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\(\frac{9}{11}\)< \(\frac{13}{15}\)
\(\frac{19}{15}\)< \(\frac{15}{11}\)
\(\frac{15}{17}x\frac{45}{13}-\frac{15}{17}x\frac{10}{13}-\frac{9}{13}x\frac{15}{17}-\frac{15}{17}\)
\(=\frac{15}{17}x\left(\frac{45}{13}-\frac{10}{13}-\frac{9}{13}-1\right)\\ =\frac{15}{17}x1=\frac{15}{17}\)
\(\frac{15}{17}\times\frac{45}{13}-\frac{15}{17}\times\frac{10}{13}-\frac{9}{13}\times\frac{15}{17}-\frac{15}{17}\)
\(=\frac{15}{17}\times\left(\frac{45}{13}-\frac{10}{13}-\frac{9}{13}-1\right)\)
\(=\frac{15}{17}\times1\)
\(=\frac{15}{17}\)
Ta có : \(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}>\frac{1}{8}\cdot4=\frac{1}{2}\)
\(\frac{1}{9}+\frac{1}{10}+...+\frac{1}{17}>\frac{1}{18}\cdot9=\frac{1}{2}\)
\(\Rightarrow\frac{1}{5}+\frac{1}{6}+...+\frac{1}{17}>\frac{1}{2}+\frac{1}{2}=1(1)\)
Ta lại có : \(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}< \frac{1}{4}\cdot4=1\)
\(\frac{1}{9}+\frac{1}{10}+...+\frac{1}{17}< \frac{1}{9}\cdot9=1\)
\(\Rightarrow\frac{1}{5}+\frac{1}{6}+...+\frac{1}{17}< 2(2)\)
Từ 1 và 2 suy ra \(1< \frac{1}{5}+\frac{1}{6}+...+\frac{1}{17}< 2\)
Toán lớp 4 chăng?
a, \(\frac{6}{7}.\frac{16}{15}.\frac{7}{6}.\frac{21}{32}=\frac{6}{7}.\frac{7}{6}.\frac{16}{15}.\frac{21}{32}\)=\(1.\frac{16}{15}.\frac{21}{32}=\frac{7}{5.2}=\frac{7}{10}\)
Phần b T2
c,\(\frac{7}{4}.\frac{11}{21}+\frac{11}{21}.\frac{5}{4}=\frac{11}{21}.\left(\frac{7}{4}+\frac{5}{4}\right)\)=\(\frac{11}{21}.3=\frac{11}{7}\)
a) \(\frac{13}{14}\)và \(\frac{14}{15}\) .
Có: \(1-\frac{13}{14}=\frac{1}{14}\)
\(1-\frac{14}{15}=\frac{1}{15}\)
Vì: \(\frac{1}{14}>\frac{1}{15}\Rightarrow\frac{13}{14}< \frac{14}{15}\)
b) \(\frac{2012}{2013}\) và \(\frac{2013}{2014}\)
Có: \(1-\frac{2012}{2013}=\frac{1}{2013}\)
\(1-\frac{2013}{2014}=\frac{1}{2014}\)
Vì: \(\frac{1}{2013}>\frac{1}{2014}\Rightarrow\frac{2012}{2013}< \frac{2013}{2014}\)
a) \(\frac{55}{32}\)
b) \(\frac{90}{48}\)
c) \(\frac{76}{15}\)
d) \(\frac{552}{119}\)
\(\frac{9}{16}+\frac{37}{32}=\frac{18}{32}+\frac{37}{32}=\frac{55}{32}\)
\(\frac{126}{48}-\frac{12}{16}=\frac{21}{8}-\frac{6}{8}=\frac{15}{8}\)
\(\frac{19}{15}\times\frac{32}{8}=\frac{19}{15}\times4=\frac{76}{15}\)
\(\frac{23}{17}:\frac{7}{24}=\frac{23}{17}.\frac{24}{7}=4\frac{76}{119}\)
Gọi số cần điền là a
Ta có \(\frac{13}{15}< \frac{17}{a}\le\frac{13}{14}\)
=> \(\frac{13\times17}{15\times17}< \frac{13\times17}{13\times a}\le\frac{13\times17}{17\times14}\)
=> 15 x 17 > 13 x a \(\ge\)17 x 14
=> 255 > 13 x a \(\ge\)238
=> 13 x a = 247
=> a = 19
Vậy a = 19
13/15 < 17/19 < 13/14