So sánh:
\(\frac{27}{13^{13}}\)và \(\frac{25}{13^{13}}+\frac{29}{13^{12}}\)
Những câu hỏi liên quan
So sánh
\(\frac{12}{13}\)và \(\frac{-12}{-13}\)
Cả hai phân số bằng nhau nha
12/13 = -12/-13 nha bạn.
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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
\(A=\frac{11}{12+13}+\frac{12}{13+14}+\frac{13}{14+15}\)
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So sánh các phân số sau bằng cách hợp lí:
a)\(\frac{13}{57}\)so sánh với \(\frac{29}{73}\)
b)\(\frac{17}{42}\)so sánh với\(\frac{13}{38}\)
c)\(\frac{7}{41}\)so sánh với \(\frac{13}{47}\)
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
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\(\frac{x-1}{13}+\frac{2x-13}{15}=\frac{3x-15}{27}+\frac{4x-27}{29}\) Giải Pt trên
\(\frac{12}{25}+\frac{5}{13}+\frac{13}{25}-\frac{18}{13}+1,875\)
\(\frac{12}{25}+\frac{5}{13}+\frac{13}{25}-\frac{18}{13}+1,875=\left(\frac{12}{25}+\frac{13}{25}\right)+\left(\frac{5}{13}-\frac{18}{13}\right)+1,875=1+\left(-1\right)+1,875=1,875\)
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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
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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 : \(\frac{2018^{13}+1}{2018^{14}+1}< \frac{2018^{12}+1}{2018^{13}+1}\)
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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
\(\Rightarrow\frac{2018^{13}+1}{2018^{14}+1}< \frac{2018^{12}+1}{2018^{13}+1}\)
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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 \(\frac{12}{13}< \frac{13}{14}.\)
Rut gon: \(A=\frac{9+\frac{9}{11}+\frac{18}{23}-\frac{27}{27}}{8+\frac{8}{11}+\frac{16}{23}-\frac{24}{37}}-\frac{2+\frac{16}{29}-\frac{24}{13}-\frac{32}{11}}{3+\frac{24}{29}-\frac{36}{13}-\frac{48}{11}}\)
so sánh\(A=\frac{31}{13}-\left(\frac{7}{32}+\frac{8}{2}\right)vaB=\left(\frac{1}{3}+\frac{12}{67}+\frac{13}{41}\right)-\left(\frac{79}{67}-\frac{28}{41}\right)\)