Question

So sánh các số hữu tỉ sau :

a) \(\dfrac{4}{9}\) và \(\dfrac{13}{18}\)                                   b) \(-\dfrac{15}{7}\) và \(-\dfrac{6}{5}\)

c) \(\dfrac{278}{37}\) và \(\dfrac{287}{46}\)                             d) \(-\dfrac{157}{623}\) và \(-\dfrac{47}{213}\)

Answer 1

Áp dụng 1.5 ta có:
a) \(\dfrac{4}{9}< 1\Rightarrow\dfrac{4}{9}< \dfrac{4+9}{9+9}=\dfrac{13}{18}\).
b) \(\dfrac{-15}{7}< 1\Rightarrow\dfrac{-15}{7}< \dfrac{-15+3}{7+3}=\dfrac{-12}{10}=\dfrac{-6}{5}\).
c) \(\dfrac{278}{37}>1\Rightarrow\dfrac{278}{37}>\dfrac{278+9}{37+9}=\dfrac{278}{46}\).
d) \(\dfrac{-157}{623}< 1\Rightarrow\dfrac{-157}{623}< \dfrac{-157+16}{623+16}=\dfrac{-141}{639}=\dfrac{-47}{213}\);

Answer 2

a) \(\dfrac{4}{9}\)và \(\dfrac{13}{18}\)

Ta có : \(\dfrac{4}{9}\)=\(\dfrac{4.2}{9.2}\)=\(\dfrac{8}{18}\)

\(\Rightarrow\)\(\dfrac{8}{18}\)>\(\dfrac{13}{18}\)

giữ nguyên \(\dfrac{13}{18}\) (vì \(8>13\))

- Vậy \(\dfrac{4}{9}>\dfrac{13}{18}\)

b)\(-\dfrac{15}{7}\)và \(-\dfrac{6}{5}\)

Ta có :\(-\dfrac{15}{7}=\dfrac{-15.5}{7.5}=\dfrac{-75}{35}\)

\(\Rightarrow\)\(-\dfrac{75}{35}< \dfrac{-42}{35}\)

\(-\dfrac{6}{5}=\dfrac{-6.7}{5.7}=\dfrac{-42}{35}\) (vì - 75>-42)

- vậy \(\dfrac{-15}{7}< \dfrac{-6}{5}\)

c)\(\dfrac{278}{37}\)và \(\dfrac{287}{46}\)

Ta có :\(\dfrac{278}{37}=\dfrac{278.46}{37.46}=\dfrac{12788}{1702}\)

\(\Rightarrow\)\(\dfrac{12788}{1702}>\dfrac{10286}{1702}\)

\(\dfrac{287}{46}=\dfrac{287.37}{46.37}=\dfrac{10286}{1702}\) (vì 12788>10286)

- vậy \(\dfrac{278}{37}>\dfrac{10286}{46}\)

d)\(-\dfrac{157}{623}\)và \(-\dfrac{47}{213}\)

\(-\dfrac{157}{623}=\dfrac{-157.213}{623.213}=\dfrac{-33441}{132699}\)

\(\Rightarrow\dfrac{-33441}{132699}< \dfrac{-29281}{132699}\)

\(\dfrac{-47}{213}=\dfrac{-47.623}{213.623}=\dfrac{-29281}{132699}\) (vì -33441<-29281)

-vậy \(-\dfrac{157}{623}< -\dfrac{47}{213}\)

Answer 3

a, Ta có : \(\dfrac{4}{9}=\dfrac{8}{18};\dfrac{13}{18}\)

Vì : 8< 13

mà 18 > 0 => \(\dfrac{8}{18}< \dfrac{13}{18}hay\dfrac{4}{9}< \dfrac{13}{18}\)

b,Ta có : \(\dfrac{-15}{7}=\dfrac{-75}{35}\);\(\dfrac{-6}{5}=\dfrac{-42}{35}\)

Vì -75 < -42 mà 35 > 0 => \(\dfrac{-75}{35}< \dfrac{-42}{35}\)

Hay \(\dfrac{-15}{7}< \dfrac{-6}{5}\)

c,Ta có : \(\dfrac{278}{37}=\dfrac{12788}{1702}\);\(\dfrac{287}{46}=\dfrac{10619}{1702}\)

Vì 12788 > 10619 mà 1702 > 0

=> \(\dfrac{12788}{1702}>\dfrac{10619}{1702}Hay\dfrac{278}{37}>\dfrac{287}{46}\)

d,Ta có : \(\dfrac{-157}{623}=\dfrac{-33441}{132699};\dfrac{-47}{213}=\dfrac{-29281}{132699}\)

Vì -33441 < -29281 mà 132699 > 0

=> \(\dfrac{-33441}{132699}< \dfrac{-29281}{132699}Hay\dfrac{-157}{623}< \dfrac{-47}{213}\)