Question

[Hoàng Anh Minh Ngọc]

Giúp mình gấp nha

Sắp xếp từ bé đến lớn

a) 17/13; 61/57; 2012/2009; 123/120

b) 101/103; 11/13; 2009/2011; 69/71

Answer 1

[Nguyễn Lê Phước Thịnh]

b: \(\dfrac{101}{103}=1-\dfrac{2}{103}\)

\(\dfrac{11}{13}=1-\dfrac{2}{13}\)

\(\dfrac{2009}{2011}=1-\dfrac{2}{2011}\)

\(\dfrac{69}{71}=1-\dfrac{2}{71}\)

Vì 13<71<103<2011

nên \(\dfrac{2}{13}>\dfrac{2}{71}>\dfrac{2}{103}>\dfrac{2}{2011}\)

=>\(-\dfrac{2}{13}< -\dfrac{2}{71}< -\dfrac{2}{103}< -\dfrac{2}{2011}\)

=>\(-\dfrac{2}{13}+1< -\dfrac{2}{71}+1< -\dfrac{2}{103}+1< -\dfrac{2}{2011}+1\)

=>\(\dfrac{11}{13}< \dfrac{69}{71}< \dfrac{101}{103}< \dfrac{2009}{2011}\)

a: \(\dfrac{17}{13}=1+\dfrac{4}{13};\dfrac{61}{57}=1+\dfrac{4}{57}\)

\(\dfrac{2012}{2009}=1+\dfrac{3}{2009};\dfrac{123}{120}=1+\dfrac{3}{120}\)

Vì \(\dfrac{3}{2009}< \dfrac{3}{120}\left(2009>120\right);\dfrac{3}{120}< \dfrac{4}{57};\dfrac{4}{57}< \dfrac{4}{13}\left(57>13\right)\)

nên \(\dfrac{2012}{2009}< \dfrac{123}{120}< \dfrac{61}{57}< \dfrac{17}{13}\)

Answer 2

[subjects]

câu a

\(\dfrac{2012}{2009}< \dfrac{123}{120}< \dfrac{61}{57}< \dfrac{17}{13}\)

câu b

\(\dfrac{11}{13}< \dfrac{69}{71}< \dfrac{101}{103}< \dfrac{2009}{2011}\)