a) \(x=\dfrac{1}{4}+\dfrac{2}{13}\)

\(x=\dfrac{13}{52}+\dfrac{8}{52}\)

⇒ \(x=\dfrac{21}{52}\)

b) \(\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}\)

\(\dfrac{x}{3}=\dfrac{14}{21}+\dfrac{-3}{21}\)

\(\dfrac{x}{3}=\dfrac{11}{21}\)

⇒ \(x=\dfrac{11.3}{21}=\dfrac{33}{21}\)

⇒ \(x=\dfrac{11}{7}\)

c) \(\dfrac{-8}{3}+\dfrac{1}{3}< x< \dfrac{-2}{7}+\dfrac{-5}{7}\)

\(\dfrac{-17}{7}< x< -1\)

⇒ \(-17< x< -7\)

⇒ \(x\in\left\{-16;-15,....;-6\right\}\)

d) \(\dfrac{1}{6}+\dfrac{2}{5}\)

\(=\dfrac{5}{30}+\dfrac{12}{30}\)

\(=\dfrac{17}{30}\)

e) \(\dfrac{3}{5}+\dfrac{-7}{4}\)

\(=\dfrac{12}{20}+\dfrac{-35}{20}\)

\(=\dfrac{-23}{20}\)

f) \(\dfrac{4}{13}+\dfrac{-12}{30}\)

\(=\dfrac{4}{13}+\dfrac{-2}{5}\)

\(=\dfrac{20}{65}+\dfrac{-26}{65}\)

\(=\dfrac{-6}{65}\)

g) \(\dfrac{-3}{29}+\dfrac{16}{58}\)

\(=\dfrac{-6}{58}+\dfrac{16}{58}\)

\(=\dfrac{10}{58}\)

h) \(\dfrac{8}{40}+\dfrac{-36}{45}\)

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

\(=\dfrac{-3}{5}\)

j) \(\dfrac{-8}{18}+\dfrac{15}{27}\)

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

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

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

câu 1) 

\(\dfrac{-12}{18}+\left(\dfrac{-21}{35}\right)=\dfrac{-19}{15}\)
câu 2) 

\(-\dfrac{3}{21}+\dfrac{6}{42}=0\)
câu 3)

\(-\dfrac{18}{24}+\dfrac{15}{21}=-\dfrac{1}{28}\)
câu 4) 

\(\dfrac{1}{6}+\dfrac{2}{5}=\dfrac{17}{30}\)
câu 5) 

\(\dfrac{3}{5}+\left(-\dfrac{7}{4}\right)=-\dfrac{23}{20}\)
câu 6) 

\(\left(-2\right)+\left(\dfrac{-5}{8}\right)=\dfrac{-21}{8}\)
câu 7) 

\(\dfrac{1}{-8}+\left(-\dfrac{5}{9}\right)=-\dfrac{49}{72}\)
câu 8) 

\(\dfrac{4}{13}+\dfrac{12}{39}=\dfrac{8}{13}\)
câu 9) 

\(\dfrac{1}{21}+\dfrac{1}{28}=\dfrac{1}{12}\)
câu 10) 

\(-\dfrac{3}{29}+\dfrac{16}{58}=\dfrac{5}{29}\)
câu 11) 

\(\dfrac{8}{40}+\left(-\dfrac{36}{45}\right)=-\dfrac{3}{5}\)
câu 12) 

\(-\dfrac{8}{18}+\left(-\dfrac{15}{27}\right)=-1\)
câu 13) 

\(\dfrac{13}{30}+\left(-\dfrac{1}{5}\right)=\dfrac{7}{30}\)
câu 14) 

\(\dfrac{2}{21}+\dfrac{1}{28}=\dfrac{11}{84}\)
câu 15) 

\(5+\left(-\dfrac{3}{4}\right)=\dfrac{17}{4}\)
câu 16) 

\(\dfrac{18}{24}+\dfrac{45}{-10}=-\dfrac{15}{4}\)

f: \(-20:2^2+\left(-5\right)^9:5^8\)

\(=-20:4-5^9:5^8\)

=-5-5

=-10

g: \(-100:5^2+\left(-7\right)\cdot\left(-3\right)^2\)

\(=-\dfrac{100}{25}-7\cdot9\)

=-4-63

=-67

h: \(-84:4+3^9:\left(-3\right)^7+\left(-5\right)^0\)

\(=-21-3^9:3^7+1\)

\(=-21-3^2+1\)

=-20-9

=-29

i: \(-29-\left[16+3\left(51-49\right)\right]\)

\(=-29-16-3\cdot2\)

=-45-6

=-51

j: \(-58\cdot75+58\cdot\left(-50\right)-58\left(-25\right)\)

\(=58\cdot\left(-75\right)+58\left(-50\right)+58\cdot25\)

\(=58\left(-75-50+25\right)\)

\(=-58\cdot100=-5800\)

`1, (10-4-6)+(5/4-9/14-5/7+7/3)

=0+187/84

=187/ 84

29/32.41/36-29/32.32/58-41/36.29/32-41/36.18/41

=-29/32.32/58-41/36.18/41

=-1/2-1/2=-1

1) 58× 75+ 58× 50 -58 × 25

= 58( 75 + 50 - 25 )

= 58 . 100

= 5800

1/ 58 x 75 + 58 x 50 - 58 x 25

= 58 x ( 75 + 50 - 25 )

= 58 x 100

= 5800

2/= \(2\frac{3}{5}-\frac{3}{5}\cdot\frac{11}{84}\)

\(=\frac{13}{5}-\frac{3}{5}\cdot\frac{11}{84}\)

\(=\frac{13}{5}-\frac{11}{140}\)

\(=\frac{364-11}{140}\)

\(=\frac{353}{140}\)

a)15/16:3/8x3/4

=15/16:6/16x12/16

=15/16x16/6x12/16

=15/6x12/16

=30/16=15/8

b)5/11x18/29-5/11x8/29+5/11x19/29

=5/11x(18/29-8/29+19/29)

=5/11x1=5/11