Ta có:\(\frac{17}{21}=\frac{17\cdot1010}{21\cdot1010}=\frac{17170}{21210}\)
Do\(17170< 21210\) nên ta áp dụng tính chất:\(\frac{a}{b}< \frac{a+c}{b+c}\) với a<b
\(\Rightarrow\frac{17170}{21210}< \frac{17170+1}{21210+1}=\frac{17171}{21211}\)
\(\Rightarrow\frac{17170}{21210}< \frac{17171}{21211}\)
Mà \(\frac{17}{21}=\frac{17170}{21210}\Rightarrow\frac{17}{21}< \frac{17171}{21211}\)
Vậy \(\frac{17}{21}< \frac{17171}{21211}\)
Có \(\frac{17}{21}=\frac{17.1010}{21.2010}=\frac{17170}{21210}\)
Áp dụng tính chất \(\frac{a}{b}< \frac{a+c}{b+c}\) với a < b ta có:
\(\frac{17170}{21210}< \frac{17170+1}{21210+1}=\frac{17171}{21211}\)
Mà \(\frac{17}{21}=\frac{17170}{21210}\Rightarrow\frac{17}{21}< \frac{17171}{21211}\)
Vậy \(\frac{17}{21}< \frac{17171}{21211}\)