So sánh
\(\frac{12}{13}\)và \(\frac{-12}{-13}\)
So sánh:
\(\frac{27}{13^{13}}\)và \(\frac{25}{13^{13}}+\frac{29}{13^{12}}\)
So sánh giá trị của các biểu thức sau:
A=\(\frac{11}{\text{(12+13)}}\) +\(\frac{12}{\text{(13+14) }}\)+\(\frac{13}{\text{(14+12)}}\) ; B= \(\frac{\text{(11+12+13)}}{(12+13+14)}\)
Ai nhanh 3 tick nha
Trả lời
\(A=\frac{11}{12+13}+\frac{12}{13+14}+\frac{1}{14+15}\)
Hay
\(A=\frac{11}{12+13}+\frac{12}{13+14}+\frac{13}{14+15}\)
mong xem lại hộ cái
so sánh
\(\frac{12}{15}và\frac{-13}{-16}\)
So Sánh \(\frac{12}{13}và\frac{11}{14}\)
ta có: 12/13=12x14/13x14= 168/182
11/14=11x13/14x13= 143/182
vì 168/182>143/182
vậy 12/13>11/14
ủng hộ nhé
so sánh : 12/13va 11/14
12:13=0,92...
11:14=0,78...
vi 0,92>0,78 nen 12/13>11/14
ai tích mình tích lại
So sánh: \(\frac{2018^{13}+1}{2018^{14}+1}\)và \(\frac{2018^{12}+1}{2018^{13}+1}\)
Đặt : \(A=\frac{2018^{13}+1}{2018^{14}+1}\); \(B=\frac{2018^{2012}+1}{2018^{2013}+1}\)
Ta có :
\(2018A=\frac{2018.\left(2018^{13}+1\right)}{2018^{14}+1}\)
\(2018A=\frac{2018^{14}+2018}{2018^{14}+1}=\frac{2018^{14}+1+2017}{2018^{14}+1}=\frac{2018^{2014}+1}{2018^{14}+1}+\frac{2017}{2018^{14}+1}=1+\frac{2017}{2018^{14}+1}\)
\(2018B=\frac{2018.\left(2018^{12}+1\right)}{2018^{13}+1}\)
\(2018B=\frac{2018^{13}+2018}{2018^{13}+1}=\frac{2018^{13}+1+2017}{2018^{13}+1}=\frac{2018^{13}+1}{2018^{13}+1}+\frac{2017}{2018^{13}+1}=1+\frac{2017}{2018^{13}+1}\)
Vì 201814 + 1 > 201813 + 1 nên \(\frac{2017}{2018^{14}+1}< \frac{2017}{2018^{13}+1}\)
\(\Rightarrow1+\frac{2017}{2018^{14}+1}< 1+\frac{2017}{2018^{13}+1}\)Hay : A < B
Vậy A < B
Đặt \(A=\frac{2018^{13}+1}{2018^{14}+1}\)và \(B=\frac{2018^{12}+1}{2018^{13}+1}\)
Ta có :
\(2018A=\frac{\left(2018^{13}+1\right)\times2018}{2018^{14}+1}\) \(2018B=\frac{\left(2018^{12}+1\right)\times2018}{2018^{13}+1}\)
\(2018A=\frac{2018^{14}+2018}{2018^{14}+1}\) \(2018B=\frac{2018^{13}+2018}{2018^{13}+1}\)
\(2018A=\frac{2018^{14}+1+2017}{2018^{14}+1}\) \(2018B=\frac{2018^{13}+1+2017}{2018^{13}+1}\)
\(2018A=1+\frac{2017}{2018^{14}+1}\) \(2018B=1+\frac{2017}{2018^{13}+1}\)
Vì \(\frac{2017}{2018^{14}+1}< \frac{2017}{2018^{13}+1}\)
\(\Rightarrow2018A< 2018B\)
\(\Rightarrow A< B\)
Vậy : \(\frac{2018^{13}+1}{2018^{14}+1}< \frac{2018^{12}+1}{2018^{13}+1}\)
Đặt \(B=\frac{2018^{13}+1}{2018^{14}+1}\Rightarrow2018B=\frac{2018.\left(2018^{13}+1\right)}{2018^{14}+1}\)
\(\Rightarrow2018B=\frac{2018^{14}+2018}{2018^{14}+1}=\frac{2018^{14}+1+2017}{2018^{14}+1}\)\(=\frac{2018^{14}+1}{2018^{14}+1}+\frac{2017}{2018^{14}+1}\)
\(=1+\frac{2017}{2018^{14}+1}\)
Đặt \(C=\frac{2018^{12}+1}{2018^{13}+1}\Rightarrow2018C=\frac{2018.\left(2018^{12}+1\right)}{2018^{13}+1}\)
\(\Rightarrow2018C=\frac{2018^{13}+2018}{2018^{13}+1}=\frac{2018^{13}+1+2017}{2018^{13}+1}\)
\(=\frac{2018^{13}+1}{2018^{13}+1}+\frac{2017}{2018^{13}+1}=1+\frac{2017}{2018^{13}+1}\)
Vì \(\frac{2017}{2018^{14}+1}< \frac{2017}{2018^{13}+1}\)
=> B < C
\(\Rightarrow\frac{2018^{13}+1}{2018^{14}+1}< \frac{2018^{12}+1}{2018^{13}+1}\)
không quy đồng mẫu số hãy so sánh hai phân số sau:\(\frac{12}{13}\)và \(\frac{13}{14}\)
so sánh phần bù:
ta thấy :1-12/13=1/13; 1-13/14=1/14
Vì 1/13>1/14 nên 12/13 < 13/14
ta có : 1-\(\frac{12}{13}\)= \(\frac{1}{13}\)
1-\(\frac{13}{14}\)= \(\frac{1}{14}\)
vì \(\frac{1}{13}\)> \(\frac{1}{14}\)nên \(\frac{12}{13}\)< \(\frac{13}{14}\)
chúc bạn học tốt !!!
Ta có : \(\frac{12}{13}=\frac{13-1}{13}=1-\frac{1}{13}\)
\(\frac{13}{14}=\frac{14-1}{14}=1-\frac{1}{14}\)
Vì \(\frac{1}{13}>\frac{1}{14}\) nên \(1-\frac{1}{13}< 1-\frac{1}{14}\)
hay \(\frac{12}{13}< \frac{13}{14}\)
Vậy \(\frac{12}{13}< \frac{13}{14}.\)
So Sánh \(\frac{12}{17}\)và \(\frac{13}{18}\)
12/17 và 13/18
Phần bù của 12/17 là:5/17
Phần bù của 13/18 là:5/18
Vì 5/18<5/17 nên 12/17 < 13/18
Xét tích \(12.18\) và \(13.17\)
Ta có:\(12.18=\left(15-3\right)\left(15+3\right)=15^2-3^2\)
\(13.17=\left(15-2\right)\left(15+2\right)=15^2-2^2\)
Vì \(15^2-3^2< 15^2-2^2\Rightarrow12.18< 13.17\)
\(\Rightarrow\frac{12}{17}< \frac{13}{18}\)
so sánh\(A=\frac{31}{13}-\left(\frac{7}{32}+\frac{8}{2}\right)vaB=\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)
so sánh phân số bằng cách hợp lý : \(\frac{12}{13}\)và \(\frac{13}{14}\)
\(1-\frac{12}{13}=\frac{13}{13}-\frac{12}{13}=\frac{1}{13}\)
\(1-\frac{13}{14}=\frac{14}{14}-\frac{13}{14}=\frac{1}{14}\)
Ta có: 13 < 14 => 1/13 > 1/14
=> 1 - 12/13 > 1 - 13/14
=> 12/13 < 13/14
Tìm phần bù :
1 - 12 / 13 = 1 / 13
1 - 13 / 14 = 1 / 14
Vì 1 /13 > 1/ 14 nên 12 / 13 bé hơn 13 / 14.
Tìm phần bù:
1 - 12 /13 = 1/13
1 - 13 /14 = 1 /14
Vì 1/13 > 1/14 nên 12/13 < 13/14