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NHÌN LÀ BIẾT PHÂN SỐ \(\frac{12}{165}\)> \(\frac{9}{450}\)

ta có \(\frac{3}{7}=\frac{3\times3}{7\times3}=\frac{9}{21}\)(quy đồng tử)
So sánh \(\frac{9}{21}\)và \(\frac{9}{17}\)ta có:
\(21>17\Rightarrow\frac{9}{17}>\frac{9}{21}\Rightarrow\frac{9}{17}>\frac{3}{7}\)
VẬY: \(\frac{9}{17}>\frac{3}{7}\)

\(\overline{abc}\times9=\overline{1abc}\Leftrightarrow9\overline{abc}=1000+\overline{abc}\Leftrightarrow8\overline{abc}=1000\Leftrightarrow\overline{abc}=125.\)
abc x 9 = 1abc
abc x 9 = 1000 + abc
abc x 9 - abc = 1000
abc x ( 9-1 ) = 1000
abc x 8 = 1000
abc = 1000 : 8
abc = 125

\(a,\frac{2001}{2002}.\frac{5}{7}.\frac{2002}{5}.\frac{7}{2001}=\left(\frac{2001}{2002}.\frac{7}{2001}\right).\left(\frac{5}{7}.\frac{2002}{5}\right)\)
\(=\frac{7}{2002}.\frac{2002}{7}=1\)
\(b,\frac{5}{7}.\frac{7}{9}.\frac{9}{11}.\frac{11}{13}=\left(\frac{5}{7}.\frac{7}{9}\right).\left(\frac{9}{11}.\frac{11}{13}\right)=\frac{5}{9}.\frac{9}{13}\)
\(=\frac{5}{13}\)

\(x-\frac{1}{3}=\frac{9}{20}\)
\(x=\frac{9}{20}+\frac{1}{3}\)
\(x=\frac{9\times3+1\times20}{60}\)
\(x=\frac{47}{60}\)

a) \(\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}\)
\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)\)
\(=\frac{5}{5}+\frac{7}{7}=1+1=2\)
a) \(\frac{3}{5}+\frac{4}{7}+\frac{2}{5}+\frac{1}{7}+\frac{2}{7}\)
\(=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{4}{7}+\frac{1}{7}+\frac{2}{7}\right)\)
= 1 + 1
= 2
b) \(\frac{4}{9}+\frac{8}{9}+\frac{12}{9}+\frac{16}{9}+...+\frac{48}{9}+\frac{52}{9}+\frac{56}{9}\)
\(=\frac{4+8+12+16+...+48+52+56}{9}\)
Xét 4 + 8 + 12 + 16 + ... + 48 + 52 + 56
Số các số hạng là:
(56 - 4) : 4 + 1 = 14 (số)
4 + 8 + 12 + 16 + ... + 48 + 52 + 56 = (56 + 4) x 14 : 2 = 420
\(\frac{4+8+12+16+...+48+52+56}{9}=\frac{420}{9}=\frac{140}{3}\)


Vì \(\frac{23}{96}< \frac{23}{92}=\frac{1}{4};\frac{1}{4}=\frac{9}{36}\) nên \(\frac{23}{96}< \frac{9}{36}\).
~ HOK TỐT ~

a ) \(\frac{5}{7}\) + \(\frac{7}{14}\)
= \(\frac{10}{14}\) + \(\frac{7}{14}\)
= \(\frac{10+7}{14}\)= \(\frac{17}{14}\)
b ) \(\frac{5}{3}\) + \(\frac{9}{12}\) + \(\frac{8}{9}\)
= \(\frac{20}{12}\) + \(\frac{9}{12}\) + \(\frac{8}{9}\)
= \(\frac{29}{12}\) + \(\frac{8}{9}\)
= \(\frac{357}{108}\)
\(\frac{9}{12}\) x \(\frac78\) : \(\frac92\)
\(\frac{63}{96}\) : \(\frac92\)
= \(\frac{21}{32}\) : \(\frac92\)
= \(\frac{21}{32}\) x \(\frac29\)
= \(\frac{42}{288}\)
= \(\frac{7}{48}\)