So sánh 27/45 và 35/89
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\(\frac{-27}{35}\)và\(\frac{-21}{40}\)
Quy đồng lên ta được: \(\frac{-27}{35}=\frac{\left(-27\right).8}{35.8}=\frac{-216}{280}\)và\(\frac{-21}{40}=\frac{\left(-21\right).7}{40.7}=\frac{-147}{280}\)
Mà \(\frac{-216}{280}< \frac{-147}{280}\)\(\Rightarrow\frac{-27}{35}< \frac{-21}{40}\)
\(\frac{-22}{45}\)và\(\frac{-17}{33}\)
Quy đồng lên ta được: \(\frac{-22}{45}=\frac{\left(-22\right).11}{45.11}=\frac{-242}{495}\)và\(\frac{-17}{33}=\frac{\left(-17\right).15}{33.15}=\frac{-255}{495}\)
Mà\(\frac{-242}{495}>\frac{-255}{495}\)\(\Rightarrow\frac{-22}{45}>\frac{-17}{33}\)
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a ) − 1 10 < 1. b ) 39 20 < 2. c ) − 1 20 > − 11 40 . d ) 5 9 > 2 9
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\(\sqrt[]{27}-\sqrt[]{35}\) và \(6-\sqrt[]{51}\)
Giả sử \(\sqrt[]{27}-\sqrt[]{35}< 6-\sqrt[]{51}\)
\(\Leftrightarrow27-2.\sqrt[]{27.35}+35< 36-12\sqrt[]{51}+51\)
\(\Leftrightarrow63-6.\sqrt[]{105}< 87-12\sqrt[]{51}\)
\(\Leftrightarrow12\sqrt[]{51}-6.\sqrt[]{105}< 24\)
\(\Leftrightarrow6\sqrt[]{3}\left(\sqrt[]{17}-\sqrt[]{35}\right)< 24\)
\(\Leftrightarrow\sqrt[]{3}\left(\sqrt[]{17}-\sqrt[]{35}\right)< 4\)
mà \(\sqrt[]{17}-\sqrt[]{35}< 0\)
\(\Leftrightarrow\sqrt[]{3}\left(\sqrt[]{17}-\sqrt[]{35}\right)< 0< 4\left(đúng\right)\)
Vậy \(\sqrt[]{27}-\sqrt[]{35}< 6-\sqrt[]{51}\)
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\(\frac{27}{45}=\frac{54}{90}>\frac{45}{90}=\frac{1}{2}\) (1)
\(\frac{35}{89}=\frac{70}{178}\frac{35}{89}\)
27/45 và 35/89 TSC là 945.
Ta có:\(\frac{27}{45}=\frac{945}{1575};\frac{35}{89}=\frac{945}{1403}\)
Vì \(\frac{945}{1575}