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tính chất trên gọi là tính chất bắc cầu, ta so sánh hai phân số với một số (phân số) thứ 3.
a) \(\dfrac{7}{13}\)\(\times\)\(\dfrac{7}{15}\)-\(\dfrac{5}{12}\)\(\times\)\(\dfrac{21}{39}+\dfrac{49}{91}\)\(\times\)\(\dfrac{8}{15}\)
= \(\dfrac{7}{13}\)\(\times\)\(\dfrac{7}{15}\)-\(\dfrac{5}{12}\times\dfrac{7}{13}+\dfrac{7}{13}\times\dfrac{8}{15}\)
= \(\dfrac{7}{13}\left(\dfrac{7}{15}-\dfrac{5}{12}+\dfrac{8}{15}\right)\)
= \(\dfrac{7}{13}\times\dfrac{7}{12}\)
= \(\dfrac{49}{156}\)
b) \(\left(\dfrac{12}{199}+\dfrac{23}{200}-\dfrac{34}{201}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)
= \(\left(\dfrac{12}{199}+\dfrac{23}{200}-\dfrac{34}{201}\right)\times0\)
= 0
a: 51/56=1-5/56
61/66=1-5/66
mà -5/56<-5/66
nên 51/56<61/66
b: 41/43<1<172/165
c: \(\dfrac{101}{506}>0>-\dfrac{707}{3534}\)
4,
a,\(\dfrac{x-1}{9}\)=\(\dfrac{8}{3}\)
[x- 1].3=9.8
[x- 1].3=72
x-1=72:3
x-1=24
x=24+1
x=25
Theo quy ước với mọi phân số lớn hơn 0 thì ta có:
\(\dfrac{a}{b}>0=>\dfrac{a}{b}< \dfrac{a+n}{b+n}\left(n\in N;n\ne0\right)\)
Áp dụng với bài trên ta => ĐPCM
CHÚC BẠN HỌC TỐT.......
2) Tinh nhanh:
a) \(\dfrac{5}{23}\) . \(\dfrac{17}{26}\) + \(\dfrac{5}{23}\) . \(\dfrac{10}{26}\) - \(\dfrac{5}{23}\)
= \(\dfrac{5}{23}\) . \(\left(\dfrac{17}{26}+\dfrac{10}{26}-1\right)\)
= \(\dfrac{5}{23}\) . \(\left(\dfrac{27}{26}-1\right)\) = \(\dfrac{5}{23}\) . \(\dfrac{1}{26}\)
= \(\dfrac{5}{598}\)
b) \(\dfrac{1}{7}.\dfrac{5}{9}+\dfrac{5}{9}.\dfrac{2}{7}+\dfrac{5}{9}.\dfrac{1}{7}+\dfrac{5}{9}.\dfrac{3}{7}\)
= \(\dfrac{5}{9}.\left(\dfrac{1}{7}+\dfrac{2}{7}+\dfrac{1}{7}+\dfrac{3}{7}\right)\)
= \(\dfrac{5}{9}\) . 1= \(\dfrac{5}{9}\)
a: 17/200>17/314
b: 11/54=22/108<22/37
c: 141/893=3/19
159/901=3/17
mà 3/19<3/17
nên 141/893<159/901
a)\(\dfrac{1212}{2323}=\dfrac{1212:101}{2323:101}=\dfrac{12}{23}\)
b)\(\dfrac{-3435}{4141}< \dfrac{-3434}{4141}=\dfrac{-3434:101}{4141:101}\)
Nhận xét:
\(\dfrac{\overline{abab}}{\overline{cdcd}}=\dfrac{\overline{ab}}{\overline{cd}}\)
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: \(\frac{4}{115}>\frac{4}{559}\\ =>1-\frac{4}{115}< 1-\frac{4}{559}\\ =>\frac{111}{115}< \frac{555}{559}\)
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 \(\dfrac{111}{115}< \dfrac{555}{559}\).