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a.\(\frac{11^4.11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5-9^8.7}:\frac{10^5-10^5.3}{10^5.11}\)
=\(\frac{11^4.11^5}{11^4-11^4.11}:\frac{9^8.3-9^8.9}{9^8.5-9^8.7}:\frac{10^5-10^5.3}{10^5.11}\)
=\(\frac{11^4.11^5}{11^4.\left(1-11\right)}:\frac{9^8.\left(3-9\right)}{9^8.\left(5-7\right)}:\frac{10^5.\left(1-3\right)}{10^5.11}
\)
=\(\frac{11^4.11^5}{11^4.\left(-10\right)}:\frac{9^8.\left(-6\right)}{9^8.\left(-2\right)}:\frac{10^5.\left(-2\right)}{10^5.11}\)
=\(\frac{11^5}{-10}:3:\frac{-2}{11}\)
=\(\frac{11^5}{-10}.\frac{1}{3}.\frac{-11}{2}\)
Chiều mình làm tiếp cho nha!👋
a) ta có \(\frac{1234}{1235}=1-\frac{1}{1235}\)
\(\frac{4319}{4320}=1-\frac{1}{4320}\)
vì \(\frac{1}{1235}>\frac{1}{4320}\Rightarrow1-\frac{1}{1235}< 1-\frac{1}{4320}\)
\(\Rightarrow\frac{1234}{1235}< \frac{4319}{4320}\)
b) ta có \(\frac{1234}{1244}=1-\frac{10}{1244}\)
\(\frac{4321}{4331}=1-\frac{10}{4331}\)
vì \(\frac{10}{1244}>\frac{10}{4331}\Rightarrow1-\frac{10}{1244}< 1-\frac{10}{4331}\)
\(\Rightarrow\frac{1234}{1244}< \frac{4321}{4331}\)
\(\Rightarrow\frac{-1234}{1244}>\frac{-4321}{4331}\)
31/32= 1 -1/32
31317/32327= 1- 1010/32327
ta có 1010/32327 x 32 = 32320/32327 <1=32/32=1/32 x 32
=> 1010/32327<1/32 => 31317/32327 > 31/32
Ta có\(\frac{-31}{-32}=\frac{31}{32}=\frac{31310}{32320}\)
Vì 31310<32320 nên \(\frac{31310}{32320}< 1\)
\(\Rightarrow\frac{31310}{32320}< \frac{31310+7}{32320+7}=\frac{31317}{32327}\)
\(\frac{-31}{-32}< \frac{31317}{32327}\)
Học tốt
b) Ta có:
\(\frac{1234.1235-1}{1234.1235}=1-\frac{1}{1234.1235}\)
\(\frac{1235.1236-1}{1235.1236}=1-\frac{1}{1235.1236}\)
DO \(\frac{1}{1234.1235}>\frac{1}{1235.1236}\)=> \(-\frac{1}{1234.1235}< -\frac{1}{1235.1236}\)
=> \(\frac{1234.1235-1}{1234.1235}< \frac{1235.1236-1}{1235.1236}\)
\(\frac{1941}{1931}=1+\frac{1}{1931}\)
\(\frac{2011}{2010}=1+\frac{1}{2010}\)
\(vi\frac{1}{1931}>\frac{1}{2010}->\frac{1941}{1931}>\frac{1}{2010}->\frac{-1941}{1931}< \frac{-2011}{2010}\)
Chọn phân số trung gian: -1
Vì \(\frac{-1941}{1931}>\frac{-1931}{1931}\) và \(\frac{-2011}{2010}< \frac{-2010}{2010}\)
\(=>\frac{-1941}{1931}>-1>\frac{-2011}{2010}\)
\(=>\frac{-1941}{1931}>\frac{-2011}{2010}\)
Hay \(M>N\)
-18/91 = -0,19...
-23/114 = -0,20...
mà 0,20...> 0,19... nên -0,19... > -0,20...
vậy -18/91 > -23/114
Ta có như sau:
a, \(\frac{8.7}{5.11}\) = \(\frac{56}{55}\); \(\frac{2.41}{3^{4^{ }}}\)= \(\frac{82}{81}\)
Suy ra \(\frac{56}{55}\)= 1+\(\frac{1}{55}\); \(\frac{82}{81}\)= 1+\(\frac{1}{81}\)
Vì \(\frac{1}{55}\)> \(\frac{1}{81}\)suy ra \(\frac{56}{55}\)< \(\frac{82}{81}\)
a) Ta có \(\frac{8.7}{5.11}=\frac{56}{55}=1+\frac{1}{55}\)
\(\frac{2.41}{3^4}=\frac{82}{81}=1+\frac{1}{81}\)
Vì \(\frac{1}{55}>\frac{1}{81}\)nên \(1+\frac{1}{55}>1+\frac{1}{81}\)nên \(\frac{8.7}{5.11}>\frac{2.41}{3^4}\)
Vậy \(\frac{8.7}{5.11}>\frac{41.2}{3^4}\)