a) \(\dfrac{-2}{5}=\dfrac{-14}{35}\)

b) \(\dfrac{9}{4}=\dfrac{\dfrac{1}{4}}{\dfrac{1}{9}}\)

c) \(\dfrac{\dfrac{7}{4}}{\dfrac{1}{2}}=\dfrac{7}{2}\)

\(A=\dfrac{1}{2}+\dfrac{1}{12}+\dfrac{1}{30}+...+\dfrac{1}{2450}\)

\(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{49.50}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{7}-...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(A=\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{49}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+...+\dfrac{1}{50}\right)\)

\(A=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}\right)-2.\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+..+\dfrac{1}{50}\right)\)

\(A=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{49}+\dfrac{1}{50}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{25}\right)\)

\(A=\dfrac{1}{26}+\dfrac{1}{27}+\dfrac{1}{28}+...+\dfrac{1}{50}=B\)

\(\Rightarrow A:B=1\)

a: \(\dfrac{15}{21}=\dfrac{5}{7}=\dfrac{30}{42}\)

=>Lập được TLT

b: \(\dfrac{0.25}{1.25}=\dfrac{1}{5}< >\dfrac{1}{7}\)

=>KO lập được TLT

c: \(0.4:\left(1+\dfrac{2}{5}\right)=0.4:1.4=\dfrac{2}{7}< >\dfrac{3}{5}\)

=>Ko lập được TLT

d: \(\dfrac{3}{5}:\dfrac{1}{7}=\dfrac{21}{5}=< >21:\dfrac{1}{5}\)

=>Ko lập được TLT

e: \(4+\dfrac{1}{2}:7+\dfrac{1}{2}=4.5:7.5=\dfrac{3}{5}< >\dfrac{2.7}{4.7}\)

=>Ko lập được TLT

f: 1/4:1/9=9/4

1/2:2/9=9/4

=>1/4:1/9=1/2:2/9

=>Lập được TLT

g: 2/7:4/11=2/7*11/4=22/28=11/14

7/2:4/11=7/2*11/4=77/8<>11/14

=>Ko lập được TLT

h: 2/5:10/2=2/5*2/10=4/50=2/25

2/1:1/4=8<>2/25

=>Ko lập được TLT

i: 2/7:7/4=2/7*4/7=8/49

16/49:2=8/49=2/7:7/4

=>Lập được TLT

3\6=2\4;2\3=4\6;4\6=2\3;4\2=6\3

\(\dfrac{3}{6}=\dfrac{2}{4};\dfrac{6}{3}=\dfrac{4}{2};\dfrac{3}{2}=\dfrac{6}{4};\dfrac{4}{6}=\dfrac{2}{3}\)

6:(-27)=(\(-6\dfrac{1}{2}\))\(:29\dfrac{1}{4}\)

\(\Leftrightarrow\)6:(-27)=\(\left(-\dfrac{13}{2}\right):\dfrac{117}{4}\)

\(\Rightarrow\)\(\left(-\dfrac{13}{2}\right):\dfrac{117}{4}\)=\(\left(-\dfrac{13}{2}\right):\dfrac{4}{117}\)=\(-\dfrac{2}{9}\)

Ta có:\(\dfrac{6}{-27}=\dfrac{-2}{9}\)

hay\(\dfrac{6}{-2}=\dfrac{-27}{9}\);\(\dfrac{6}{-2}=\dfrac{27}{-9}\);\(\dfrac{2}{-9}=\dfrac{6}{-27}\)

a: \(\dfrac{5}{-9}=\dfrac{15}{-27};\dfrac{5}{15}=\dfrac{-9}{-27};\dfrac{-9}{5}=\dfrac{-27}{15};\dfrac{15}{5}=\dfrac{-27}{-9}\)

d: \(\dfrac{12}{15}=\dfrac{16}{20};\dfrac{12}{16}=\dfrac{15}{20};\dfrac{15}{12}=\dfrac{20}{16};\dfrac{16}{12}=\dfrac{20}{15}\)

1)

a) \(1\dfrac{5}{6}=\dfrac{-x}{5}\)

\(\Rightarrow\dfrac{11}{6}=\dfrac{-x}{5}\)

\(\Rightarrow-x=\dfrac{5.11}{6}=\dfrac{55}{6}\)

\(\Rightarrow x=-\dfrac{55}{6}\)

b) 4,25 : 8 = -3,5 : x

\(\dfrac{4,25}{8}=\dfrac{-3,5}{x}\)

\(x=\dfrac{-3,5.8}{4,25}\)

\(x=\dfrac{-28}{4,25}\)

2.

\(-\dfrac{12}{1,6}=\dfrac{55}{-7\dfrac{1}{3}}\)

\(\Rightarrow-\dfrac{12}{1,6}=\dfrac{55}{-\dfrac{22}{3}}\)

Ta có thể lặp đc các tỉ lệ thức sau:

\(-\dfrac{12}{1,6}=\dfrac{55}{-\dfrac{22}{3}}\)

\(\dfrac{-\dfrac{22}{3}}{1,6}=\dfrac{55}{-12}\)

\(-\dfrac{12}{55}=\dfrac{1,6}{-\dfrac{22}{3}}\)

\(\dfrac{1,6}{-12}=\dfrac{-\dfrac{22}{3}}{55}\)