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c)
\(\frac{19}{18}=1+\frac{1}{18}\)
\(\frac{2017}{2016}=1+\frac{1}{2016}\)
Vì \(\frac{1}{18}>\frac{1}{2016}\)
Vậy \(\frac{19}{18}>\frac{2017}{2016}\)
d)
\(\frac{133}{173}=\frac{130+3}{170+3}=\frac{13+0,3}{17+0,3}\)
Ta có :
\(\frac{a}{b}< \frac{a+x}{b+x}\forall a;b;x>0\)
Vậy \(\frac{13}{17}< \frac{133}{173}\)
a ) Ta có :
\(1-\frac{41}{91}=\frac{50}{91}\) \(=\frac{500}{910}\) ; \(1-\frac{411}{911}=\frac{500}{911}\)
Vì \(\frac{500}{910}>\frac{500}{911}\)nên \(\frac{41}{91}< \frac{411}{911}\)
b ) Ta có :
\(1-\frac{113}{115}=\frac{2}{115}\) ; \(1-\frac{93}{95}=\frac{2}{95}\)
Vì \(\frac{2}{115}< \frac{2}{95}\)nên \(\frac{113}{115}>\frac{93}{95}\).
c ) Quy đồng TS ta có :
\(\frac{13}{53}=\frac{143}{583}\) ; \(\frac{11}{30}=\frac{143}{390}\)
Vì \(\frac{143}{583}< \frac{143}{390}\)nên \(\frac{13}{53}< \frac{11}{30}\).
\(a)\) Ta có :
\(\frac{51}{85}=\frac{3}{5}\)
\(\frac{58}{145}=\frac{2}{5}\)
Vì \(\frac{3}{5}>\frac{2}{5}\) nên \(\frac{51}{85}>\frac{58}{145}\)
Vậy \(\frac{51}{85}>\frac{58}{145}\)
\(b)\) Ta có :
\(\frac{69}{-230}=\frac{-3}{10}\)
\(\frac{-39}{143}=\frac{-3}{11}\)
Vì \(\frac{-3}{10}< \frac{-3}{11}\) nên \(\frac{69}{-230}< \frac{-39}{143}\)
Vậy \(\frac{69}{-230}< \frac{-39}{143}\)
\(c)\) Ta có :
\(1+\frac{-7}{41}=\frac{34}{41}\)
\(1+\frac{13}{-47}=\frac{34}{47}\)
Vì \(\frac{34}{41}>\frac{34}{47}\) nên \(1+\frac{-7}{41}>1+\frac{13}{-47}\) hay \(\frac{-7}{41}>\frac{13}{-47}\)
Vậy \(\frac{-7}{41}>\frac{13}{-47}\)
\(d)\) Ta có :
\(1-\frac{40}{49}=\frac{9}{49}\)
\(\frac{15}{21}=\frac{5}{7}=\frac{35}{49}< \frac{40}{49}\)
Vậy \(\frac{40}{49}>\frac{15}{21}\)
a) \(\frac{34}{13}=2\frac{8}{13}\)
Vì 2 > 1 nên \(2\frac{8}{13}>1\frac{7}{9}\)
hay \(\frac{34}{13}>1\frac{7}{9}\)
b) \(\frac{7}{9}=1-\frac{2}{9}\)
\(\frac{13}{15}=1-\frac{2}{15}\)
Vì \(\frac{2}{9}>\frac{2}{15}\) nên \(\frac{7}{9}< \frac{13}{15}\)
a) Ta có:
\(1\frac{7}{9}=\frac{16}{9}=\frac{208}{117}\)
\(\frac{34}{13}=\frac{306}{117}\)
Vì \(306>208\)
\(\Rightarrow\frac{306}{117}>\frac{208}{117}\)
\(\Rightarrow\frac{34}{13}>1\frac{7}{9}\)
b) Ta có:
\(\frac{7}{9}=\frac{35}{45}\)
\(\frac{13}{15}=\frac{39}{45}\)
Vì \(39>35\)
\(\Rightarrow\frac{39}{45}>\frac{35}{45}\)
\(\Rightarrow\frac{13}{15}>\frac{7}{9}\)
a,
\(-\frac{13}{38}=-1--\frac{25}{38}=-1+\frac{25}{38}\)
\(\frac{29}{-88}=-\frac{29}{88}=-1--\frac{59}{88}=-1+\frac{59}{88}\)
Vì \(\frac{25}{38}< \frac{59}{88}\Rightarrow-\frac{13}{38}< \frac{29}{-88}\)
b,
Ta có:
3301 > 3300 = [33]100 = 27100
5199 < 5200 = [52]100 = 25100
Mà 27100 > 25100 => 3301 > 5199
c,
\(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{\left[2n+1\right]\left[2n+3\right]}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2n+1}-\frac{1}{2n+3}\)
\(=1-\frac{1}{2n+3}< 1\)
Vậy P < 1
\(5^{199}=\left(5^{\frac{199}{301}}\right)^{301}\)
\(5^{\frac{199}{301}}< 3^1\)
\(\Leftrightarrow5^{199}< 3^{301}\)
a) 13/57=13+16/57+16=29/73 ( Ghi nhớ SKG Toán 6)
-=> 13/57 < 29/73
b) 17/42 = 17-4/42-4 = 13/38
=> 17/42 > 13/38
c)7/41 = 7+6/41+6= 13/47
=> 7/41<13/47