Question

1.so sánh bằng cách hợp lí nhất

a)\(\frac{201}{205}\)và\(\frac{2013}{2015}\) b)\(\frac{133}{135}\)và\(\frac{1313}{1515}\)

2.so sánh bằng cách thuận tiện nhất

a)\(\frac{103}{105}\)và\(\frac{205}{208}\) b)\(\frac{1995}{1999}\)và\(\frac{2009}{2015}\) c)\(\frac{1111}{1212}\)và\(\frac{141414}{151515}\)

Answer 1

\(1,\frac{201}{205}=1-\frac{4}{205};\frac{2013}{2015}=1-\frac{2}{2015}=1-\frac{4}{4030}.Vì:205< 4030nen:\frac{4}{205}>\frac{4}{4030}\Rightarrow\frac{201}{205}< \frac{2013}{2015}\)

\(b,\frac{133}{135}=1-\frac{2}{135};\frac{1313}{1515}=\frac{13}{15}=1-\frac{2}{15}.Mà:15< 135nen:\frac{2}{135}< \frac{2}{15}\Rightarrow\frac{133}{135}>\frac{1313}{1515}\)

\(2,\frac{103}{105}=1-\frac{2}{105};\frac{205}{208}=1-\frac{2}{208}.\text{Dễ thấy: 105.1,5 bé hơn 208 nên:}\frac{103}{105}< \frac{205}{208}\)

\(b,tươngtựa\)

\(c,\frac{1111}{1212}=\frac{11}{12}=1-\frac{1}{12};\frac{141414}{151515}=\frac{14}{15}=1-\frac{1}{15}.Mà:12< 15nen:\frac{1111}{1212}< \frac{141414}{151515}\)