Question

[Nguyễn Ngọc Gia Hân]

So sánh :

a. \(\dfrac{23}{99}\) và \(\dfrac{232323}{999999}\)

b. \(\dfrac{-63}{84}\) và \(\dfrac{65}{-91}\)

c. \(\dfrac{111}{115}\) và \(\dfrac{555}{559}\)

Answer 1

[Nguyễn Trần Thành Đạt]

a) Ta có:

\(\frac{232323}{999999}=\frac{23.10101}{99.10101}=\frac{23}{99}\)

Vì : \(\frac{23}{99}=\frac{23}{99}\\ =>\frac{23}{99}=\frac{232323}{999999}\)

b) \(-\frac{63}{84}=-\frac{3}{4}\\ \frac{65}{-91}=-\frac{5}{7}\)

Vì: \(-\frac{3}{4}< -\frac{5}{7}\\ =>-\frac{63}{84}< \frac{65}{-91}\)

c) Ta có: \(\frac{111}{115}=1-\frac{4}{115}\\ \frac{555}{559}=1-\frac{4}{559}\)

Vì: \(\frac{4}{115}>\frac{4}{559}\\ =>1-\frac{4}{115}< 1-\frac{4}{559}\\ =>\frac{111}{115}< \frac{555}{559}\)

Answer 2

[Nguyễn Lưu Vũ Quang]

a) \(\dfrac{23}{99}\) và \(\dfrac{232323}{999999}\)

* Giữ nguyên \(\dfrac{23}{99}\).

* Rút gọn \(\dfrac{232323}{999999}=\dfrac{23}{99}\).

Vì \(\dfrac{23}{99}=\dfrac{23}{99}\) nên \(\dfrac{23}{99}=\dfrac{232323}{999999}\)

Vậy \(\dfrac{23}{99}=\dfrac{232323}{999999}\).

b) \(\dfrac{-63}{84}\) và \(\dfrac{65}{-91}\)

\(\circledast\) Rút gọn:

\(\dfrac{-63}{84}=\dfrac{-3}{4}\) ; \(\dfrac{65}{-91}=\dfrac{-5}{7}\)

\(\circledast\) Quy đồng:

Mẫu chung: 28

\(\dfrac{-3}{4}=\dfrac{-3.7}{4\cdot7}=\dfrac{-21}{28}\)

\(\dfrac{-5}{7}=\dfrac{-5\cdot4}{7\cdot4}=\dfrac{-20}{28}\)

Vì \(\dfrac{-21}{28}< \dfrac{-20}{28}\) nên \(\dfrac{-63}{84}< \dfrac{65}{-91}\).

Vậy \(\dfrac{-63}{84}< \dfrac{65}{-91}\).

c) \(\dfrac{111}{115}\) và \(\dfrac{555}{559}\)

\(\dfrac{111}{115}=1-\dfrac{4}{115}\) ; \(\dfrac{555}{559}=1-\dfrac{4}{559}\)

Vì \(\dfrac{4}{115}>\dfrac{4}{559}\)

\(\Rightarrow\) \(1-\dfrac{4}{115}< 1-\dfrac{4}{559}\)

\(\Rightarrow\) \(\dfrac{111}{115}< \dfrac{555}{559}\)

Vậy \(\dfrac{111}{115}< \dfrac{555}{559}\).