Question

Bài 6 : so sanh :
a) \(\dfrac{89}{-13}\text{và}\dfrac{1}{123}\)
b)\(\dfrac{-13}{15}\text{và}\dfrac{-31}{30}\)
c)\(\dfrac{125}{123}\text{và}\dfrac{99}{97}\)
d)\(\dfrac{125}{126}\text{và}\dfrac{987}{986}\)

Answer 1

a,

\(\dfrac{89}{-13}< 0< \dfrac{1}{123}\\ \Rightarrow\dfrac{89}{-13}< \dfrac{1}{123}\)

Vậy \(\dfrac{89}{-13}< \dfrac{1}{123}\)

b,

\(\dfrac{-13}{15}>\dfrac{-15}{15}=-1=\dfrac{-30}{30}>\dfrac{-31}{30}\)

Vậy \(\dfrac{-13}{15}>\dfrac{-31}{30}\)

c,

\(\dfrac{125}{123}=\dfrac{123}{123}+\dfrac{2}{123}=1+\dfrac{2}{123}\\ \dfrac{99}{97}=\dfrac{97}{97}+\dfrac{2}{97}=1+\dfrac{2}{97}\)

Vì \(\dfrac{2}{97}>\dfrac{2}{123}\Rightarrow1+\dfrac{2}{97}>1+\dfrac{2}{123}\Leftrightarrow\dfrac{99}{97}>\dfrac{125}{123}\)

Vậy \(\dfrac{99}{97}>\dfrac{125}{123}\)

d,

\(\dfrac{125}{126}< \dfrac{126}{126}=1=\dfrac{986}{986}< \dfrac{987}{986}\)

Vậy \(\dfrac{125}{126}< \dfrac{987}{986}\)