{9}=\dfrac{4+7}{9}=\dfrac{11}{9}\)

c: \(\dfrac{6}{7}-\dfrac{4}{7}=\dfrac{6-4}{7}=\dfrac{2}{7}\)

d: \(\dfrac{17}{19}-\dfrac{12}{19}=\dfrac{17-12}{19}=\dfrac{5}{19}\)

\(a.\)

\(-\dfrac{2}{9}+\dfrac{7}{-9}=\dfrac{-2}{9}-\dfrac{7}{9}=\dfrac{-2-7}{9}=\dfrac{-9}{9}=-1\)

\(b.\)

\(\dfrac{1}{-6}+\dfrac{13}{-15}=-\dfrac{1}{6}-\dfrac{13}{15}=\dfrac{\left(-1\right)\cdot5-13\cdot2}{30}=\dfrac{-5-26}{30}=\dfrac{-31}{30}\)

\(c.\)

\(\dfrac{5}{-6}+\dfrac{-5}{12}+\dfrac{7}{18}=\dfrac{-5}{6}-\dfrac{5}{12}+\dfrac{7}{18}=\dfrac{\left(-5\right)\cdot6-5\cdot3+7\cdot2}{36}=\dfrac{-31}{36}\)

a) \(\dfrac{-2}{9}+\dfrac{7}{-9}=\dfrac{-2+-7}{9}=-1\) 

b)\(\dfrac{1}{-6}+\dfrac{13}{-15}=\dfrac{-5}{30}+\dfrac{26}{30}=\dfrac{-5+26}{30}=\dfrac{7}{10}\) 

c) \(\dfrac{5}{-6}+\dfrac{-5}{12}+\dfrac{7}{18}=\dfrac{-30}{36}+\dfrac{-15}{36}+\dfrac{18}{36}=\dfrac{-30+-15+18}{36}=\dfrac{-3}{4}\)

a) \(\dfrac{-5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{4}{-9}+\dfrac{7}{15}\)

=\(\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)+\dfrac{-2}{11}\)

=\(\left(-1\right)+1+\dfrac{-2}{11}\)

=\(\dfrac{-2}{11}\)

b) \(\left(\dfrac{-5}{12}+\dfrac{6}{11}\right)+\left(\dfrac{7}{17}+\dfrac{5}{11}+\dfrac{5}{12}\right)\)

=\(\dfrac{-5}{12}+\dfrac{6}{11}+\dfrac{7}{17}+\dfrac{5}{11}+\dfrac{5}{12}\)

=\(\left(\dfrac{-5}{12}+\dfrac{5}{12}\right)+\left(\dfrac{6}{11}+\dfrac{5}{11}\right)+\dfrac{7}{17}\)

=\(0+0+\dfrac{7}{17}\)

=\(\dfrac{7}{17}\)

c) A= \(49\dfrac{8}{23}-\left(5\dfrac{7}{32}+14\dfrac{8}{23}\right)\)

A=\(49\dfrac{8}{23}-5\dfrac{7}{32}-14\dfrac{8}{23}\)

A=\(\left(49\dfrac{8}{23}-14\dfrac{8}{23}\right)-5\dfrac{7}{32}\)

A=\(35-5\dfrac{7}{32}\)

A=\(35-\dfrac{167}{32}=\dfrac{953}{32}\)

d) C=\(\dfrac{-3}{7}.\dfrac{5}{9}+\dfrac{4}{9}.\dfrac{-3}{7}+2\dfrac{3}{7}\)

C=\(\dfrac{-3}{7}.\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{17}{7}\)

C=\(\dfrac{-3}{7}.1+\dfrac{17}{7}\)

C=\(\dfrac{-3}{7}+\dfrac{17}{7}=2\)

a, `(-5)/9+8/15+(-2)/11+4/(-9)+7/15`

`=-5/9+8/15-2/11-4/9+7/15`

`=(-5/9-4/9)+(8/15+7/15)-2/11`

`=-9/9+15/15-2/11`

`=-1+1-2/11`

`=-2/11`

b, `((-5)/12+6/11)+(7/17+5/11+5/12)`

`=-5/12+6/11+7/17+5/11+5/12`

`=(-5/12+5/12)+(6/11+5/11)+7/17`

`=0+11/11+7/17`

`=1+7/17`

`=17/17+7/17`

`=24/17`

c, `A=49 8/23 - (5 7/32 + 14 8/23)`

`A=49 8/23 - 5 7/32 - 14 8/23`

`A=(49 8/23 - 14 8/23)-5 7/32`

`A=35 - 167/32`

`A=953/32`

d, `C=(-3)/7.5/9+4/9.(-3)/7+2 3/7`

`C=-3/7 . 5/9-4/9 . 3/7+17/7`

`C=-3/7.(5/9+4/9)+17/7`

`C=-3/7 . 1+17/7`

`C=2`

a) Ta có: \(\dfrac{-5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{-4}{9}+\dfrac{7}{15}\)

\(=\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}\)

\(=-1+1-\dfrac{2}{11}\)

\(=-\dfrac{2}{11}\)

b) Ta có: \(\left(\dfrac{-5}{12}+\dfrac{6}{11}\right)+\left(\dfrac{7}{11}+\dfrac{5}{11}+\dfrac{5}{12}\right)\)

\(=\left(\dfrac{-5}{12}+\dfrac{5}{12}\right)+\left(\dfrac{6}{11}+\dfrac{7}{11}+\dfrac{5}{11}\right)\)

\(=\dfrac{18}{11}\)

c) Ta có: \(A=49\dfrac{8}{23}-\left(5\dfrac{7}{32}+14\dfrac{8}{23}\right)\)

\(=49+\dfrac{8}{23}-14-\dfrac{8}{23}-5-\dfrac{7}{32}\)

\(=30-\dfrac{7}{32}=\dfrac{953}{32}\)

a)  $\frac{3}{5} \times \frac{6}{7} = \frac{{3 \times 6}}{{5 \times 7}} = \frac{{18}}{{35}}$                                                 

 b) $\frac{2}{9} \times \frac{{18}}{3} = \frac{{2 \times 18}}{{9 \times 3}} = \frac{{36}}{{27}} = \frac{4}{3}$

c)  $\frac{5}{7} \times 12 = \frac{{5 \times 12}}{7} = \frac{{60}}{7}$                                            

d)  $21 \times \frac{2}{7} = \frac{{21 \times 2}}{7} = \frac{{42}}{7} = 6$

14/16 + 10/16 = 24/16 =3/2

21/5

92/63

16/27

\(\dfrac{14+10}{16}=\dfrac{24}{16}\)

\(\dfrac{60+24}{20}=\dfrac{84}{20}\)

\(\dfrac{92}{63}\)

\(\dfrac{32}{54}\)

a.3/2

b.21/5

c.92/63

d.16/27

a: \(\dfrac{3}{8}+\dfrac{7}{8}=\dfrac{3+7}{8}=\dfrac{10}{8}=\dfrac{5}{4}\)

b: \(\dfrac{7}{9}-\dfrac{4}{9}=\dfrac{7-4}{9}=\dfrac{3}{9}=\dfrac{1}{3}\)

c: \(\dfrac{5}{6}+\dfrac{1}{8}=\dfrac{20}{24}+\dfrac{3}{24}=\dfrac{20+3}{24}=\dfrac{23}{24}\)

d: \(\dfrac{9}{15}-\dfrac{2}{5}=\dfrac{3}{5}-\dfrac{2}{5}=\dfrac{3-2}{5}=\dfrac{1}{5}\)

e: \(\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{9}{5}=\dfrac{2+3+9}{5}=\dfrac{14}{5}\)

g: \(\dfrac{8}{10}-\dfrac{1}{10}-\dfrac{3}{10}=\dfrac{8-1-3}{10}=\dfrac{4}{10}=\dfrac{2}{5}\)

h: \(\dfrac{23}{7}-\dfrac{4}{7}+\dfrac{2}{7}=\dfrac{23-4+2}{7}=\dfrac{21}{7}=3\)

a)<

b)>

c)=

d)=

a)<

b)>

c)=

d)=

a) \(\dfrac{3}{5}+\dfrac{1}{6}=\dfrac{18}{30}+\dfrac{5}{30}=\dfrac{23}{30}\)

b) \(4+\dfrac{2}{5}=\dfrac{20}{5}+\dfrac{2}{5}=\dfrac{22}{5}\)

c) \(\dfrac{25}{12}-\dfrac{7}{6}=\dfrac{25}{12}-\dfrac{14}{12}=\dfrac{11}{12}\)

d) \(\dfrac{9}{7}-\dfrac{7}{6}=\dfrac{54}{42}-\dfrac{49}{42}=\dfrac{5}{42}\)

d) \(\dfrac{3}{7}\times\dfrac{2}{5}=\dfrac{3\times2}{7\times5}=\dfrac{6}{35}\)

A=18/30+5/30=23/30

B=20/5+2/5=22/5

C=25/12-14/12=11/12

D=54/42-49/42=5/42

E=6/35

18/30 + 5/30 = 23/30

20/5 + 2/5 = 22/5

25/12 - 14/12 = 11/12

3/7 x 2/5 = 6/35

a: \(\dfrac{7}{3}+\dfrac{4}{9}=\dfrac{21}{9}+\dfrac{4}{9}=\dfrac{21+4}{9}=\dfrac{25}{9}\)

b: \(\dfrac{3}{14}+6=\dfrac{3+6\cdot14}{14}=\dfrac{84+3}{14}=\dfrac{87}{14}\)

c: \(\dfrac{7}{8}-\dfrac{1}{2}=\dfrac{7}{8}-\dfrac{4}{8}=\dfrac{7-4}{8}=\dfrac{3}{8}\)

d: \(5-\dfrac{9}{10}=\dfrac{50}{10}-\dfrac{9}{10}=\dfrac{50-9}{10}=\dfrac{41}{10}\)