Question

[Trần Thị Kim Ngân]

Bài 1:So sánh các số hữu tỉ sau:

a)\(\dfrac{-13}{40}\) và \(\dfrac{12}{-40}\)                 b)\(\dfrac{-5}{6}\) và \(\dfrac{-91}{104}\)                    c)\(\dfrac{-15}{21}\) và \(\dfrac{-36}{44}\)

d)\(\dfrac{-16}{30}\) và \(\dfrac{-35}{84}\)                 e)\(\dfrac{-5}{91}\) và \(\dfrac{-501}{9191}\)                   f)\(\dfrac{-11}{3^7.7^3}\) và \(\dfrac{-78}{3^7.7^4}\)

Answer 1

[HT.Phong (9A5)]

a) Ta có:

\(13>12=>\dfrac{13}{40}>\dfrac{12}{40}=>\dfrac{-13}{40}< \dfrac{-12}{40}\)

b) Ta có: 

\(\dfrac{-91}{104}=\dfrac{-13}{14}=\dfrac{1}{14}-1< \dfrac{1}{6}-1=\dfrac{-5}{6}\) 

c) Ta có: 

\(\dfrac{-15}{21}=\dfrac{-5}{7}=1-\dfrac{2}{7}\\ \dfrac{-36}{44}=\dfrac{-9}{11}=1-\dfrac{2}{11}\)

Mà: \(\dfrac{2}{7}>\dfrac{2}{11}=>\dfrac{-2}{7}< \dfrac{-2}{11}=>1-\dfrac{2}{7}< 1-\dfrac{2}{11}=>-\dfrac{15}{21}< \dfrac{-36}{44}\) 

Answer 2

[HT.Phong (9A5)]

d) Ta có:

\(\dfrac{-16}{30}=\dfrac{-8}{15}=\dfrac{7}{15}-1\\ \dfrac{-35}{84}=\dfrac{-5}{12}=\dfrac{7}{12}-1\)

Mà: \(\dfrac{7}{15}< \dfrac{7}{12}=>\dfrac{7}{15}-1< \dfrac{7}{12}-1=>-\dfrac{16}{30}< \dfrac{-35}{84}\)

e) Ta có:

\(\dfrac{-5}{91}=\dfrac{-5\cdot101}{91\cdot101}=\dfrac{-505}{9191}< \dfrac{-501}{9191}\)

f) Ta có: 

\(\dfrac{-11}{3^7\cdot7^3}=\dfrac{-11\cdot7}{3^7\cdot7^3\cdot7}=\dfrac{-77}{3^7\cdot7^4}>\dfrac{-78}{3^7\cdot7^4}\)