\(\dfrac{7}{21}+\dfrac{-9}{36}=\dfrac{1}{3}+\dfrac{-1}{4}=\dfrac{4}{12}+\dfrac{-3}{12}=\dfrac{1}{12}\)

\(\dfrac{-12}{18}+\dfrac{-21}{35}=\dfrac{-2}{3}+\dfrac{-3}{5}=\dfrac{-10}{15}+\dfrac{-9}{15}=\dfrac{-19}{15}\)

\(\dfrac{-18}{14}+\dfrac{15}{-21}=\dfrac{-9}{7}+\dfrac{-5}{7}=\dfrac{-14}{7}=-2\)

\(\dfrac{3}{21}+\dfrac{-6}{42}=\dfrac{1}{7}+\dfrac{-1}{7}=0\)

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

a) \(\dfrac{1}{2}.\dfrac{1}{-3}+\dfrac{1}{-3}.\dfrac{1}{4}+\dfrac{1}{4}.\dfrac{1}{-5}+\dfrac{1}{-5}.\dfrac{1}{6}\)

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

\(=\dfrac{1}{-3}.\dfrac{3}{4}+\dfrac{1}{-5}.\dfrac{5}{12}\)

\(=\left(-\dfrac{1}{4}\right)+\left(-\dfrac{1}{12}\right)\)

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

b) \(A=\dfrac{81^4.3^{10}.27^5.3^{12}}{3^{18}.9^3.243^2}\)

\(=\dfrac{9^8.9^8.9^{13}.9^{10}}{9^{16}.9^3.9^3}\)

\(=\dfrac{9^{39}}{9^{22}}\)

\(=9^{17}\)

\(A=\dfrac{81^4\cdot3^{10}\cdot27^5\cdot3^{12}}{3^{18}\cdot9^3\cdot243^2}=\dfrac{3^{16}\cdot3^{10}\cdot3^{15}\cdot3^{12}}{3^{18}\cdot3^6\cdot3^{10}}=\dfrac{3^{53}}{3^{34}}=3^{19}\)

Vậy A = 3¹⁹

Ngân Hà làm đúng phần a) nhưng làm sai phần b) nên mk chỉ làm phần b) thôi

Ta có: \(\dfrac{-4}{12}+\dfrac{18}{45}+\dfrac{-6}{9}+\dfrac{21}{35}+\dfrac{6}{30}\)

\(=\dfrac{-1}{3}+\dfrac{-2}{3}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{6}{30}\)

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

\(=\dfrac{1}{5}\)

1)1/6 - - 5/6 = 1/6 + 5/6 = 1

2)6/13 - -14/39 = 6/13 + 14/39= 32/39

3)4/5 - 4/-18 = 4/5 + 4/18= 46/45

4)7/21 - 9/-36 = 7/21 + 9/36 = 7/12

5)-12/18 - -21/35  = -12/18 + 21/35 = -1/15

6)-3/21 - 6/42 = -2/7

7)-18/24 - 15/21 = -41/28

8)1/6 - 2/5 =-7/30

1: Ta có: \(\dfrac{x+4}{4}+\dfrac{3x-7}{5}=\dfrac{7x+2}{20}\)

\(\Leftrightarrow5x+20+12x-28=7x+2\)

\(\Leftrightarrow17x-7x=2+8=10\)

hay x=1

2: Ta có: \(\dfrac{x}{6}+\dfrac{1-3x}{9}=\dfrac{-x+1}{12}\)

\(\Leftrightarrow\dfrac{6x}{36}+\dfrac{4\left(1-3x\right)}{36}=\dfrac{3\left(-x+1\right)}{36}\)

\(\Leftrightarrow6x+4-12x=-3x+3\)

\(\Leftrightarrow-6x+3x=3-4\)

hay \(x=\dfrac{1}{3}\)

3: Ta có: \(\dfrac{x-3}{3}-\dfrac{x+2}{12}=\dfrac{2x-1}{4}\)

\(\Leftrightarrow4x-12-x-2=6x-3\)

\(\Leftrightarrow3x-14-6x+3=0\)

\(\Leftrightarrow-3x=11\)

hay \(x=-\dfrac{11}{3}\)

4: Ta có: \(\dfrac{x-2}{4}-\dfrac{2x+3}{3}=\dfrac{x+6}{12}\)

\(\Leftrightarrow3x-6-8x-12=x+6\)

\(\Leftrightarrow-5x-x=6+18\)

hay x=-4

5: Ta có: \(\dfrac{2x-1}{12}-\dfrac{3-x}{18}=\dfrac{-1}{36}\)

\(\Leftrightarrow6x-3+2x-6=-1\)

\(\Leftrightarrow8x=8\)

hay x=1

Câu 1:

\(-\dfrac{5}{7}\cdot\dfrac{7}{-45}=\dfrac{1}{9}\) ; \(-\dfrac{3}{10}\cdot-30=9\) ; \(-12\cdot-\dfrac{2}{36}=\dfrac{2}{3}\)

Caau2;3;4;5,... tự bấm máy tính là ra

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

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

\(\dfrac{3}{8}+\dfrac{4}{8}=\dfrac{3+4}{8}=\dfrac{7}{8}\)

\(\dfrac{6}{9}+\dfrac{2}{9}=\dfrac{6+2}{9}=\dfrac{8}{9}\)

\(\dfrac{12}{18}+\dfrac{7}{18}=\dfrac{12+7}{18}=\dfrac{19}{18}\)

\(\dfrac{7}{4}+\dfrac{2}{4}=\dfrac{7+2}{4}=\dfrac{9}{4}\)

e: \(D=\dfrac{-10}{12}-\dfrac{7}{12}-\dfrac{4}{12}=\dfrac{-21}{12}=-\dfrac{7}{4}\)

f: \(F=\dfrac{-27}{36}+\dfrac{12}{36}+\dfrac{10}{36}=\dfrac{-5}{36}\)

g: \(G=\dfrac{209}{99}+\dfrac{36}{99}+\dfrac{66}{99}=\dfrac{311}{99}\)

h: \(H=\dfrac{10}{24}-\dfrac{42}{24}+\dfrac{3}{24}=-\dfrac{29}{24}\)

\(D=\dfrac{-5}{6}+\dfrac{-7}{12}-\dfrac{1}{3}=-\dfrac{7}{4}\)

\(F=\dfrac{-3}{4}+\dfrac{1}{3}-\dfrac{-5}{18}=-\dfrac{5}{36}\)

\(G=\dfrac{19}{9}-\dfrac{-4}{11}+\dfrac{2}{3}=\dfrac{311}{99}\)

\(H=\dfrac{5}{12}+\dfrac{-7}{4}-\dfrac{1}{-8}=-\dfrac{29}{24}\)

\(e,D=\dfrac{-5}{6}+\dfrac{-7}{12}-\dfrac{1}{3}=\dfrac{-10}{12}+\dfrac{-7}{12}-\dfrac{4}{12}=\dfrac{\left(-10\right)+\left(-7\right)-4}{12}=\dfrac{-21}{12}=\dfrac{-7}{4}\\ f,F=\dfrac{-3}{4}+\dfrac{1}{3}-\dfrac{-5}{18} =\dfrac{-27}{36}+\dfrac{12}{36}-\dfrac{-10}{36}=\dfrac{\left(-27\right)+12-\left(-10\right)}{36}=\dfrac{-5}{36}\)

\(g,G=\dfrac{19}{9}-\dfrac{-4}{11}+\dfrac{2}{3}=\dfrac{209}{99}-\dfrac{-36}{99}+\dfrac{66}{99}=\dfrac{209-\left(-36\right)+66}{99}=\dfrac{311}{99}\\ h,H=\dfrac{5}{12}+\dfrac{-7}{4}-\dfrac{1}{-8}=\dfrac{5}{12}-\dfrac{7}{4}+\dfrac{1}{8}=\dfrac{10}{24}-\dfrac{42}{24}+\dfrac{3}{24}=\dfrac{10-42+3}{24}=\dfrac{-29}{24}\)