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a) \(\frac{2}{5}< \frac{8}{11}\)
b) \(\frac{5}{7}>\frac{7}{15}\)
Bài 2:
a, \(\dfrac{5}{23}\) \(\times\) \(\dfrac{17}{26}\) + \(\dfrac{5}{23}\) \(\times\) \(\dfrac{9}{26}\)
= \(\dfrac{5}{23}\) \(\times\) ( \(\dfrac{17}{26}\) + \(\dfrac{9}{26}\))
= \(\dfrac{5}{23}\) \(\times\) \(\dfrac{26}{26}\)
= \(\dfrac{5}{23}\)
b, \(\dfrac{3}{4}\) \(\times\) \(\dfrac{7}{9}\) + \(\dfrac{7}{4}\) \(\times\) \(\dfrac{3}{9}\)
= \(\dfrac{7}{12}\) + \(\dfrac{7}{12}\)
= \(\dfrac{14}{12}\)
= \(\dfrac{7}{6}\)
Ta có:\(1-\frac{13}{7}=-\frac{6}{7}\)
\(1-\frac{7}{15}=\frac{8}{15}\)
Vì \(-\frac{6}{7}< \frac{8}{15}\)
\(\Rightarrow\frac{13}{7}< \frac{7}{15}\)
\(\dfrac{7}{18}=\dfrac{7.4}{18.4}=\dfrac{28}{72}\); \(\dfrac{9}{8}=\dfrac{9.9}{8.9}=\dfrac{81}{72}\)
\(\dfrac{2}{3}=\dfrac{2.20}{3.20}=\dfrac{40}{60};\dfrac{3}{4}=\dfrac{3.15}{4.15}=\dfrac{45}{60};\dfrac{6}{5}=\dfrac{6.12}{5.12}=\dfrac{72}{60}\)
\(\dfrac{13}{12}=\dfrac{13.5}{12.5}=\dfrac{65}{60};\dfrac{5}{6}=\dfrac{5.10}{6.10}=\dfrac{50}{60};\dfrac{4}{5}=\dfrac{4.12}{12.5}=\dfrac{48}{60}\)
\(\dfrac{9}{8}=\dfrac{9.8}{8.6}=\dfrac{72}{48};\dfrac{7}{24}=\dfrac{7.2}{24.2}=\dfrac{14}{48};\dfrac{41}{48}\)
\(\frac{13}{27}>\frac{7}{15}\)
Vì
\(\frac{13}{27}-\frac{7}{15}=\frac{2}{135}\)
\(\frac{7}{15}-\frac{13}{27}=\)Không trừ được(ra số âm)
Quy tắc phép trừ
+)a - b = c (a > b)
+)a - b = -c (a < b)
Nên \(\frac{13}{27}>\frac{7}{15}\)
a, \(\dfrac{11}{13}\) = \(1-\dfrac{2}{13}\); \(\dfrac{97}{99}\) = 1 - \(\dfrac{2}{99}\)
Vì \(\dfrac{2}{13}\) > \(\dfrac{2}{99}\)
Vậy \(\dfrac{11}{13}\) < \(\dfrac{77}{99}\)
a) \(\frac{7}{9}\)và \(\frac{11}{13}\)
Ta có : \(1-\frac{7}{9}=\frac{2}{9};1-\frac{11}{13}=\frac{2}{13}\)
Vì \(\frac{2}{9}>\frac{2}{13}\)nên \(\frac{7}{9}< \frac{11}{13}\).
b) \(\frac{125}{121}\)và \(\frac{413}{409}\)
Ta có : \(\frac{125}{121}-1=\frac{4}{121};\frac{413}{409}-1=\frac{4}{409}\)
Vì \(\frac{4}{121}>\frac{4}{409}\)nên \(\frac{125}{121}>\frac{413}{409}\)
c) \(\frac{8}{7}\)và \(\frac{4}{5}\)
Vì \(\frac{8}{7}>1;1>\frac{4}{5}\)nên \(\frac{8}{7}>\frac{4}{5}\)
d) \(\frac{46}{35}\)và \(\frac{41}{38}\)
Chon phân số trung gian là : \(\frac{46}{38}\)
Vì \(\frac{46}{35}>\frac{46}{38};\frac{46}{38}>\frac{41}{38}\)nên \(\frac{46}{35}>\frac{41}{38}\)