Quy đồng ( đây ngu toán không logic )

a)\(\dfrac{3}{6};\dfrac{2}{6};\dfrac{4}{6}\Rightarrow\dfrac{4}{6}>\dfrac{3}{6}>\dfrac{2}{6}\)

b)\(\dfrac{16}{9};\dfrac{24}{13}=\dfrac{208}{117};\dfrac{216}{117}\Rightarrow\dfrac{216}{117}>\dfrac{208}{117}\)

c)(Trời ơi cái đề bài)

h)\(\dfrac{27}{82};\dfrac{26}{75}=\dfrac{2025}{6150};\dfrac{2132}{6150}\Rightarrow\dfrac{2025}{6150}< \dfrac{2132}{6150}\)

d)(Trời ơi giống câu c)

i)\(\dfrac{-49}{78};\dfrac{64}{-95}=\dfrac{-4655}{7410};\dfrac{4992}{7410}\Rightarrow\dfrac{-4655}{7410}< \dfrac{4992}{7410}\)

P/s : Tự kết luận mỗi câu

a,\(\dfrac{1}{2}=\dfrac{1.3}{2.3}=\dfrac{3}{6}\),\(\dfrac{1}{3}=\dfrac{1.2}{3.2}=\dfrac{2}{6}\),\(\dfrac{2}{3}=\dfrac{2.2}{3.2}=\dfrac{4}{6}\)

vì có mẫu chung là 6 nên ta so sánh tử\(\Rightarrow\)ta so sánh 3,2,4

vì 2<3<4\(\Rightarrow\)\(\dfrac{2}{6}< \dfrac{3}{6}< \dfrac{4}{6}\Rightarrow\dfrac{1}{3}< \dfrac{1}{2}< \dfrac{2}{3}\)

a, Vì \(-\dfrac{1}{2}< 0\) => \(-\dfrac{1}{2}\) là số nhỏ nhất trong 3 số

Ta có: \(\dfrac{4}{9}:\dfrac{3}{7}=\dfrac{4\cdot7}{3\cdot9}=\dfrac{28}{27}>1\)

\(\Rightarrow\dfrac{4}{9}>\dfrac{3}{7}>-\dfrac{1}{2}\)

e, \(\dfrac{3^{10}+1}{3^9+1}\) và \(\dfrac{3^9+1}{3^8+1}\)

Ta có: \(A=\dfrac{3^{10}+1}{3^9+1}>1>\dfrac{3^{10}+1+2}{3^9+1+2}=\dfrac{3^{10}+3}{3^9+3}=\dfrac{3\left(3^9+1\right)}{3\left(3^8+1\right)}\)

\(=\dfrac{3^9+1}{3^8+1}=B\)

\(\Rightarrow A>B\)

\(\dfrac{-49}{78}\)<\(\dfrac{0}{78}\)=0=\(\dfrac{0}{-95}\)<\(\dfrac{64}{-95}\)

hông chắc nha :)

b/ sao mà so sánh cùng một lúc bốn phân số được bạn :(

bạn nào giải được giúp mình với

a) \(\dfrac{-1}{20}=\dfrac{-7}{140}\)

\(\dfrac{5}{7}=\dfrac{100}{140}\)

mà -7<100

nên \(-\dfrac{1}{20}< \dfrac{5}{7}\)

b) \(\dfrac{216}{217}< 1\)

\(1< \dfrac{1164}{1163}\)

nên \(\dfrac{216}{217}< \dfrac{1164}{1163}\)

c) \(\dfrac{-12}{17}=\dfrac{-180}{255}\)

\(\dfrac{-14}{15}=\dfrac{-238}{255}\)

mà -180>-238

nên \(-\dfrac{12}{17}>\dfrac{-14}{15}\)

d) \(\dfrac{27}{29}>0\)

\(0>-\dfrac{2727}{2929}\)

nên \(\dfrac{27}{29}>-\dfrac{2727}{2929}\)

\(a,\dfrac{-15}{17}=-1+\dfrac{2}{17}\\ -\dfrac{19}{21}=-1+\dfrac{2}{21}\\ Vì:\dfrac{2}{17}>\dfrac{2}{21}\Rightarrow-1+\dfrac{2}{17}>-1+\dfrac{2}{21}\Rightarrow-\dfrac{15}{17}>-\dfrac{19}{21}\\ b,-\dfrac{24}{35}=-1+\dfrac{11}{35};-\dfrac{19}{30}=-1+\dfrac{11}{30}\\ Vì:\dfrac{11}{35}< \dfrac{11}{30}\Rightarrow-1+\dfrac{11}{35}< -1+\dfrac{11}{30}\\ \Rightarrow-\dfrac{24}{35}< -\dfrac{19}{30}\)

\(P=\dfrac{32}{64}\cdot\dfrac{-57}{19}+\dfrac{35}{21}\cdot\dfrac{22}{44}=\dfrac{1}{2}\left(-3+\dfrac{5}{3}\right)=\dfrac{1}{2}\cdot\dfrac{-4}{3}=\dfrac{-2}{3}\)

\(Q=\dfrac{75}{125}\cdot\dfrac{82}{164}+\dfrac{49}{98}\cdot\dfrac{-35}{105}=\dfrac{1}{2}\left(\dfrac{3}{5}-\dfrac{1}{3}\right)=\dfrac{1}{2}\cdot\dfrac{4}{15}=\dfrac{2}{15}\)