So sánh phân số:
a) \(\dfrac{-15}{17}\)và\(\dfrac{-19}{21}\) c) \(\dfrac{-317}{633}\)và \(\dfrac{-371}{743}\)
b)\(\dfrac{-23}{49}\)và \(\dfrac{-25}{47}\) d) \(\dfrac{-24}{35}\) và \(\dfrac{-19}{30}\)
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a) -23/49 = -1081/2303
-25/47 = -1225/2303
=> -1081/2303 > -1225/2303 hay -23/49 > -25/47
b) -317/633 = -235531/470319
-371/743 = -234843/470319
=> -235531/470319 < -234843/470319 hay -317/633 < -371/743
a) Ta có \(\dfrac{23}{27}>\dfrac{23}{29};\dfrac{23}{29}>\dfrac{22}{29}\)
Vậy \(\dfrac{23}{27}>\dfrac{22}{29}\)
b) Ta có \(\dfrac{15}{25}=1-\dfrac{2}{5}\)
\(\dfrac{25}{49}=1-\dfrac{24}{49}\)
Vì \(\dfrac{2}{5}=\dfrac{24}{60}< \dfrac{24}{49}\)
Vậy \(\dfrac{15}{25}>\dfrac{25}{49}\)
a, Ta có: \(-\dfrac{317}{633}< -\dfrac{1}{2}\left(1\right)\)
\(\dfrac{-371}{743}>-\dfrac{1}{2}\left(2\right)\)
Từ (1); (2), Suy ra:
\(-\dfrac{317}{633}< \dfrac{-371}{743}\)
b, Ta có: \(\dfrac{-24}{35}< \dfrac{-24}{36}=\dfrac{-2}{3}\left(1\right)\)
\(\dfrac{-19}{30}>\dfrac{-20}{30}=\dfrac{-2}{3}\left(2\right)\)
Từ (1); (2) Suy ra:
\(\dfrac{-24}{35}< \dfrac{-19}{30}\)
a,
Ta có:
\(\dfrac{3}{7}=1-\dfrac{4}{7}\)
\(\dfrac{11}{15}=1-\dfrac{4}{15}\)
So sánh phân số \(\dfrac{4}{7}\) và \(\dfrac{4}{15}\)
Vì \(7< 15\) nên \(\dfrac{1}{7}>\dfrac{1}{15}\)
\(\Rightarrow1-\dfrac{4}{7}< 1-\dfrac{4}{15}\)
Vậy \(\dfrac{3}{7}< \dfrac{11}{15}\)
b)
\(\dfrac{-11}{6}< -1< \dfrac{-8}{9}\) nên \(\dfrac{-11}{6}< \dfrac{-8}{9}\)
c)
\(\dfrac{305}{25}=\dfrac{305:5}{25:5}=\dfrac{61}{5}\)
Ta có:
Mẫu số chung 2 phân số: 80
\(\dfrac{297}{16}=\dfrac{297*5}{16*5}=\dfrac{1485}{80}\)
\(\dfrac{61}{5}=\dfrac{61*16}{5*16}=\dfrac{976}{80}\)
Vì \(1485>976\) nên\(\dfrac{1485}{80}>\dfrac{976}{80}\)
Vậy \(\dfrac{297}{16}>\dfrac{305}{25}\)
d,
$\frac{-205}{317}=\frac{-205:-1}{317:-1}=\frac{205}{-317}$
Ta có:
Mẫu số chung 2 phân số: -35187
\(\dfrac{205}{-317}=\dfrac{205*111}{-317*111}=\dfrac{22755}{-35187}\)
\(\dfrac{-83}{111}=\dfrac{-83*-317}{111*-317}=\dfrac{26311}{-35187}\)
Vì \(22755< 26311\) nên\(\dfrac{22755}{-35187}< \dfrac{26311}{-35187}\)
Vậy \(\dfrac{-205}{317}< \dfrac{-83}{111}\)
Câu d, mình làm sai, cho mình sửa lại:
\(\dfrac{-205}{317}=\dfrac{-22755}{35187}\)
\(\dfrac{-83}{111}=\dfrac{-26311}{35187}\)
Vậy là \(-22755>-26311\) hay \(\dfrac{-205}{317}>\dfrac{-83}{111}\)
Câu 1:
a) \(\dfrac{-15}{17}\) và \(\dfrac{-19}{21}\)
Ta có: \(\dfrac{-15}{17}=-1+\dfrac{2}{17}\); \(\dfrac{-19}{21}=-1+\dfrac{2}{21}\)
Vì \(\dfrac{2}{17}>\dfrac{2}{21}\)
Do đó: \(\dfrac{-15}{17}>\dfrac{19}{-23}\)
b) \(\dfrac{-13}{19}\) và \(\dfrac{19}{-23}\)
Ta có: \(\dfrac{19}{23}>\dfrac{19}{25}\); \(\dfrac{13}{19}=1-\dfrac{6}{19}\); \(\dfrac{19}{25}=1-\dfrac{6}{25}\)
mà \(\dfrac{6}{19}>\dfrac{6}{25}\) \(\Rightarrow\dfrac{13}{19}< \dfrac{19}{25}< \dfrac{19}{23}\)
Vì \(\dfrac{13}{19}< \dfrac{19}{23}\Rightarrow\dfrac{-13}{19}>\dfrac{19}{-23}\)
c) \(\dfrac{-24}{35}\) và \(\dfrac{-19}{30}\)
Ta có: \(\dfrac{-24}{35}=-1+\dfrac{19}{35}\);\(\dfrac{-19}{30}=-1+\dfrac{11}{30}\)
Vì \(\dfrac{11}{35}< \dfrac{11}{30}\)
Do đó: \(\dfrac{-24}{35}< \dfrac{-19}{30}\)
d) \(\dfrac{-1941}{1931}\) và \(\dfrac{-2011}{2001}\); \(\dfrac{-2011}{2001}=-1+\dfrac{10}{2001}\)
Vì \(\dfrac{10}{1931}< \dfrac{10}{1001}\)
Do đó: \(\dfrac{-1941}{1931}< \dfrac{-2011}{2001}\)
Ta có: \(\dfrac{-1941}{1931}=-1+\dfrac{10}{1931}\)
Sorry câu d mình viết ngược:
Làm lại:
d) \(\dfrac{-1941}{1931}\) và \(\dfrac{-2011}{2001}\)
Ta có: \(\dfrac{-1941}{1931}=-1+\dfrac{10}{1931};\)
\(\dfrac{-2011}{2001}=-1+\dfrac{10}{2001}\)
Vì \(\dfrac{10}{1931}< \dfrac{10}{1001}\)
Do đó: \(\dfrac{-1941}{1931}< \dfrac{-2011}{2001}\)
\(a,\dfrac{-15}{17}=-1+\dfrac{2}{17}\\ -\dfrac{19}{21}=-1+\dfrac{2}{21}\\ Vì:\dfrac{2}{17}>\dfrac{2}{21}\Rightarrow-1+\dfrac{2}{17}>-1+\dfrac{2}{21}\Rightarrow-\dfrac{15}{17}>-\dfrac{19}{21}\\ b,-\dfrac{24}{35}=-1+\dfrac{11}{35};-\dfrac{19}{30}=-1+\dfrac{11}{30}\\ Vì:\dfrac{11}{35}< \dfrac{11}{30}\Rightarrow-1+\dfrac{11}{35}< -1+\dfrac{11}{30}\\ \Rightarrow-\dfrac{24}{35}< -\dfrac{19}{30}\)