Câu hỏi của Tran Le Hoang Vu

Question

so sánh hai phân số:M=10¹⁹+1/10²⁰+1và N=10²⁰+1/10²¹+1

Phong · Accepted Answer

Ta có tính chất: $\dfrac{a}{b}< \dfrac{a+m}{b+m}$

$N=\dfrac{10^{20}+1}{10^{21}+1}< \dfrac{10^{20}+1+9}{10^{21}+1+9}$

$\Rightarrow N< \dfrac{10^{20}+10}{10^{21}+10}$

$\Rightarrow N< \dfrac{10\left(10^{19}+1\right)}{10\left(10^{20}+1\right)}$

$\Rightarrow N< \dfrac{10^{19}+1}{10^{20}+1}$

$\Rightarrow N< M$

Câu trả lời:

Ta có tính chất: $\dfrac{a}{b}< \dfrac{a+m}{b+m}$

$N=\dfrac{10^{20}+1}{10^{21}+1}< \dfrac{10^{20}+1+9}{10^{21}+1+9}$

$\Rightarrow N< \dfrac{10^{20}+10}{10^{21}+10}$

$\Rightarrow N< \dfrac{10\left(10^{19}+1\right)}{10\left(10^{20}+1\right)}$

$\Rightarrow N< \dfrac{10^{19}+1}{10^{20}+1}$

$\Rightarrow N< M$